Embed Size (px)
DESCRIPTION
Operations and Algebraic Thinking in First Grade. Amanda Maydeck Elaenia Serdehely Pamela Henning. What is Algebra?. http://0-ediv.alexanderstreet.com.innopac.library.unr.edu/view/1737930. Algebra in First Grade. - PowerPoint PPT Presentation
Citation preview
Operations and Algebraic Thinking in First GradeAmanda MaydeckElaenia SerdehelyPamela Henning
What is Algebra
bull http0-edivalexanderstreetcominnopaclibraryunreduview1737930
Algebra in First Grade
bull Teaching just computation and arithmetic ldquois an inadequate benchmark because a lot of interesting mathematics in primary school does not depend on the ability of students to successfully apply specific arithmetic algorithmsrdquo (Lopez and Estrella 2011)
Algebra in First Gradebull First Graders learn the meaning of +1 +2 +5 is the same as
moving up this many spaces on the number line They learn the inverse of this meaning that -1 -2 -5 is the same as moving back this many spaces on the number line Students do not need to count both numbers to solve the problem
bull First graders start to discover patterns in numbers and use this to solve addition and subtraction problems First graders first learn their doubles facts and use this to solve doubles +1
bull First Graders also discover how to make groups of ten This helps build fluency in addition and subtraction problems
bull First Graders learn the meaning of the equal sign to be the same as Students look at problems and determine if the statement is true or false This is the beginning to learning how to balance an equation
Represent and solve problems involving addition and subtraction
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem2
bull 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
What does it look likebull Teachers pose questions that relate to familiar
contexts for students that result in the use of addition or subtraction
bull Problems can consist of problem structure in which the bull Result is unknownbull Change is unknownbull Start is unknown
bull Students must use their understanding of addition and subtraction to work through context based problems
What does it look like
bull httpwwwteachertubecom8809viewVideophpvideo_id=44503
Example Problem1OA19 boys and 8 girls were in the class How many children were
in the class in allResult unknown
Possible algebraic equations 9+8= 8+9= = 9+8 = 8+9
Samples provided by illustrative mathematics
1OA117 children were in the class 9 were boys and the rest were girls How many girls were in the class
Addend Unknown (Change)
Possible algebraic equations 17=9+ 17= + 99+ =17 +9=17 17ndash9=
Samples provided by illustrative mathematics
1OA117 children were in the class There were some boys and
8 girls How many boys were in the classAddend Unknown (Start)
Possible algebraic equations 17=8+
17= + 8 8+ =17 +8=17 17ndash8=
Samples provided by illustrative mathematics
1OA2
bull Jasmine has eight daisies and three vases - one large one medium-sized and one small She puts 5 daisies in the large vase 2 in the medium vase and 1 in the small vase
bull Can you find another way to put daisies so that there are the most in the large vase and least in the small vase
bull Try to find as many ways as you can put the daisies in the vases with the most in the large vase and the least in the smallest vase If you think you have found them all explain how you know those are all the possibilities
Samples provided by illustrative mathematics
What does it look like
Misconceptionsbull Students may have difficulty identifying the
logical structure of the word problem bull Wording may make it difficult for students to decipher
between join or separate problems with start unknown being the most difficultbull Language in compare problems might be challenging for
ELL students based on confusing vocabularybull Equal sign can be misinterpreted as operational
rather than relationalbull When faced with a representational problem with
three addends students may leave out the third addend or lack organization in their problem
Progressionbull In order for first grade students to be able to
represent and solve problems involving addition and subtractionbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of representing addition and subtraction problems algebraically in order tobull 2OA1 Use addition and subtraction within 100 to solve
one- and two-step word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using drawings and equations with a symbol for the unknown number to represent the problem
Progressionbull In Kindergarten students learn their numbers by
associating objects with numbers They use this knowledge to solve addition and subtraction problems within 10 This leads in to students being able to solve addition and subtraction problems within 20 without using objects By the end of first grade students can solve addition and subtraction problems by counting up This leads into second grade where students learn how to solve addition and subtraction problems within 100 Students know addition and subtraction facts with fluency in single digit problems
Understand and apply properties of operations and the relationship between addition and subtractionbull 1OA3 Apply properties of operations as
strategies to add and subtract Examples If 8 + 3 = 11 is known then 3 + 8 = 11 is also known (Commutative property of addition) To add 2 + 6 + 4 the second two numbers can be added to make a ten so 2 + 6 + 4 = 2 + 10 = 12 (Associative property of addition)
bull 1OA4 Understand subtraction as an unknown-addend problem For example subtract 10 ndash 8 by finding the number that makes 10 when added to 8
What does it look likebull Students should be able to differentiate between
and use thebull Communicative property of addition (3+2=2+3)bull Associative property of addition (4+1=3+2)
bull Students will use what they know about unknown addend problems to relate subtraction to addition (Fact Families)
Example ProblemsCommunicative Property
bull Build a two-color train using less than ten connecting cubes Place cubes of the same color together
bull Draw your train and write a number sentence to describe it from left to right
bull Flip your train draw it again and write the turn around fact
bull Repeat with other two color trains
2 + 3 = 5 3 + 2 = 5
Example provided by K-5MathTeachingResourcescom
ExampleAssociative Property
1OA4Choose a domino
Draw the domino
Write a fact family for the domino you chose Repeat with other dominoes
6 + 3 = 9 3 + 6 = 9 9 - 3 = 6 9 - 6 = 3
Example provided by K-5MathTeachingResourcescom
Misconceptionsbull Students might be confused about the meaning of the
equals sign In the problem 2+4=3+3 students may want to substitute first 3 in the second problem with a 6 This is because they may see the equal sign as a symbol indicating that the answer should follow
bull Students be unsure if each property (associative or communicative) works consistently bull Teacher must provide many examples to deter this misconception
bull Students many times confuse the order of numbers in a fact family resulting in an incorrect number sentence
Progressionbull First they develop understanding of number
conceptsbull Using understanding of number concepts
students are able to add and subtract within 10bull Following the mastery of addition and subtraction
within 10 students progress to addition and facts between 11-20 and then 20-100
bull During this process students are taught addition and subtraction together to help relate one to the other
Progressionbull In order for first grade students to be able to
apply properties of operations and find relationships between addition and subtraction they must firstbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of properties of operations and find relationships between addition and subtraction they willbull 2NBT9 Explain why addition and subtraction strategies
work using place value and the properties of operations
Add and subtract within 20bull 1OA5 Relate counting to addition and subtraction
(eg by counting on 2 to add 2) bull 1OA6 Add and subtract within 20 demonstrating
fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
What does it look likebull Students use many different strategies to add and
subtract Strategies can includebull Counting onbull Using the number linebull Using counters to represent addition and subtraction
problemsbull Acting out problemsbull Using modelsbull Drawing picturesbull And many morehellip
What does it look likebull httpwwwbrainpopjrcommath
additionandsubtractioncountingon
What does it look like5+4=
Misconceptionsbull Students may struggle with the use of their
manipulativesbull Double hopping on the number linebull Losing track of countersbull Sloppy drawingsbull Etchellip
bull Students might confuse the + and ndash signbull Many times students are more apt to add rather
than subtract Because of this they will not look at the sign and assume addition
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
What is Algebra
bull http0-edivalexanderstreetcominnopaclibraryunreduview1737930
Algebra in First Grade
bull Teaching just computation and arithmetic ldquois an inadequate benchmark because a lot of interesting mathematics in primary school does not depend on the ability of students to successfully apply specific arithmetic algorithmsrdquo (Lopez and Estrella 2011)
Algebra in First Gradebull First Graders learn the meaning of +1 +2 +5 is the same as
moving up this many spaces on the number line They learn the inverse of this meaning that -1 -2 -5 is the same as moving back this many spaces on the number line Students do not need to count both numbers to solve the problem
bull First graders start to discover patterns in numbers and use this to solve addition and subtraction problems First graders first learn their doubles facts and use this to solve doubles +1
bull First Graders also discover how to make groups of ten This helps build fluency in addition and subtraction problems
bull First Graders learn the meaning of the equal sign to be the same as Students look at problems and determine if the statement is true or false This is the beginning to learning how to balance an equation
Represent and solve problems involving addition and subtraction
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem2
bull 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
What does it look likebull Teachers pose questions that relate to familiar
contexts for students that result in the use of addition or subtraction
bull Problems can consist of problem structure in which the bull Result is unknownbull Change is unknownbull Start is unknown
bull Students must use their understanding of addition and subtraction to work through context based problems
What does it look like
bull httpwwwteachertubecom8809viewVideophpvideo_id=44503
Example Problem1OA19 boys and 8 girls were in the class How many children were
in the class in allResult unknown
Possible algebraic equations 9+8= 8+9= = 9+8 = 8+9
Samples provided by illustrative mathematics
1OA117 children were in the class 9 were boys and the rest were girls How many girls were in the class
Addend Unknown (Change)
Possible algebraic equations 17=9+ 17= + 99+ =17 +9=17 17ndash9=
Samples provided by illustrative mathematics
1OA117 children were in the class There were some boys and
8 girls How many boys were in the classAddend Unknown (Start)
Possible algebraic equations 17=8+
17= + 8 8+ =17 +8=17 17ndash8=
Samples provided by illustrative mathematics
1OA2
bull Jasmine has eight daisies and three vases - one large one medium-sized and one small She puts 5 daisies in the large vase 2 in the medium vase and 1 in the small vase
bull Can you find another way to put daisies so that there are the most in the large vase and least in the small vase
bull Try to find as many ways as you can put the daisies in the vases with the most in the large vase and the least in the smallest vase If you think you have found them all explain how you know those are all the possibilities
Samples provided by illustrative mathematics
What does it look like
Misconceptionsbull Students may have difficulty identifying the
logical structure of the word problem bull Wording may make it difficult for students to decipher
between join or separate problems with start unknown being the most difficultbull Language in compare problems might be challenging for
ELL students based on confusing vocabularybull Equal sign can be misinterpreted as operational
rather than relationalbull When faced with a representational problem with
three addends students may leave out the third addend or lack organization in their problem
Progressionbull In order for first grade students to be able to
represent and solve problems involving addition and subtractionbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of representing addition and subtraction problems algebraically in order tobull 2OA1 Use addition and subtraction within 100 to solve
one- and two-step word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using drawings and equations with a symbol for the unknown number to represent the problem
Progressionbull In Kindergarten students learn their numbers by
associating objects with numbers They use this knowledge to solve addition and subtraction problems within 10 This leads in to students being able to solve addition and subtraction problems within 20 without using objects By the end of first grade students can solve addition and subtraction problems by counting up This leads into second grade where students learn how to solve addition and subtraction problems within 100 Students know addition and subtraction facts with fluency in single digit problems
Understand and apply properties of operations and the relationship between addition and subtractionbull 1OA3 Apply properties of operations as
strategies to add and subtract Examples If 8 + 3 = 11 is known then 3 + 8 = 11 is also known (Commutative property of addition) To add 2 + 6 + 4 the second two numbers can be added to make a ten so 2 + 6 + 4 = 2 + 10 = 12 (Associative property of addition)
bull 1OA4 Understand subtraction as an unknown-addend problem For example subtract 10 ndash 8 by finding the number that makes 10 when added to 8
What does it look likebull Students should be able to differentiate between
and use thebull Communicative property of addition (3+2=2+3)bull Associative property of addition (4+1=3+2)
bull Students will use what they know about unknown addend problems to relate subtraction to addition (Fact Families)
Example ProblemsCommunicative Property
bull Build a two-color train using less than ten connecting cubes Place cubes of the same color together
bull Draw your train and write a number sentence to describe it from left to right
bull Flip your train draw it again and write the turn around fact
bull Repeat with other two color trains
2 + 3 = 5 3 + 2 = 5
Example provided by K-5MathTeachingResourcescom
ExampleAssociative Property
1OA4Choose a domino
Draw the domino
Write a fact family for the domino you chose Repeat with other dominoes
6 + 3 = 9 3 + 6 = 9 9 - 3 = 6 9 - 6 = 3
Example provided by K-5MathTeachingResourcescom
Misconceptionsbull Students might be confused about the meaning of the
equals sign In the problem 2+4=3+3 students may want to substitute first 3 in the second problem with a 6 This is because they may see the equal sign as a symbol indicating that the answer should follow
bull Students be unsure if each property (associative or communicative) works consistently bull Teacher must provide many examples to deter this misconception
bull Students many times confuse the order of numbers in a fact family resulting in an incorrect number sentence
Progressionbull First they develop understanding of number
conceptsbull Using understanding of number concepts
students are able to add and subtract within 10bull Following the mastery of addition and subtraction
within 10 students progress to addition and facts between 11-20 and then 20-100
bull During this process students are taught addition and subtraction together to help relate one to the other
Progressionbull In order for first grade students to be able to
apply properties of operations and find relationships between addition and subtraction they must firstbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of properties of operations and find relationships between addition and subtraction they willbull 2NBT9 Explain why addition and subtraction strategies
work using place value and the properties of operations
Add and subtract within 20bull 1OA5 Relate counting to addition and subtraction
(eg by counting on 2 to add 2) bull 1OA6 Add and subtract within 20 demonstrating
fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
What does it look likebull Students use many different strategies to add and
subtract Strategies can includebull Counting onbull Using the number linebull Using counters to represent addition and subtraction
problemsbull Acting out problemsbull Using modelsbull Drawing picturesbull And many morehellip
What does it look likebull httpwwwbrainpopjrcommath
additionandsubtractioncountingon
What does it look like5+4=
Misconceptionsbull Students may struggle with the use of their
manipulativesbull Double hopping on the number linebull Losing track of countersbull Sloppy drawingsbull Etchellip
bull Students might confuse the + and ndash signbull Many times students are more apt to add rather
than subtract Because of this they will not look at the sign and assume addition
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
Algebra in First Grade
bull Teaching just computation and arithmetic ldquois an inadequate benchmark because a lot of interesting mathematics in primary school does not depend on the ability of students to successfully apply specific arithmetic algorithmsrdquo (Lopez and Estrella 2011)
Algebra in First Gradebull First Graders learn the meaning of +1 +2 +5 is the same as
moving up this many spaces on the number line They learn the inverse of this meaning that -1 -2 -5 is the same as moving back this many spaces on the number line Students do not need to count both numbers to solve the problem
bull First graders start to discover patterns in numbers and use this to solve addition and subtraction problems First graders first learn their doubles facts and use this to solve doubles +1
bull First Graders also discover how to make groups of ten This helps build fluency in addition and subtraction problems
bull First Graders learn the meaning of the equal sign to be the same as Students look at problems and determine if the statement is true or false This is the beginning to learning how to balance an equation
Represent and solve problems involving addition and subtraction
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem2
bull 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
What does it look likebull Teachers pose questions that relate to familiar
contexts for students that result in the use of addition or subtraction
bull Problems can consist of problem structure in which the bull Result is unknownbull Change is unknownbull Start is unknown
bull Students must use their understanding of addition and subtraction to work through context based problems
What does it look like
bull httpwwwteachertubecom8809viewVideophpvideo_id=44503
Example Problem1OA19 boys and 8 girls were in the class How many children were
in the class in allResult unknown
Possible algebraic equations 9+8= 8+9= = 9+8 = 8+9
Samples provided by illustrative mathematics
1OA117 children were in the class 9 were boys and the rest were girls How many girls were in the class
Addend Unknown (Change)
Possible algebraic equations 17=9+ 17= + 99+ =17 +9=17 17ndash9=
Samples provided by illustrative mathematics
1OA117 children were in the class There were some boys and
8 girls How many boys were in the classAddend Unknown (Start)
Possible algebraic equations 17=8+
17= + 8 8+ =17 +8=17 17ndash8=
Samples provided by illustrative mathematics
1OA2
bull Jasmine has eight daisies and three vases - one large one medium-sized and one small She puts 5 daisies in the large vase 2 in the medium vase and 1 in the small vase
bull Can you find another way to put daisies so that there are the most in the large vase and least in the small vase
bull Try to find as many ways as you can put the daisies in the vases with the most in the large vase and the least in the smallest vase If you think you have found them all explain how you know those are all the possibilities
Samples provided by illustrative mathematics
What does it look like
Misconceptionsbull Students may have difficulty identifying the
logical structure of the word problem bull Wording may make it difficult for students to decipher
between join or separate problems with start unknown being the most difficultbull Language in compare problems might be challenging for
ELL students based on confusing vocabularybull Equal sign can be misinterpreted as operational
rather than relationalbull When faced with a representational problem with
three addends students may leave out the third addend or lack organization in their problem
Progressionbull In order for first grade students to be able to
represent and solve problems involving addition and subtractionbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of representing addition and subtraction problems algebraically in order tobull 2OA1 Use addition and subtraction within 100 to solve
one- and two-step word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using drawings and equations with a symbol for the unknown number to represent the problem
Progressionbull In Kindergarten students learn their numbers by
associating objects with numbers They use this knowledge to solve addition and subtraction problems within 10 This leads in to students being able to solve addition and subtraction problems within 20 without using objects By the end of first grade students can solve addition and subtraction problems by counting up This leads into second grade where students learn how to solve addition and subtraction problems within 100 Students know addition and subtraction facts with fluency in single digit problems
Understand and apply properties of operations and the relationship between addition and subtractionbull 1OA3 Apply properties of operations as
strategies to add and subtract Examples If 8 + 3 = 11 is known then 3 + 8 = 11 is also known (Commutative property of addition) To add 2 + 6 + 4 the second two numbers can be added to make a ten so 2 + 6 + 4 = 2 + 10 = 12 (Associative property of addition)
bull 1OA4 Understand subtraction as an unknown-addend problem For example subtract 10 ndash 8 by finding the number that makes 10 when added to 8
What does it look likebull Students should be able to differentiate between
and use thebull Communicative property of addition (3+2=2+3)bull Associative property of addition (4+1=3+2)
bull Students will use what they know about unknown addend problems to relate subtraction to addition (Fact Families)
Example ProblemsCommunicative Property
bull Build a two-color train using less than ten connecting cubes Place cubes of the same color together
bull Draw your train and write a number sentence to describe it from left to right
bull Flip your train draw it again and write the turn around fact
bull Repeat with other two color trains
2 + 3 = 5 3 + 2 = 5
Example provided by K-5MathTeachingResourcescom
ExampleAssociative Property
1OA4Choose a domino
Draw the domino
Write a fact family for the domino you chose Repeat with other dominoes
6 + 3 = 9 3 + 6 = 9 9 - 3 = 6 9 - 6 = 3
Example provided by K-5MathTeachingResourcescom
Misconceptionsbull Students might be confused about the meaning of the
equals sign In the problem 2+4=3+3 students may want to substitute first 3 in the second problem with a 6 This is because they may see the equal sign as a symbol indicating that the answer should follow
bull Students be unsure if each property (associative or communicative) works consistently bull Teacher must provide many examples to deter this misconception
bull Students many times confuse the order of numbers in a fact family resulting in an incorrect number sentence
Progressionbull First they develop understanding of number
conceptsbull Using understanding of number concepts
students are able to add and subtract within 10bull Following the mastery of addition and subtraction
within 10 students progress to addition and facts between 11-20 and then 20-100
bull During this process students are taught addition and subtraction together to help relate one to the other
Progressionbull In order for first grade students to be able to
apply properties of operations and find relationships between addition and subtraction they must firstbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of properties of operations and find relationships between addition and subtraction they willbull 2NBT9 Explain why addition and subtraction strategies
work using place value and the properties of operations
Add and subtract within 20bull 1OA5 Relate counting to addition and subtraction
(eg by counting on 2 to add 2) bull 1OA6 Add and subtract within 20 demonstrating
fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
What does it look likebull Students use many different strategies to add and
subtract Strategies can includebull Counting onbull Using the number linebull Using counters to represent addition and subtraction
problemsbull Acting out problemsbull Using modelsbull Drawing picturesbull And many morehellip
What does it look likebull httpwwwbrainpopjrcommath
additionandsubtractioncountingon
What does it look like5+4=
Misconceptionsbull Students may struggle with the use of their
manipulativesbull Double hopping on the number linebull Losing track of countersbull Sloppy drawingsbull Etchellip
bull Students might confuse the + and ndash signbull Many times students are more apt to add rather
than subtract Because of this they will not look at the sign and assume addition
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
Algebra in First Gradebull First Graders learn the meaning of +1 +2 +5 is the same as
moving up this many spaces on the number line They learn the inverse of this meaning that -1 -2 -5 is the same as moving back this many spaces on the number line Students do not need to count both numbers to solve the problem
bull First graders start to discover patterns in numbers and use this to solve addition and subtraction problems First graders first learn their doubles facts and use this to solve doubles +1
bull First Graders also discover how to make groups of ten This helps build fluency in addition and subtraction problems
bull First Graders learn the meaning of the equal sign to be the same as Students look at problems and determine if the statement is true or false This is the beginning to learning how to balance an equation
Represent and solve problems involving addition and subtraction
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem2
bull 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
What does it look likebull Teachers pose questions that relate to familiar
contexts for students that result in the use of addition or subtraction
bull Problems can consist of problem structure in which the bull Result is unknownbull Change is unknownbull Start is unknown
bull Students must use their understanding of addition and subtraction to work through context based problems
What does it look like
bull httpwwwteachertubecom8809viewVideophpvideo_id=44503
Example Problem1OA19 boys and 8 girls were in the class How many children were
in the class in allResult unknown
Possible algebraic equations 9+8= 8+9= = 9+8 = 8+9
Samples provided by illustrative mathematics
1OA117 children were in the class 9 were boys and the rest were girls How many girls were in the class
Addend Unknown (Change)
Possible algebraic equations 17=9+ 17= + 99+ =17 +9=17 17ndash9=
Samples provided by illustrative mathematics
1OA117 children were in the class There were some boys and
8 girls How many boys were in the classAddend Unknown (Start)
Possible algebraic equations 17=8+
17= + 8 8+ =17 +8=17 17ndash8=
Samples provided by illustrative mathematics
1OA2
bull Jasmine has eight daisies and three vases - one large one medium-sized and one small She puts 5 daisies in the large vase 2 in the medium vase and 1 in the small vase
bull Can you find another way to put daisies so that there are the most in the large vase and least in the small vase
bull Try to find as many ways as you can put the daisies in the vases with the most in the large vase and the least in the smallest vase If you think you have found them all explain how you know those are all the possibilities
Samples provided by illustrative mathematics
What does it look like
Misconceptionsbull Students may have difficulty identifying the
logical structure of the word problem bull Wording may make it difficult for students to decipher
between join or separate problems with start unknown being the most difficultbull Language in compare problems might be challenging for
ELL students based on confusing vocabularybull Equal sign can be misinterpreted as operational
rather than relationalbull When faced with a representational problem with
three addends students may leave out the third addend or lack organization in their problem
Progressionbull In order for first grade students to be able to
represent and solve problems involving addition and subtractionbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of representing addition and subtraction problems algebraically in order tobull 2OA1 Use addition and subtraction within 100 to solve
one- and two-step word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using drawings and equations with a symbol for the unknown number to represent the problem
Progressionbull In Kindergarten students learn their numbers by
associating objects with numbers They use this knowledge to solve addition and subtraction problems within 10 This leads in to students being able to solve addition and subtraction problems within 20 without using objects By the end of first grade students can solve addition and subtraction problems by counting up This leads into second grade where students learn how to solve addition and subtraction problems within 100 Students know addition and subtraction facts with fluency in single digit problems
Understand and apply properties of operations and the relationship between addition and subtractionbull 1OA3 Apply properties of operations as
strategies to add and subtract Examples If 8 + 3 = 11 is known then 3 + 8 = 11 is also known (Commutative property of addition) To add 2 + 6 + 4 the second two numbers can be added to make a ten so 2 + 6 + 4 = 2 + 10 = 12 (Associative property of addition)
bull 1OA4 Understand subtraction as an unknown-addend problem For example subtract 10 ndash 8 by finding the number that makes 10 when added to 8
What does it look likebull Students should be able to differentiate between
and use thebull Communicative property of addition (3+2=2+3)bull Associative property of addition (4+1=3+2)
bull Students will use what they know about unknown addend problems to relate subtraction to addition (Fact Families)
Example ProblemsCommunicative Property
bull Build a two-color train using less than ten connecting cubes Place cubes of the same color together
bull Draw your train and write a number sentence to describe it from left to right
bull Flip your train draw it again and write the turn around fact
bull Repeat with other two color trains
2 + 3 = 5 3 + 2 = 5
Example provided by K-5MathTeachingResourcescom
ExampleAssociative Property
1OA4Choose a domino
Draw the domino
Write a fact family for the domino you chose Repeat with other dominoes
6 + 3 = 9 3 + 6 = 9 9 - 3 = 6 9 - 6 = 3
Example provided by K-5MathTeachingResourcescom
Misconceptionsbull Students might be confused about the meaning of the
equals sign In the problem 2+4=3+3 students may want to substitute first 3 in the second problem with a 6 This is because they may see the equal sign as a symbol indicating that the answer should follow
bull Students be unsure if each property (associative or communicative) works consistently bull Teacher must provide many examples to deter this misconception
bull Students many times confuse the order of numbers in a fact family resulting in an incorrect number sentence
Progressionbull First they develop understanding of number
conceptsbull Using understanding of number concepts
students are able to add and subtract within 10bull Following the mastery of addition and subtraction
within 10 students progress to addition and facts between 11-20 and then 20-100
bull During this process students are taught addition and subtraction together to help relate one to the other
Progressionbull In order for first grade students to be able to
apply properties of operations and find relationships between addition and subtraction they must firstbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of properties of operations and find relationships between addition and subtraction they willbull 2NBT9 Explain why addition and subtraction strategies
work using place value and the properties of operations
Add and subtract within 20bull 1OA5 Relate counting to addition and subtraction
(eg by counting on 2 to add 2) bull 1OA6 Add and subtract within 20 demonstrating
fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
What does it look likebull Students use many different strategies to add and
subtract Strategies can includebull Counting onbull Using the number linebull Using counters to represent addition and subtraction
problemsbull Acting out problemsbull Using modelsbull Drawing picturesbull And many morehellip
What does it look likebull httpwwwbrainpopjrcommath
additionandsubtractioncountingon
What does it look like5+4=
Misconceptionsbull Students may struggle with the use of their
manipulativesbull Double hopping on the number linebull Losing track of countersbull Sloppy drawingsbull Etchellip
bull Students might confuse the + and ndash signbull Many times students are more apt to add rather
than subtract Because of this they will not look at the sign and assume addition
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
Represent and solve problems involving addition and subtraction
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem2
bull 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
What does it look likebull Teachers pose questions that relate to familiar
contexts for students that result in the use of addition or subtraction
bull Problems can consist of problem structure in which the bull Result is unknownbull Change is unknownbull Start is unknown
bull Students must use their understanding of addition and subtraction to work through context based problems
What does it look like
bull httpwwwteachertubecom8809viewVideophpvideo_id=44503
Example Problem1OA19 boys and 8 girls were in the class How many children were
in the class in allResult unknown
Possible algebraic equations 9+8= 8+9= = 9+8 = 8+9
Samples provided by illustrative mathematics
1OA117 children were in the class 9 were boys and the rest were girls How many girls were in the class
Addend Unknown (Change)
Possible algebraic equations 17=9+ 17= + 99+ =17 +9=17 17ndash9=
Samples provided by illustrative mathematics
1OA117 children were in the class There were some boys and
8 girls How many boys were in the classAddend Unknown (Start)
Possible algebraic equations 17=8+
17= + 8 8+ =17 +8=17 17ndash8=
Samples provided by illustrative mathematics
1OA2
bull Jasmine has eight daisies and three vases - one large one medium-sized and one small She puts 5 daisies in the large vase 2 in the medium vase and 1 in the small vase
bull Can you find another way to put daisies so that there are the most in the large vase and least in the small vase
bull Try to find as many ways as you can put the daisies in the vases with the most in the large vase and the least in the smallest vase If you think you have found them all explain how you know those are all the possibilities
Samples provided by illustrative mathematics
What does it look like
Misconceptionsbull Students may have difficulty identifying the
logical structure of the word problem bull Wording may make it difficult for students to decipher
between join or separate problems with start unknown being the most difficultbull Language in compare problems might be challenging for
ELL students based on confusing vocabularybull Equal sign can be misinterpreted as operational
rather than relationalbull When faced with a representational problem with
three addends students may leave out the third addend or lack organization in their problem
Progressionbull In order for first grade students to be able to
represent and solve problems involving addition and subtractionbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of representing addition and subtraction problems algebraically in order tobull 2OA1 Use addition and subtraction within 100 to solve
one- and two-step word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using drawings and equations with a symbol for the unknown number to represent the problem
Progressionbull In Kindergarten students learn their numbers by
associating objects with numbers They use this knowledge to solve addition and subtraction problems within 10 This leads in to students being able to solve addition and subtraction problems within 20 without using objects By the end of first grade students can solve addition and subtraction problems by counting up This leads into second grade where students learn how to solve addition and subtraction problems within 100 Students know addition and subtraction facts with fluency in single digit problems
Understand and apply properties of operations and the relationship between addition and subtractionbull 1OA3 Apply properties of operations as
strategies to add and subtract Examples If 8 + 3 = 11 is known then 3 + 8 = 11 is also known (Commutative property of addition) To add 2 + 6 + 4 the second two numbers can be added to make a ten so 2 + 6 + 4 = 2 + 10 = 12 (Associative property of addition)
bull 1OA4 Understand subtraction as an unknown-addend problem For example subtract 10 ndash 8 by finding the number that makes 10 when added to 8
What does it look likebull Students should be able to differentiate between
and use thebull Communicative property of addition (3+2=2+3)bull Associative property of addition (4+1=3+2)
bull Students will use what they know about unknown addend problems to relate subtraction to addition (Fact Families)
Example ProblemsCommunicative Property
bull Build a two-color train using less than ten connecting cubes Place cubes of the same color together
bull Draw your train and write a number sentence to describe it from left to right
bull Flip your train draw it again and write the turn around fact
bull Repeat with other two color trains
2 + 3 = 5 3 + 2 = 5
Example provided by K-5MathTeachingResourcescom
ExampleAssociative Property
1OA4Choose a domino
Draw the domino
Write a fact family for the domino you chose Repeat with other dominoes
6 + 3 = 9 3 + 6 = 9 9 - 3 = 6 9 - 6 = 3
Example provided by K-5MathTeachingResourcescom
Misconceptionsbull Students might be confused about the meaning of the
equals sign In the problem 2+4=3+3 students may want to substitute first 3 in the second problem with a 6 This is because they may see the equal sign as a symbol indicating that the answer should follow
bull Students be unsure if each property (associative or communicative) works consistently bull Teacher must provide many examples to deter this misconception
bull Students many times confuse the order of numbers in a fact family resulting in an incorrect number sentence
Progressionbull First they develop understanding of number
conceptsbull Using understanding of number concepts
students are able to add and subtract within 10bull Following the mastery of addition and subtraction
within 10 students progress to addition and facts between 11-20 and then 20-100
bull During this process students are taught addition and subtraction together to help relate one to the other
Progressionbull In order for first grade students to be able to
apply properties of operations and find relationships between addition and subtraction they must firstbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of properties of operations and find relationships between addition and subtraction they willbull 2NBT9 Explain why addition and subtraction strategies
work using place value and the properties of operations
Add and subtract within 20bull 1OA5 Relate counting to addition and subtraction
(eg by counting on 2 to add 2) bull 1OA6 Add and subtract within 20 demonstrating
fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
What does it look likebull Students use many different strategies to add and
subtract Strategies can includebull Counting onbull Using the number linebull Using counters to represent addition and subtraction
problemsbull Acting out problemsbull Using modelsbull Drawing picturesbull And many morehellip
What does it look likebull httpwwwbrainpopjrcommath
additionandsubtractioncountingon
What does it look like5+4=
Misconceptionsbull Students may struggle with the use of their
manipulativesbull Double hopping on the number linebull Losing track of countersbull Sloppy drawingsbull Etchellip
bull Students might confuse the + and ndash signbull Many times students are more apt to add rather
than subtract Because of this they will not look at the sign and assume addition
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
What does it look likebull Teachers pose questions that relate to familiar
contexts for students that result in the use of addition or subtraction
bull Problems can consist of problem structure in which the bull Result is unknownbull Change is unknownbull Start is unknown
bull Students must use their understanding of addition and subtraction to work through context based problems
What does it look like
bull httpwwwteachertubecom8809viewVideophpvideo_id=44503
Example Problem1OA19 boys and 8 girls were in the class How many children were
in the class in allResult unknown
Possible algebraic equations 9+8= 8+9= = 9+8 = 8+9
Samples provided by illustrative mathematics
1OA117 children were in the class 9 were boys and the rest were girls How many girls were in the class
Addend Unknown (Change)
Possible algebraic equations 17=9+ 17= + 99+ =17 +9=17 17ndash9=
Samples provided by illustrative mathematics
1OA117 children were in the class There were some boys and
8 girls How many boys were in the classAddend Unknown (Start)
Possible algebraic equations 17=8+
17= + 8 8+ =17 +8=17 17ndash8=
Samples provided by illustrative mathematics
1OA2
bull Jasmine has eight daisies and three vases - one large one medium-sized and one small She puts 5 daisies in the large vase 2 in the medium vase and 1 in the small vase
bull Can you find another way to put daisies so that there are the most in the large vase and least in the small vase
bull Try to find as many ways as you can put the daisies in the vases with the most in the large vase and the least in the smallest vase If you think you have found them all explain how you know those are all the possibilities
Samples provided by illustrative mathematics
What does it look like
Misconceptionsbull Students may have difficulty identifying the
logical structure of the word problem bull Wording may make it difficult for students to decipher
between join or separate problems with start unknown being the most difficultbull Language in compare problems might be challenging for
ELL students based on confusing vocabularybull Equal sign can be misinterpreted as operational
rather than relationalbull When faced with a representational problem with
three addends students may leave out the third addend or lack organization in their problem
Progressionbull In order for first grade students to be able to
represent and solve problems involving addition and subtractionbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of representing addition and subtraction problems algebraically in order tobull 2OA1 Use addition and subtraction within 100 to solve
one- and two-step word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using drawings and equations with a symbol for the unknown number to represent the problem
Progressionbull In Kindergarten students learn their numbers by
associating objects with numbers They use this knowledge to solve addition and subtraction problems within 10 This leads in to students being able to solve addition and subtraction problems within 20 without using objects By the end of first grade students can solve addition and subtraction problems by counting up This leads into second grade where students learn how to solve addition and subtraction problems within 100 Students know addition and subtraction facts with fluency in single digit problems
Understand and apply properties of operations and the relationship between addition and subtractionbull 1OA3 Apply properties of operations as
strategies to add and subtract Examples If 8 + 3 = 11 is known then 3 + 8 = 11 is also known (Commutative property of addition) To add 2 + 6 + 4 the second two numbers can be added to make a ten so 2 + 6 + 4 = 2 + 10 = 12 (Associative property of addition)
bull 1OA4 Understand subtraction as an unknown-addend problem For example subtract 10 ndash 8 by finding the number that makes 10 when added to 8
What does it look likebull Students should be able to differentiate between
and use thebull Communicative property of addition (3+2=2+3)bull Associative property of addition (4+1=3+2)
bull Students will use what they know about unknown addend problems to relate subtraction to addition (Fact Families)
Example ProblemsCommunicative Property
bull Build a two-color train using less than ten connecting cubes Place cubes of the same color together
bull Draw your train and write a number sentence to describe it from left to right
bull Flip your train draw it again and write the turn around fact
bull Repeat with other two color trains
2 + 3 = 5 3 + 2 = 5
Example provided by K-5MathTeachingResourcescom
ExampleAssociative Property
1OA4Choose a domino
Draw the domino
Write a fact family for the domino you chose Repeat with other dominoes
6 + 3 = 9 3 + 6 = 9 9 - 3 = 6 9 - 6 = 3
Example provided by K-5MathTeachingResourcescom
Misconceptionsbull Students might be confused about the meaning of the
equals sign In the problem 2+4=3+3 students may want to substitute first 3 in the second problem with a 6 This is because they may see the equal sign as a symbol indicating that the answer should follow
bull Students be unsure if each property (associative or communicative) works consistently bull Teacher must provide many examples to deter this misconception
bull Students many times confuse the order of numbers in a fact family resulting in an incorrect number sentence
Progressionbull First they develop understanding of number
conceptsbull Using understanding of number concepts
students are able to add and subtract within 10bull Following the mastery of addition and subtraction
within 10 students progress to addition and facts between 11-20 and then 20-100
bull During this process students are taught addition and subtraction together to help relate one to the other
Progressionbull In order for first grade students to be able to
apply properties of operations and find relationships between addition and subtraction they must firstbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of properties of operations and find relationships between addition and subtraction they willbull 2NBT9 Explain why addition and subtraction strategies
work using place value and the properties of operations
Add and subtract within 20bull 1OA5 Relate counting to addition and subtraction
(eg by counting on 2 to add 2) bull 1OA6 Add and subtract within 20 demonstrating
fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
What does it look likebull Students use many different strategies to add and
subtract Strategies can includebull Counting onbull Using the number linebull Using counters to represent addition and subtraction
problemsbull Acting out problemsbull Using modelsbull Drawing picturesbull And many morehellip
What does it look likebull httpwwwbrainpopjrcommath
additionandsubtractioncountingon
What does it look like5+4=
Misconceptionsbull Students may struggle with the use of their
manipulativesbull Double hopping on the number linebull Losing track of countersbull Sloppy drawingsbull Etchellip
bull Students might confuse the + and ndash signbull Many times students are more apt to add rather
than subtract Because of this they will not look at the sign and assume addition
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
What does it look like
bull httpwwwteachertubecom8809viewVideophpvideo_id=44503
Example Problem1OA19 boys and 8 girls were in the class How many children were
in the class in allResult unknown
Possible algebraic equations 9+8= 8+9= = 9+8 = 8+9
Samples provided by illustrative mathematics
1OA117 children were in the class 9 were boys and the rest were girls How many girls were in the class
Addend Unknown (Change)
Possible algebraic equations 17=9+ 17= + 99+ =17 +9=17 17ndash9=
Samples provided by illustrative mathematics
1OA117 children were in the class There were some boys and
8 girls How many boys were in the classAddend Unknown (Start)
Possible algebraic equations 17=8+
17= + 8 8+ =17 +8=17 17ndash8=
Samples provided by illustrative mathematics
1OA2
bull Jasmine has eight daisies and three vases - one large one medium-sized and one small She puts 5 daisies in the large vase 2 in the medium vase and 1 in the small vase
bull Can you find another way to put daisies so that there are the most in the large vase and least in the small vase
bull Try to find as many ways as you can put the daisies in the vases with the most in the large vase and the least in the smallest vase If you think you have found them all explain how you know those are all the possibilities
Samples provided by illustrative mathematics
What does it look like
Misconceptionsbull Students may have difficulty identifying the
logical structure of the word problem bull Wording may make it difficult for students to decipher
between join or separate problems with start unknown being the most difficultbull Language in compare problems might be challenging for
ELL students based on confusing vocabularybull Equal sign can be misinterpreted as operational
rather than relationalbull When faced with a representational problem with
three addends students may leave out the third addend or lack organization in their problem
Progressionbull In order for first grade students to be able to
represent and solve problems involving addition and subtractionbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of representing addition and subtraction problems algebraically in order tobull 2OA1 Use addition and subtraction within 100 to solve
one- and two-step word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using drawings and equations with a symbol for the unknown number to represent the problem
Progressionbull In Kindergarten students learn their numbers by
associating objects with numbers They use this knowledge to solve addition and subtraction problems within 10 This leads in to students being able to solve addition and subtraction problems within 20 without using objects By the end of first grade students can solve addition and subtraction problems by counting up This leads into second grade where students learn how to solve addition and subtraction problems within 100 Students know addition and subtraction facts with fluency in single digit problems
Understand and apply properties of operations and the relationship between addition and subtractionbull 1OA3 Apply properties of operations as
strategies to add and subtract Examples If 8 + 3 = 11 is known then 3 + 8 = 11 is also known (Commutative property of addition) To add 2 + 6 + 4 the second two numbers can be added to make a ten so 2 + 6 + 4 = 2 + 10 = 12 (Associative property of addition)
bull 1OA4 Understand subtraction as an unknown-addend problem For example subtract 10 ndash 8 by finding the number that makes 10 when added to 8
What does it look likebull Students should be able to differentiate between
and use thebull Communicative property of addition (3+2=2+3)bull Associative property of addition (4+1=3+2)
bull Students will use what they know about unknown addend problems to relate subtraction to addition (Fact Families)
Example ProblemsCommunicative Property
bull Build a two-color train using less than ten connecting cubes Place cubes of the same color together
bull Draw your train and write a number sentence to describe it from left to right
bull Flip your train draw it again and write the turn around fact
bull Repeat with other two color trains
2 + 3 = 5 3 + 2 = 5
Example provided by K-5MathTeachingResourcescom
ExampleAssociative Property
1OA4Choose a domino
Draw the domino
Write a fact family for the domino you chose Repeat with other dominoes
6 + 3 = 9 3 + 6 = 9 9 - 3 = 6 9 - 6 = 3
Example provided by K-5MathTeachingResourcescom
Misconceptionsbull Students might be confused about the meaning of the
equals sign In the problem 2+4=3+3 students may want to substitute first 3 in the second problem with a 6 This is because they may see the equal sign as a symbol indicating that the answer should follow
bull Students be unsure if each property (associative or communicative) works consistently bull Teacher must provide many examples to deter this misconception
bull Students many times confuse the order of numbers in a fact family resulting in an incorrect number sentence
Progressionbull First they develop understanding of number
conceptsbull Using understanding of number concepts
students are able to add and subtract within 10bull Following the mastery of addition and subtraction
within 10 students progress to addition and facts between 11-20 and then 20-100
bull During this process students are taught addition and subtraction together to help relate one to the other
Progressionbull In order for first grade students to be able to
apply properties of operations and find relationships between addition and subtraction they must firstbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of properties of operations and find relationships between addition and subtraction they willbull 2NBT9 Explain why addition and subtraction strategies
work using place value and the properties of operations
Add and subtract within 20bull 1OA5 Relate counting to addition and subtraction
(eg by counting on 2 to add 2) bull 1OA6 Add and subtract within 20 demonstrating
fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
What does it look likebull Students use many different strategies to add and
subtract Strategies can includebull Counting onbull Using the number linebull Using counters to represent addition and subtraction
problemsbull Acting out problemsbull Using modelsbull Drawing picturesbull And many morehellip
What does it look likebull httpwwwbrainpopjrcommath
additionandsubtractioncountingon
What does it look like5+4=
Misconceptionsbull Students may struggle with the use of their
manipulativesbull Double hopping on the number linebull Losing track of countersbull Sloppy drawingsbull Etchellip
bull Students might confuse the + and ndash signbull Many times students are more apt to add rather
than subtract Because of this they will not look at the sign and assume addition
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
Example Problem1OA19 boys and 8 girls were in the class How many children were
in the class in allResult unknown
Possible algebraic equations 9+8= 8+9= = 9+8 = 8+9
Samples provided by illustrative mathematics
1OA117 children were in the class 9 were boys and the rest were girls How many girls were in the class
Addend Unknown (Change)
Possible algebraic equations 17=9+ 17= + 99+ =17 +9=17 17ndash9=
Samples provided by illustrative mathematics
1OA117 children were in the class There were some boys and
8 girls How many boys were in the classAddend Unknown (Start)
Possible algebraic equations 17=8+
17= + 8 8+ =17 +8=17 17ndash8=
Samples provided by illustrative mathematics
1OA2
bull Jasmine has eight daisies and three vases - one large one medium-sized and one small She puts 5 daisies in the large vase 2 in the medium vase and 1 in the small vase
bull Can you find another way to put daisies so that there are the most in the large vase and least in the small vase
bull Try to find as many ways as you can put the daisies in the vases with the most in the large vase and the least in the smallest vase If you think you have found them all explain how you know those are all the possibilities
Samples provided by illustrative mathematics
What does it look like
Misconceptionsbull Students may have difficulty identifying the
logical structure of the word problem bull Wording may make it difficult for students to decipher
between join or separate problems with start unknown being the most difficultbull Language in compare problems might be challenging for
ELL students based on confusing vocabularybull Equal sign can be misinterpreted as operational
rather than relationalbull When faced with a representational problem with
three addends students may leave out the third addend or lack organization in their problem
Progressionbull In order for first grade students to be able to
represent and solve problems involving addition and subtractionbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of representing addition and subtraction problems algebraically in order tobull 2OA1 Use addition and subtraction within 100 to solve
one- and two-step word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using drawings and equations with a symbol for the unknown number to represent the problem
Progressionbull In Kindergarten students learn their numbers by
associating objects with numbers They use this knowledge to solve addition and subtraction problems within 10 This leads in to students being able to solve addition and subtraction problems within 20 without using objects By the end of first grade students can solve addition and subtraction problems by counting up This leads into second grade where students learn how to solve addition and subtraction problems within 100 Students know addition and subtraction facts with fluency in single digit problems
Understand and apply properties of operations and the relationship between addition and subtractionbull 1OA3 Apply properties of operations as
strategies to add and subtract Examples If 8 + 3 = 11 is known then 3 + 8 = 11 is also known (Commutative property of addition) To add 2 + 6 + 4 the second two numbers can be added to make a ten so 2 + 6 + 4 = 2 + 10 = 12 (Associative property of addition)
bull 1OA4 Understand subtraction as an unknown-addend problem For example subtract 10 ndash 8 by finding the number that makes 10 when added to 8
What does it look likebull Students should be able to differentiate between
and use thebull Communicative property of addition (3+2=2+3)bull Associative property of addition (4+1=3+2)
bull Students will use what they know about unknown addend problems to relate subtraction to addition (Fact Families)
Example ProblemsCommunicative Property
bull Build a two-color train using less than ten connecting cubes Place cubes of the same color together
bull Draw your train and write a number sentence to describe it from left to right
bull Flip your train draw it again and write the turn around fact
bull Repeat with other two color trains
2 + 3 = 5 3 + 2 = 5
Example provided by K-5MathTeachingResourcescom
ExampleAssociative Property
1OA4Choose a domino
Draw the domino
Write a fact family for the domino you chose Repeat with other dominoes
6 + 3 = 9 3 + 6 = 9 9 - 3 = 6 9 - 6 = 3
Example provided by K-5MathTeachingResourcescom
Misconceptionsbull Students might be confused about the meaning of the
equals sign In the problem 2+4=3+3 students may want to substitute first 3 in the second problem with a 6 This is because they may see the equal sign as a symbol indicating that the answer should follow
bull Students be unsure if each property (associative or communicative) works consistently bull Teacher must provide many examples to deter this misconception
bull Students many times confuse the order of numbers in a fact family resulting in an incorrect number sentence
Progressionbull First they develop understanding of number
conceptsbull Using understanding of number concepts
students are able to add and subtract within 10bull Following the mastery of addition and subtraction
within 10 students progress to addition and facts between 11-20 and then 20-100
bull During this process students are taught addition and subtraction together to help relate one to the other
Progressionbull In order for first grade students to be able to
apply properties of operations and find relationships between addition and subtraction they must firstbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of properties of operations and find relationships between addition and subtraction they willbull 2NBT9 Explain why addition and subtraction strategies
work using place value and the properties of operations
Add and subtract within 20bull 1OA5 Relate counting to addition and subtraction
(eg by counting on 2 to add 2) bull 1OA6 Add and subtract within 20 demonstrating
fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
What does it look likebull Students use many different strategies to add and
subtract Strategies can includebull Counting onbull Using the number linebull Using counters to represent addition and subtraction
problemsbull Acting out problemsbull Using modelsbull Drawing picturesbull And many morehellip
What does it look likebull httpwwwbrainpopjrcommath
additionandsubtractioncountingon
What does it look like5+4=
Misconceptionsbull Students may struggle with the use of their
manipulativesbull Double hopping on the number linebull Losing track of countersbull Sloppy drawingsbull Etchellip
bull Students might confuse the + and ndash signbull Many times students are more apt to add rather
than subtract Because of this they will not look at the sign and assume addition
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
1OA117 children were in the class 9 were boys and the rest were girls How many girls were in the class
Addend Unknown (Change)
Possible algebraic equations 17=9+ 17= + 99+ =17 +9=17 17ndash9=
Samples provided by illustrative mathematics
1OA117 children were in the class There were some boys and
8 girls How many boys were in the classAddend Unknown (Start)
Possible algebraic equations 17=8+
17= + 8 8+ =17 +8=17 17ndash8=
Samples provided by illustrative mathematics
1OA2
bull Jasmine has eight daisies and three vases - one large one medium-sized and one small She puts 5 daisies in the large vase 2 in the medium vase and 1 in the small vase
bull Can you find another way to put daisies so that there are the most in the large vase and least in the small vase
bull Try to find as many ways as you can put the daisies in the vases with the most in the large vase and the least in the smallest vase If you think you have found them all explain how you know those are all the possibilities
Samples provided by illustrative mathematics
What does it look like
Misconceptionsbull Students may have difficulty identifying the
logical structure of the word problem bull Wording may make it difficult for students to decipher
between join or separate problems with start unknown being the most difficultbull Language in compare problems might be challenging for
ELL students based on confusing vocabularybull Equal sign can be misinterpreted as operational
rather than relationalbull When faced with a representational problem with
three addends students may leave out the third addend or lack organization in their problem
Progressionbull In order for first grade students to be able to
represent and solve problems involving addition and subtractionbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of representing addition and subtraction problems algebraically in order tobull 2OA1 Use addition and subtraction within 100 to solve
one- and two-step word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using drawings and equations with a symbol for the unknown number to represent the problem
Progressionbull In Kindergarten students learn their numbers by
associating objects with numbers They use this knowledge to solve addition and subtraction problems within 10 This leads in to students being able to solve addition and subtraction problems within 20 without using objects By the end of first grade students can solve addition and subtraction problems by counting up This leads into second grade where students learn how to solve addition and subtraction problems within 100 Students know addition and subtraction facts with fluency in single digit problems
Understand and apply properties of operations and the relationship between addition and subtractionbull 1OA3 Apply properties of operations as
strategies to add and subtract Examples If 8 + 3 = 11 is known then 3 + 8 = 11 is also known (Commutative property of addition) To add 2 + 6 + 4 the second two numbers can be added to make a ten so 2 + 6 + 4 = 2 + 10 = 12 (Associative property of addition)
bull 1OA4 Understand subtraction as an unknown-addend problem For example subtract 10 ndash 8 by finding the number that makes 10 when added to 8
What does it look likebull Students should be able to differentiate between
and use thebull Communicative property of addition (3+2=2+3)bull Associative property of addition (4+1=3+2)
bull Students will use what they know about unknown addend problems to relate subtraction to addition (Fact Families)
Example ProblemsCommunicative Property
bull Build a two-color train using less than ten connecting cubes Place cubes of the same color together
bull Draw your train and write a number sentence to describe it from left to right
bull Flip your train draw it again and write the turn around fact
bull Repeat with other two color trains
2 + 3 = 5 3 + 2 = 5
Example provided by K-5MathTeachingResourcescom
ExampleAssociative Property
1OA4Choose a domino
Draw the domino
Write a fact family for the domino you chose Repeat with other dominoes
6 + 3 = 9 3 + 6 = 9 9 - 3 = 6 9 - 6 = 3
Example provided by K-5MathTeachingResourcescom
Misconceptionsbull Students might be confused about the meaning of the
equals sign In the problem 2+4=3+3 students may want to substitute first 3 in the second problem with a 6 This is because they may see the equal sign as a symbol indicating that the answer should follow
bull Students be unsure if each property (associative or communicative) works consistently bull Teacher must provide many examples to deter this misconception
bull Students many times confuse the order of numbers in a fact family resulting in an incorrect number sentence
Progressionbull First they develop understanding of number
conceptsbull Using understanding of number concepts
students are able to add and subtract within 10bull Following the mastery of addition and subtraction
within 10 students progress to addition and facts between 11-20 and then 20-100
bull During this process students are taught addition and subtraction together to help relate one to the other
Progressionbull In order for first grade students to be able to
apply properties of operations and find relationships between addition and subtraction they must firstbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of properties of operations and find relationships between addition and subtraction they willbull 2NBT9 Explain why addition and subtraction strategies
work using place value and the properties of operations
Add and subtract within 20bull 1OA5 Relate counting to addition and subtraction
(eg by counting on 2 to add 2) bull 1OA6 Add and subtract within 20 demonstrating
fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
What does it look likebull Students use many different strategies to add and
subtract Strategies can includebull Counting onbull Using the number linebull Using counters to represent addition and subtraction
problemsbull Acting out problemsbull Using modelsbull Drawing picturesbull And many morehellip
What does it look likebull httpwwwbrainpopjrcommath
additionandsubtractioncountingon
What does it look like5+4=
Misconceptionsbull Students may struggle with the use of their
manipulativesbull Double hopping on the number linebull Losing track of countersbull Sloppy drawingsbull Etchellip
bull Students might confuse the + and ndash signbull Many times students are more apt to add rather
than subtract Because of this they will not look at the sign and assume addition
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
1OA117 children were in the class There were some boys and
8 girls How many boys were in the classAddend Unknown (Start)
Possible algebraic equations 17=8+
17= + 8 8+ =17 +8=17 17ndash8=
Samples provided by illustrative mathematics
1OA2
bull Jasmine has eight daisies and three vases - one large one medium-sized and one small She puts 5 daisies in the large vase 2 in the medium vase and 1 in the small vase
bull Can you find another way to put daisies so that there are the most in the large vase and least in the small vase
bull Try to find as many ways as you can put the daisies in the vases with the most in the large vase and the least in the smallest vase If you think you have found them all explain how you know those are all the possibilities
Samples provided by illustrative mathematics
What does it look like
Misconceptionsbull Students may have difficulty identifying the
logical structure of the word problem bull Wording may make it difficult for students to decipher
between join or separate problems with start unknown being the most difficultbull Language in compare problems might be challenging for
ELL students based on confusing vocabularybull Equal sign can be misinterpreted as operational
rather than relationalbull When faced with a representational problem with
three addends students may leave out the third addend or lack organization in their problem
Progressionbull In order for first grade students to be able to
represent and solve problems involving addition and subtractionbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of representing addition and subtraction problems algebraically in order tobull 2OA1 Use addition and subtraction within 100 to solve
one- and two-step word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using drawings and equations with a symbol for the unknown number to represent the problem
Progressionbull In Kindergarten students learn their numbers by
associating objects with numbers They use this knowledge to solve addition and subtraction problems within 10 This leads in to students being able to solve addition and subtraction problems within 20 without using objects By the end of first grade students can solve addition and subtraction problems by counting up This leads into second grade where students learn how to solve addition and subtraction problems within 100 Students know addition and subtraction facts with fluency in single digit problems
Understand and apply properties of operations and the relationship between addition and subtractionbull 1OA3 Apply properties of operations as
strategies to add and subtract Examples If 8 + 3 = 11 is known then 3 + 8 = 11 is also known (Commutative property of addition) To add 2 + 6 + 4 the second two numbers can be added to make a ten so 2 + 6 + 4 = 2 + 10 = 12 (Associative property of addition)
bull 1OA4 Understand subtraction as an unknown-addend problem For example subtract 10 ndash 8 by finding the number that makes 10 when added to 8
What does it look likebull Students should be able to differentiate between
and use thebull Communicative property of addition (3+2=2+3)bull Associative property of addition (4+1=3+2)
bull Students will use what they know about unknown addend problems to relate subtraction to addition (Fact Families)
Example ProblemsCommunicative Property
bull Build a two-color train using less than ten connecting cubes Place cubes of the same color together
bull Draw your train and write a number sentence to describe it from left to right
bull Flip your train draw it again and write the turn around fact
bull Repeat with other two color trains
2 + 3 = 5 3 + 2 = 5
Example provided by K-5MathTeachingResourcescom
ExampleAssociative Property
1OA4Choose a domino
Draw the domino
Write a fact family for the domino you chose Repeat with other dominoes
6 + 3 = 9 3 + 6 = 9 9 - 3 = 6 9 - 6 = 3
Example provided by K-5MathTeachingResourcescom
Misconceptionsbull Students might be confused about the meaning of the
equals sign In the problem 2+4=3+3 students may want to substitute first 3 in the second problem with a 6 This is because they may see the equal sign as a symbol indicating that the answer should follow
bull Students be unsure if each property (associative or communicative) works consistently bull Teacher must provide many examples to deter this misconception
bull Students many times confuse the order of numbers in a fact family resulting in an incorrect number sentence
Progressionbull First they develop understanding of number
conceptsbull Using understanding of number concepts
students are able to add and subtract within 10bull Following the mastery of addition and subtraction
within 10 students progress to addition and facts between 11-20 and then 20-100
bull During this process students are taught addition and subtraction together to help relate one to the other
Progressionbull In order for first grade students to be able to
apply properties of operations and find relationships between addition and subtraction they must firstbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of properties of operations and find relationships between addition and subtraction they willbull 2NBT9 Explain why addition and subtraction strategies
work using place value and the properties of operations
Add and subtract within 20bull 1OA5 Relate counting to addition and subtraction
(eg by counting on 2 to add 2) bull 1OA6 Add and subtract within 20 demonstrating
fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
What does it look likebull Students use many different strategies to add and
subtract Strategies can includebull Counting onbull Using the number linebull Using counters to represent addition and subtraction
problemsbull Acting out problemsbull Using modelsbull Drawing picturesbull And many morehellip
What does it look likebull httpwwwbrainpopjrcommath
additionandsubtractioncountingon
What does it look like5+4=
Misconceptionsbull Students may struggle with the use of their
manipulativesbull Double hopping on the number linebull Losing track of countersbull Sloppy drawingsbull Etchellip
bull Students might confuse the + and ndash signbull Many times students are more apt to add rather
than subtract Because of this they will not look at the sign and assume addition
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
1OA2
bull Jasmine has eight daisies and three vases - one large one medium-sized and one small She puts 5 daisies in the large vase 2 in the medium vase and 1 in the small vase
bull Can you find another way to put daisies so that there are the most in the large vase and least in the small vase
bull Try to find as many ways as you can put the daisies in the vases with the most in the large vase and the least in the smallest vase If you think you have found them all explain how you know those are all the possibilities
Samples provided by illustrative mathematics
What does it look like
Misconceptionsbull Students may have difficulty identifying the
logical structure of the word problem bull Wording may make it difficult for students to decipher
between join or separate problems with start unknown being the most difficultbull Language in compare problems might be challenging for
ELL students based on confusing vocabularybull Equal sign can be misinterpreted as operational
rather than relationalbull When faced with a representational problem with
three addends students may leave out the third addend or lack organization in their problem
Progressionbull In order for first grade students to be able to
represent and solve problems involving addition and subtractionbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of representing addition and subtraction problems algebraically in order tobull 2OA1 Use addition and subtraction within 100 to solve
one- and two-step word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using drawings and equations with a symbol for the unknown number to represent the problem
Progressionbull In Kindergarten students learn their numbers by
associating objects with numbers They use this knowledge to solve addition and subtraction problems within 10 This leads in to students being able to solve addition and subtraction problems within 20 without using objects By the end of first grade students can solve addition and subtraction problems by counting up This leads into second grade where students learn how to solve addition and subtraction problems within 100 Students know addition and subtraction facts with fluency in single digit problems
Understand and apply properties of operations and the relationship between addition and subtractionbull 1OA3 Apply properties of operations as
strategies to add and subtract Examples If 8 + 3 = 11 is known then 3 + 8 = 11 is also known (Commutative property of addition) To add 2 + 6 + 4 the second two numbers can be added to make a ten so 2 + 6 + 4 = 2 + 10 = 12 (Associative property of addition)
bull 1OA4 Understand subtraction as an unknown-addend problem For example subtract 10 ndash 8 by finding the number that makes 10 when added to 8
What does it look likebull Students should be able to differentiate between
and use thebull Communicative property of addition (3+2=2+3)bull Associative property of addition (4+1=3+2)
bull Students will use what they know about unknown addend problems to relate subtraction to addition (Fact Families)
Example ProblemsCommunicative Property
bull Build a two-color train using less than ten connecting cubes Place cubes of the same color together
bull Draw your train and write a number sentence to describe it from left to right
bull Flip your train draw it again and write the turn around fact
bull Repeat with other two color trains
2 + 3 = 5 3 + 2 = 5
Example provided by K-5MathTeachingResourcescom
ExampleAssociative Property
1OA4Choose a domino
Draw the domino
Write a fact family for the domino you chose Repeat with other dominoes
6 + 3 = 9 3 + 6 = 9 9 - 3 = 6 9 - 6 = 3
Example provided by K-5MathTeachingResourcescom
Misconceptionsbull Students might be confused about the meaning of the
equals sign In the problem 2+4=3+3 students may want to substitute first 3 in the second problem with a 6 This is because they may see the equal sign as a symbol indicating that the answer should follow
bull Students be unsure if each property (associative or communicative) works consistently bull Teacher must provide many examples to deter this misconception
bull Students many times confuse the order of numbers in a fact family resulting in an incorrect number sentence
Progressionbull First they develop understanding of number
conceptsbull Using understanding of number concepts
students are able to add and subtract within 10bull Following the mastery of addition and subtraction
within 10 students progress to addition and facts between 11-20 and then 20-100
bull During this process students are taught addition and subtraction together to help relate one to the other
Progressionbull In order for first grade students to be able to
apply properties of operations and find relationships between addition and subtraction they must firstbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of properties of operations and find relationships between addition and subtraction they willbull 2NBT9 Explain why addition and subtraction strategies
work using place value and the properties of operations
Add and subtract within 20bull 1OA5 Relate counting to addition and subtraction
(eg by counting on 2 to add 2) bull 1OA6 Add and subtract within 20 demonstrating
fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
What does it look likebull Students use many different strategies to add and
subtract Strategies can includebull Counting onbull Using the number linebull Using counters to represent addition and subtraction
problemsbull Acting out problemsbull Using modelsbull Drawing picturesbull And many morehellip
What does it look likebull httpwwwbrainpopjrcommath
additionandsubtractioncountingon
What does it look like5+4=
Misconceptionsbull Students may struggle with the use of their
manipulativesbull Double hopping on the number linebull Losing track of countersbull Sloppy drawingsbull Etchellip
bull Students might confuse the + and ndash signbull Many times students are more apt to add rather
than subtract Because of this they will not look at the sign and assume addition
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
What does it look like
Misconceptionsbull Students may have difficulty identifying the
logical structure of the word problem bull Wording may make it difficult for students to decipher
between join or separate problems with start unknown being the most difficultbull Language in compare problems might be challenging for
ELL students based on confusing vocabularybull Equal sign can be misinterpreted as operational
rather than relationalbull When faced with a representational problem with
three addends students may leave out the third addend or lack organization in their problem
Progressionbull In order for first grade students to be able to
represent and solve problems involving addition and subtractionbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of representing addition and subtraction problems algebraically in order tobull 2OA1 Use addition and subtraction within 100 to solve
one- and two-step word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using drawings and equations with a symbol for the unknown number to represent the problem
Progressionbull In Kindergarten students learn their numbers by
associating objects with numbers They use this knowledge to solve addition and subtraction problems within 10 This leads in to students being able to solve addition and subtraction problems within 20 without using objects By the end of first grade students can solve addition and subtraction problems by counting up This leads into second grade where students learn how to solve addition and subtraction problems within 100 Students know addition and subtraction facts with fluency in single digit problems
Understand and apply properties of operations and the relationship between addition and subtractionbull 1OA3 Apply properties of operations as
strategies to add and subtract Examples If 8 + 3 = 11 is known then 3 + 8 = 11 is also known (Commutative property of addition) To add 2 + 6 + 4 the second two numbers can be added to make a ten so 2 + 6 + 4 = 2 + 10 = 12 (Associative property of addition)
bull 1OA4 Understand subtraction as an unknown-addend problem For example subtract 10 ndash 8 by finding the number that makes 10 when added to 8
What does it look likebull Students should be able to differentiate between
and use thebull Communicative property of addition (3+2=2+3)bull Associative property of addition (4+1=3+2)
bull Students will use what they know about unknown addend problems to relate subtraction to addition (Fact Families)
Example ProblemsCommunicative Property
bull Build a two-color train using less than ten connecting cubes Place cubes of the same color together
bull Draw your train and write a number sentence to describe it from left to right
bull Flip your train draw it again and write the turn around fact
bull Repeat with other two color trains
2 + 3 = 5 3 + 2 = 5
Example provided by K-5MathTeachingResourcescom
ExampleAssociative Property
1OA4Choose a domino
Draw the domino
Write a fact family for the domino you chose Repeat with other dominoes
6 + 3 = 9 3 + 6 = 9 9 - 3 = 6 9 - 6 = 3
Example provided by K-5MathTeachingResourcescom
Misconceptionsbull Students might be confused about the meaning of the
equals sign In the problem 2+4=3+3 students may want to substitute first 3 in the second problem with a 6 This is because they may see the equal sign as a symbol indicating that the answer should follow
bull Students be unsure if each property (associative or communicative) works consistently bull Teacher must provide many examples to deter this misconception
bull Students many times confuse the order of numbers in a fact family resulting in an incorrect number sentence
Progressionbull First they develop understanding of number
conceptsbull Using understanding of number concepts
students are able to add and subtract within 10bull Following the mastery of addition and subtraction
within 10 students progress to addition and facts between 11-20 and then 20-100
bull During this process students are taught addition and subtraction together to help relate one to the other
Progressionbull In order for first grade students to be able to
apply properties of operations and find relationships between addition and subtraction they must firstbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of properties of operations and find relationships between addition and subtraction they willbull 2NBT9 Explain why addition and subtraction strategies
work using place value and the properties of operations
Add and subtract within 20bull 1OA5 Relate counting to addition and subtraction
(eg by counting on 2 to add 2) bull 1OA6 Add and subtract within 20 demonstrating
fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
What does it look likebull Students use many different strategies to add and
subtract Strategies can includebull Counting onbull Using the number linebull Using counters to represent addition and subtraction
problemsbull Acting out problemsbull Using modelsbull Drawing picturesbull And many morehellip
What does it look likebull httpwwwbrainpopjrcommath
additionandsubtractioncountingon
What does it look like5+4=
Misconceptionsbull Students may struggle with the use of their
manipulativesbull Double hopping on the number linebull Losing track of countersbull Sloppy drawingsbull Etchellip
bull Students might confuse the + and ndash signbull Many times students are more apt to add rather
than subtract Because of this they will not look at the sign and assume addition
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
Misconceptionsbull Students may have difficulty identifying the
logical structure of the word problem bull Wording may make it difficult for students to decipher
between join or separate problems with start unknown being the most difficultbull Language in compare problems might be challenging for
ELL students based on confusing vocabularybull Equal sign can be misinterpreted as operational
rather than relationalbull When faced with a representational problem with
three addends students may leave out the third addend or lack organization in their problem
Progressionbull In order for first grade students to be able to
represent and solve problems involving addition and subtractionbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of representing addition and subtraction problems algebraically in order tobull 2OA1 Use addition and subtraction within 100 to solve
one- and two-step word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using drawings and equations with a symbol for the unknown number to represent the problem
Progressionbull In Kindergarten students learn their numbers by
associating objects with numbers They use this knowledge to solve addition and subtraction problems within 10 This leads in to students being able to solve addition and subtraction problems within 20 without using objects By the end of first grade students can solve addition and subtraction problems by counting up This leads into second grade where students learn how to solve addition and subtraction problems within 100 Students know addition and subtraction facts with fluency in single digit problems
Understand and apply properties of operations and the relationship between addition and subtractionbull 1OA3 Apply properties of operations as
strategies to add and subtract Examples If 8 + 3 = 11 is known then 3 + 8 = 11 is also known (Commutative property of addition) To add 2 + 6 + 4 the second two numbers can be added to make a ten so 2 + 6 + 4 = 2 + 10 = 12 (Associative property of addition)
bull 1OA4 Understand subtraction as an unknown-addend problem For example subtract 10 ndash 8 by finding the number that makes 10 when added to 8
What does it look likebull Students should be able to differentiate between
and use thebull Communicative property of addition (3+2=2+3)bull Associative property of addition (4+1=3+2)
bull Students will use what they know about unknown addend problems to relate subtraction to addition (Fact Families)
Example ProblemsCommunicative Property
bull Build a two-color train using less than ten connecting cubes Place cubes of the same color together
bull Draw your train and write a number sentence to describe it from left to right
bull Flip your train draw it again and write the turn around fact
bull Repeat with other two color trains
2 + 3 = 5 3 + 2 = 5
Example provided by K-5MathTeachingResourcescom
ExampleAssociative Property
1OA4Choose a domino
Draw the domino
Write a fact family for the domino you chose Repeat with other dominoes
6 + 3 = 9 3 + 6 = 9 9 - 3 = 6 9 - 6 = 3
Example provided by K-5MathTeachingResourcescom
Misconceptionsbull Students might be confused about the meaning of the
equals sign In the problem 2+4=3+3 students may want to substitute first 3 in the second problem with a 6 This is because they may see the equal sign as a symbol indicating that the answer should follow
bull Students be unsure if each property (associative or communicative) works consistently bull Teacher must provide many examples to deter this misconception
bull Students many times confuse the order of numbers in a fact family resulting in an incorrect number sentence
Progressionbull First they develop understanding of number
conceptsbull Using understanding of number concepts
students are able to add and subtract within 10bull Following the mastery of addition and subtraction
within 10 students progress to addition and facts between 11-20 and then 20-100
bull During this process students are taught addition and subtraction together to help relate one to the other
Progressionbull In order for first grade students to be able to
apply properties of operations and find relationships between addition and subtraction they must firstbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of properties of operations and find relationships between addition and subtraction they willbull 2NBT9 Explain why addition and subtraction strategies
work using place value and the properties of operations
Add and subtract within 20bull 1OA5 Relate counting to addition and subtraction
(eg by counting on 2 to add 2) bull 1OA6 Add and subtract within 20 demonstrating
fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
What does it look likebull Students use many different strategies to add and
subtract Strategies can includebull Counting onbull Using the number linebull Using counters to represent addition and subtraction
problemsbull Acting out problemsbull Using modelsbull Drawing picturesbull And many morehellip
What does it look likebull httpwwwbrainpopjrcommath
additionandsubtractioncountingon
What does it look like5+4=
Misconceptionsbull Students may struggle with the use of their
manipulativesbull Double hopping on the number linebull Losing track of countersbull Sloppy drawingsbull Etchellip
bull Students might confuse the + and ndash signbull Many times students are more apt to add rather
than subtract Because of this they will not look at the sign and assume addition
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
Progressionbull In order for first grade students to be able to
represent and solve problems involving addition and subtractionbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of representing addition and subtraction problems algebraically in order tobull 2OA1 Use addition and subtraction within 100 to solve
one- and two-step word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using drawings and equations with a symbol for the unknown number to represent the problem
Progressionbull In Kindergarten students learn their numbers by
associating objects with numbers They use this knowledge to solve addition and subtraction problems within 10 This leads in to students being able to solve addition and subtraction problems within 20 without using objects By the end of first grade students can solve addition and subtraction problems by counting up This leads into second grade where students learn how to solve addition and subtraction problems within 100 Students know addition and subtraction facts with fluency in single digit problems
Understand and apply properties of operations and the relationship between addition and subtractionbull 1OA3 Apply properties of operations as
strategies to add and subtract Examples If 8 + 3 = 11 is known then 3 + 8 = 11 is also known (Commutative property of addition) To add 2 + 6 + 4 the second two numbers can be added to make a ten so 2 + 6 + 4 = 2 + 10 = 12 (Associative property of addition)
bull 1OA4 Understand subtraction as an unknown-addend problem For example subtract 10 ndash 8 by finding the number that makes 10 when added to 8
What does it look likebull Students should be able to differentiate between
and use thebull Communicative property of addition (3+2=2+3)bull Associative property of addition (4+1=3+2)
bull Students will use what they know about unknown addend problems to relate subtraction to addition (Fact Families)
Example ProblemsCommunicative Property
bull Build a two-color train using less than ten connecting cubes Place cubes of the same color together
bull Draw your train and write a number sentence to describe it from left to right
bull Flip your train draw it again and write the turn around fact
bull Repeat with other two color trains
2 + 3 = 5 3 + 2 = 5
Example provided by K-5MathTeachingResourcescom
ExampleAssociative Property
1OA4Choose a domino
Draw the domino
Write a fact family for the domino you chose Repeat with other dominoes
6 + 3 = 9 3 + 6 = 9 9 - 3 = 6 9 - 6 = 3
Example provided by K-5MathTeachingResourcescom
Misconceptionsbull Students might be confused about the meaning of the
equals sign In the problem 2+4=3+3 students may want to substitute first 3 in the second problem with a 6 This is because they may see the equal sign as a symbol indicating that the answer should follow
bull Students be unsure if each property (associative or communicative) works consistently bull Teacher must provide many examples to deter this misconception
bull Students many times confuse the order of numbers in a fact family resulting in an incorrect number sentence
Progressionbull First they develop understanding of number
conceptsbull Using understanding of number concepts
students are able to add and subtract within 10bull Following the mastery of addition and subtraction
within 10 students progress to addition and facts between 11-20 and then 20-100
bull During this process students are taught addition and subtraction together to help relate one to the other
Progressionbull In order for first grade students to be able to
apply properties of operations and find relationships between addition and subtraction they must firstbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of properties of operations and find relationships between addition and subtraction they willbull 2NBT9 Explain why addition and subtraction strategies
work using place value and the properties of operations
Add and subtract within 20bull 1OA5 Relate counting to addition and subtraction
(eg by counting on 2 to add 2) bull 1OA6 Add and subtract within 20 demonstrating
fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
What does it look likebull Students use many different strategies to add and
subtract Strategies can includebull Counting onbull Using the number linebull Using counters to represent addition and subtraction
problemsbull Acting out problemsbull Using modelsbull Drawing picturesbull And many morehellip
What does it look likebull httpwwwbrainpopjrcommath
additionandsubtractioncountingon
What does it look like5+4=
Misconceptionsbull Students may struggle with the use of their
manipulativesbull Double hopping on the number linebull Losing track of countersbull Sloppy drawingsbull Etchellip
bull Students might confuse the + and ndash signbull Many times students are more apt to add rather
than subtract Because of this they will not look at the sign and assume addition
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
Progressionbull Following first grade students will use their
understanding of representing addition and subtraction problems algebraically in order tobull 2OA1 Use addition and subtraction within 100 to solve
one- and two-step word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using drawings and equations with a symbol for the unknown number to represent the problem
Progressionbull In Kindergarten students learn their numbers by
associating objects with numbers They use this knowledge to solve addition and subtraction problems within 10 This leads in to students being able to solve addition and subtraction problems within 20 without using objects By the end of first grade students can solve addition and subtraction problems by counting up This leads into second grade where students learn how to solve addition and subtraction problems within 100 Students know addition and subtraction facts with fluency in single digit problems
Understand and apply properties of operations and the relationship between addition and subtractionbull 1OA3 Apply properties of operations as
strategies to add and subtract Examples If 8 + 3 = 11 is known then 3 + 8 = 11 is also known (Commutative property of addition) To add 2 + 6 + 4 the second two numbers can be added to make a ten so 2 + 6 + 4 = 2 + 10 = 12 (Associative property of addition)
bull 1OA4 Understand subtraction as an unknown-addend problem For example subtract 10 ndash 8 by finding the number that makes 10 when added to 8
What does it look likebull Students should be able to differentiate between
and use thebull Communicative property of addition (3+2=2+3)bull Associative property of addition (4+1=3+2)
bull Students will use what they know about unknown addend problems to relate subtraction to addition (Fact Families)
Example ProblemsCommunicative Property
bull Build a two-color train using less than ten connecting cubes Place cubes of the same color together
bull Draw your train and write a number sentence to describe it from left to right
bull Flip your train draw it again and write the turn around fact
bull Repeat with other two color trains
2 + 3 = 5 3 + 2 = 5
Example provided by K-5MathTeachingResourcescom
ExampleAssociative Property
1OA4Choose a domino
Draw the domino
Write a fact family for the domino you chose Repeat with other dominoes
6 + 3 = 9 3 + 6 = 9 9 - 3 = 6 9 - 6 = 3
Example provided by K-5MathTeachingResourcescom
Misconceptionsbull Students might be confused about the meaning of the
equals sign In the problem 2+4=3+3 students may want to substitute first 3 in the second problem with a 6 This is because they may see the equal sign as a symbol indicating that the answer should follow
bull Students be unsure if each property (associative or communicative) works consistently bull Teacher must provide many examples to deter this misconception
bull Students many times confuse the order of numbers in a fact family resulting in an incorrect number sentence
Progressionbull First they develop understanding of number
conceptsbull Using understanding of number concepts
students are able to add and subtract within 10bull Following the mastery of addition and subtraction
within 10 students progress to addition and facts between 11-20 and then 20-100
bull During this process students are taught addition and subtraction together to help relate one to the other
Progressionbull In order for first grade students to be able to
apply properties of operations and find relationships between addition and subtraction they must firstbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of properties of operations and find relationships between addition and subtraction they willbull 2NBT9 Explain why addition and subtraction strategies
work using place value and the properties of operations
Add and subtract within 20bull 1OA5 Relate counting to addition and subtraction
(eg by counting on 2 to add 2) bull 1OA6 Add and subtract within 20 demonstrating
fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
What does it look likebull Students use many different strategies to add and
subtract Strategies can includebull Counting onbull Using the number linebull Using counters to represent addition and subtraction
problemsbull Acting out problemsbull Using modelsbull Drawing picturesbull And many morehellip
What does it look likebull httpwwwbrainpopjrcommath
additionandsubtractioncountingon
What does it look like5+4=
Misconceptionsbull Students may struggle with the use of their
manipulativesbull Double hopping on the number linebull Losing track of countersbull Sloppy drawingsbull Etchellip
bull Students might confuse the + and ndash signbull Many times students are more apt to add rather
than subtract Because of this they will not look at the sign and assume addition
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
Progressionbull In Kindergarten students learn their numbers by
associating objects with numbers They use this knowledge to solve addition and subtraction problems within 10 This leads in to students being able to solve addition and subtraction problems within 20 without using objects By the end of first grade students can solve addition and subtraction problems by counting up This leads into second grade where students learn how to solve addition and subtraction problems within 100 Students know addition and subtraction facts with fluency in single digit problems
Understand and apply properties of operations and the relationship between addition and subtractionbull 1OA3 Apply properties of operations as
strategies to add and subtract Examples If 8 + 3 = 11 is known then 3 + 8 = 11 is also known (Commutative property of addition) To add 2 + 6 + 4 the second two numbers can be added to make a ten so 2 + 6 + 4 = 2 + 10 = 12 (Associative property of addition)
bull 1OA4 Understand subtraction as an unknown-addend problem For example subtract 10 ndash 8 by finding the number that makes 10 when added to 8
What does it look likebull Students should be able to differentiate between
and use thebull Communicative property of addition (3+2=2+3)bull Associative property of addition (4+1=3+2)
bull Students will use what they know about unknown addend problems to relate subtraction to addition (Fact Families)
Example ProblemsCommunicative Property
bull Build a two-color train using less than ten connecting cubes Place cubes of the same color together
bull Draw your train and write a number sentence to describe it from left to right
bull Flip your train draw it again and write the turn around fact
bull Repeat with other two color trains
2 + 3 = 5 3 + 2 = 5
Example provided by K-5MathTeachingResourcescom
ExampleAssociative Property
1OA4Choose a domino
Draw the domino
Write a fact family for the domino you chose Repeat with other dominoes
6 + 3 = 9 3 + 6 = 9 9 - 3 = 6 9 - 6 = 3
Example provided by K-5MathTeachingResourcescom
Misconceptionsbull Students might be confused about the meaning of the
equals sign In the problem 2+4=3+3 students may want to substitute first 3 in the second problem with a 6 This is because they may see the equal sign as a symbol indicating that the answer should follow
bull Students be unsure if each property (associative or communicative) works consistently bull Teacher must provide many examples to deter this misconception
bull Students many times confuse the order of numbers in a fact family resulting in an incorrect number sentence
Progressionbull First they develop understanding of number
conceptsbull Using understanding of number concepts
students are able to add and subtract within 10bull Following the mastery of addition and subtraction
within 10 students progress to addition and facts between 11-20 and then 20-100
bull During this process students are taught addition and subtraction together to help relate one to the other
Progressionbull In order for first grade students to be able to
apply properties of operations and find relationships between addition and subtraction they must firstbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of properties of operations and find relationships between addition and subtraction they willbull 2NBT9 Explain why addition and subtraction strategies
work using place value and the properties of operations
Add and subtract within 20bull 1OA5 Relate counting to addition and subtraction
(eg by counting on 2 to add 2) bull 1OA6 Add and subtract within 20 demonstrating
fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
What does it look likebull Students use many different strategies to add and
subtract Strategies can includebull Counting onbull Using the number linebull Using counters to represent addition and subtraction
problemsbull Acting out problemsbull Using modelsbull Drawing picturesbull And many morehellip
What does it look likebull httpwwwbrainpopjrcommath
additionandsubtractioncountingon
What does it look like5+4=
Misconceptionsbull Students may struggle with the use of their
manipulativesbull Double hopping on the number linebull Losing track of countersbull Sloppy drawingsbull Etchellip
bull Students might confuse the + and ndash signbull Many times students are more apt to add rather
than subtract Because of this they will not look at the sign and assume addition
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
Understand and apply properties of operations and the relationship between addition and subtractionbull 1OA3 Apply properties of operations as
strategies to add and subtract Examples If 8 + 3 = 11 is known then 3 + 8 = 11 is also known (Commutative property of addition) To add 2 + 6 + 4 the second two numbers can be added to make a ten so 2 + 6 + 4 = 2 + 10 = 12 (Associative property of addition)
bull 1OA4 Understand subtraction as an unknown-addend problem For example subtract 10 ndash 8 by finding the number that makes 10 when added to 8
What does it look likebull Students should be able to differentiate between
and use thebull Communicative property of addition (3+2=2+3)bull Associative property of addition (4+1=3+2)
bull Students will use what they know about unknown addend problems to relate subtraction to addition (Fact Families)
Example ProblemsCommunicative Property
bull Build a two-color train using less than ten connecting cubes Place cubes of the same color together
bull Draw your train and write a number sentence to describe it from left to right
bull Flip your train draw it again and write the turn around fact
bull Repeat with other two color trains
2 + 3 = 5 3 + 2 = 5
Example provided by K-5MathTeachingResourcescom
ExampleAssociative Property
1OA4Choose a domino
Draw the domino
Write a fact family for the domino you chose Repeat with other dominoes
6 + 3 = 9 3 + 6 = 9 9 - 3 = 6 9 - 6 = 3
Example provided by K-5MathTeachingResourcescom
Misconceptionsbull Students might be confused about the meaning of the
equals sign In the problem 2+4=3+3 students may want to substitute first 3 in the second problem with a 6 This is because they may see the equal sign as a symbol indicating that the answer should follow
bull Students be unsure if each property (associative or communicative) works consistently bull Teacher must provide many examples to deter this misconception
bull Students many times confuse the order of numbers in a fact family resulting in an incorrect number sentence
Progressionbull First they develop understanding of number
conceptsbull Using understanding of number concepts
students are able to add and subtract within 10bull Following the mastery of addition and subtraction
within 10 students progress to addition and facts between 11-20 and then 20-100
bull During this process students are taught addition and subtraction together to help relate one to the other
Progressionbull In order for first grade students to be able to
apply properties of operations and find relationships between addition and subtraction they must firstbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of properties of operations and find relationships between addition and subtraction they willbull 2NBT9 Explain why addition and subtraction strategies
work using place value and the properties of operations
Add and subtract within 20bull 1OA5 Relate counting to addition and subtraction
(eg by counting on 2 to add 2) bull 1OA6 Add and subtract within 20 demonstrating
fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
What does it look likebull Students use many different strategies to add and
subtract Strategies can includebull Counting onbull Using the number linebull Using counters to represent addition and subtraction
problemsbull Acting out problemsbull Using modelsbull Drawing picturesbull And many morehellip
What does it look likebull httpwwwbrainpopjrcommath
additionandsubtractioncountingon
What does it look like5+4=
Misconceptionsbull Students may struggle with the use of their
manipulativesbull Double hopping on the number linebull Losing track of countersbull Sloppy drawingsbull Etchellip
bull Students might confuse the + and ndash signbull Many times students are more apt to add rather
than subtract Because of this they will not look at the sign and assume addition
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
What does it look likebull Students should be able to differentiate between
and use thebull Communicative property of addition (3+2=2+3)bull Associative property of addition (4+1=3+2)
bull Students will use what they know about unknown addend problems to relate subtraction to addition (Fact Families)
Example ProblemsCommunicative Property
bull Build a two-color train using less than ten connecting cubes Place cubes of the same color together
bull Draw your train and write a number sentence to describe it from left to right
bull Flip your train draw it again and write the turn around fact
bull Repeat with other two color trains
2 + 3 = 5 3 + 2 = 5
Example provided by K-5MathTeachingResourcescom
ExampleAssociative Property
1OA4Choose a domino
Draw the domino
Write a fact family for the domino you chose Repeat with other dominoes
6 + 3 = 9 3 + 6 = 9 9 - 3 = 6 9 - 6 = 3
Example provided by K-5MathTeachingResourcescom
Misconceptionsbull Students might be confused about the meaning of the
equals sign In the problem 2+4=3+3 students may want to substitute first 3 in the second problem with a 6 This is because they may see the equal sign as a symbol indicating that the answer should follow
bull Students be unsure if each property (associative or communicative) works consistently bull Teacher must provide many examples to deter this misconception
bull Students many times confuse the order of numbers in a fact family resulting in an incorrect number sentence
Progressionbull First they develop understanding of number
conceptsbull Using understanding of number concepts
students are able to add and subtract within 10bull Following the mastery of addition and subtraction
within 10 students progress to addition and facts between 11-20 and then 20-100
bull During this process students are taught addition and subtraction together to help relate one to the other
Progressionbull In order for first grade students to be able to
apply properties of operations and find relationships between addition and subtraction they must firstbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of properties of operations and find relationships between addition and subtraction they willbull 2NBT9 Explain why addition and subtraction strategies
work using place value and the properties of operations
Add and subtract within 20bull 1OA5 Relate counting to addition and subtraction
(eg by counting on 2 to add 2) bull 1OA6 Add and subtract within 20 demonstrating
fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
What does it look likebull Students use many different strategies to add and
subtract Strategies can includebull Counting onbull Using the number linebull Using counters to represent addition and subtraction
problemsbull Acting out problemsbull Using modelsbull Drawing picturesbull And many morehellip
What does it look likebull httpwwwbrainpopjrcommath
additionandsubtractioncountingon
What does it look like5+4=
Misconceptionsbull Students may struggle with the use of their
manipulativesbull Double hopping on the number linebull Losing track of countersbull Sloppy drawingsbull Etchellip
bull Students might confuse the + and ndash signbull Many times students are more apt to add rather
than subtract Because of this they will not look at the sign and assume addition
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
Example ProblemsCommunicative Property
bull Build a two-color train using less than ten connecting cubes Place cubes of the same color together
bull Draw your train and write a number sentence to describe it from left to right
bull Flip your train draw it again and write the turn around fact
bull Repeat with other two color trains
2 + 3 = 5 3 + 2 = 5
Example provided by K-5MathTeachingResourcescom
ExampleAssociative Property
1OA4Choose a domino
Draw the domino
Write a fact family for the domino you chose Repeat with other dominoes
6 + 3 = 9 3 + 6 = 9 9 - 3 = 6 9 - 6 = 3
Example provided by K-5MathTeachingResourcescom
Misconceptionsbull Students might be confused about the meaning of the
equals sign In the problem 2+4=3+3 students may want to substitute first 3 in the second problem with a 6 This is because they may see the equal sign as a symbol indicating that the answer should follow
bull Students be unsure if each property (associative or communicative) works consistently bull Teacher must provide many examples to deter this misconception
bull Students many times confuse the order of numbers in a fact family resulting in an incorrect number sentence
Progressionbull First they develop understanding of number
conceptsbull Using understanding of number concepts
students are able to add and subtract within 10bull Following the mastery of addition and subtraction
within 10 students progress to addition and facts between 11-20 and then 20-100
bull During this process students are taught addition and subtraction together to help relate one to the other
Progressionbull In order for first grade students to be able to
apply properties of operations and find relationships between addition and subtraction they must firstbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of properties of operations and find relationships between addition and subtraction they willbull 2NBT9 Explain why addition and subtraction strategies
work using place value and the properties of operations
Add and subtract within 20bull 1OA5 Relate counting to addition and subtraction
(eg by counting on 2 to add 2) bull 1OA6 Add and subtract within 20 demonstrating
fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
What does it look likebull Students use many different strategies to add and
subtract Strategies can includebull Counting onbull Using the number linebull Using counters to represent addition and subtraction
problemsbull Acting out problemsbull Using modelsbull Drawing picturesbull And many morehellip
What does it look likebull httpwwwbrainpopjrcommath
additionandsubtractioncountingon
What does it look like5+4=
Misconceptionsbull Students may struggle with the use of their
manipulativesbull Double hopping on the number linebull Losing track of countersbull Sloppy drawingsbull Etchellip
bull Students might confuse the + and ndash signbull Many times students are more apt to add rather
than subtract Because of this they will not look at the sign and assume addition
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
ExampleAssociative Property
1OA4Choose a domino
Draw the domino
Write a fact family for the domino you chose Repeat with other dominoes
6 + 3 = 9 3 + 6 = 9 9 - 3 = 6 9 - 6 = 3
Example provided by K-5MathTeachingResourcescom
Misconceptionsbull Students might be confused about the meaning of the
equals sign In the problem 2+4=3+3 students may want to substitute first 3 in the second problem with a 6 This is because they may see the equal sign as a symbol indicating that the answer should follow
bull Students be unsure if each property (associative or communicative) works consistently bull Teacher must provide many examples to deter this misconception
bull Students many times confuse the order of numbers in a fact family resulting in an incorrect number sentence
Progressionbull First they develop understanding of number
conceptsbull Using understanding of number concepts
students are able to add and subtract within 10bull Following the mastery of addition and subtraction
within 10 students progress to addition and facts between 11-20 and then 20-100
bull During this process students are taught addition and subtraction together to help relate one to the other
Progressionbull In order for first grade students to be able to
apply properties of operations and find relationships between addition and subtraction they must firstbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of properties of operations and find relationships between addition and subtraction they willbull 2NBT9 Explain why addition and subtraction strategies
work using place value and the properties of operations
Add and subtract within 20bull 1OA5 Relate counting to addition and subtraction
(eg by counting on 2 to add 2) bull 1OA6 Add and subtract within 20 demonstrating
fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
What does it look likebull Students use many different strategies to add and
subtract Strategies can includebull Counting onbull Using the number linebull Using counters to represent addition and subtraction
problemsbull Acting out problemsbull Using modelsbull Drawing picturesbull And many morehellip
What does it look likebull httpwwwbrainpopjrcommath
additionandsubtractioncountingon
What does it look like5+4=
Misconceptionsbull Students may struggle with the use of their
manipulativesbull Double hopping on the number linebull Losing track of countersbull Sloppy drawingsbull Etchellip
bull Students might confuse the + and ndash signbull Many times students are more apt to add rather
than subtract Because of this they will not look at the sign and assume addition
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
1OA4Choose a domino
Draw the domino
Write a fact family for the domino you chose Repeat with other dominoes
6 + 3 = 9 3 + 6 = 9 9 - 3 = 6 9 - 6 = 3
Example provided by K-5MathTeachingResourcescom
Misconceptionsbull Students might be confused about the meaning of the
equals sign In the problem 2+4=3+3 students may want to substitute first 3 in the second problem with a 6 This is because they may see the equal sign as a symbol indicating that the answer should follow
bull Students be unsure if each property (associative or communicative) works consistently bull Teacher must provide many examples to deter this misconception
bull Students many times confuse the order of numbers in a fact family resulting in an incorrect number sentence
Progressionbull First they develop understanding of number
conceptsbull Using understanding of number concepts
students are able to add and subtract within 10bull Following the mastery of addition and subtraction
within 10 students progress to addition and facts between 11-20 and then 20-100
bull During this process students are taught addition and subtraction together to help relate one to the other
Progressionbull In order for first grade students to be able to
apply properties of operations and find relationships between addition and subtraction they must firstbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of properties of operations and find relationships between addition and subtraction they willbull 2NBT9 Explain why addition and subtraction strategies
work using place value and the properties of operations
Add and subtract within 20bull 1OA5 Relate counting to addition and subtraction
(eg by counting on 2 to add 2) bull 1OA6 Add and subtract within 20 demonstrating
fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
What does it look likebull Students use many different strategies to add and
subtract Strategies can includebull Counting onbull Using the number linebull Using counters to represent addition and subtraction
problemsbull Acting out problemsbull Using modelsbull Drawing picturesbull And many morehellip
What does it look likebull httpwwwbrainpopjrcommath
additionandsubtractioncountingon
What does it look like5+4=
Misconceptionsbull Students may struggle with the use of their
manipulativesbull Double hopping on the number linebull Losing track of countersbull Sloppy drawingsbull Etchellip
bull Students might confuse the + and ndash signbull Many times students are more apt to add rather
than subtract Because of this they will not look at the sign and assume addition
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
Misconceptionsbull Students might be confused about the meaning of the
equals sign In the problem 2+4=3+3 students may want to substitute first 3 in the second problem with a 6 This is because they may see the equal sign as a symbol indicating that the answer should follow
bull Students be unsure if each property (associative or communicative) works consistently bull Teacher must provide many examples to deter this misconception
bull Students many times confuse the order of numbers in a fact family resulting in an incorrect number sentence
Progressionbull First they develop understanding of number
conceptsbull Using understanding of number concepts
students are able to add and subtract within 10bull Following the mastery of addition and subtraction
within 10 students progress to addition and facts between 11-20 and then 20-100
bull During this process students are taught addition and subtraction together to help relate one to the other
Progressionbull In order for first grade students to be able to
apply properties of operations and find relationships between addition and subtraction they must firstbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of properties of operations and find relationships between addition and subtraction they willbull 2NBT9 Explain why addition and subtraction strategies
work using place value and the properties of operations
Add and subtract within 20bull 1OA5 Relate counting to addition and subtraction
(eg by counting on 2 to add 2) bull 1OA6 Add and subtract within 20 demonstrating
fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
What does it look likebull Students use many different strategies to add and
subtract Strategies can includebull Counting onbull Using the number linebull Using counters to represent addition and subtraction
problemsbull Acting out problemsbull Using modelsbull Drawing picturesbull And many morehellip
What does it look likebull httpwwwbrainpopjrcommath
additionandsubtractioncountingon
What does it look like5+4=
Misconceptionsbull Students may struggle with the use of their
manipulativesbull Double hopping on the number linebull Losing track of countersbull Sloppy drawingsbull Etchellip
bull Students might confuse the + and ndash signbull Many times students are more apt to add rather
than subtract Because of this they will not look at the sign and assume addition
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
Progressionbull First they develop understanding of number
conceptsbull Using understanding of number concepts
students are able to add and subtract within 10bull Following the mastery of addition and subtraction
within 10 students progress to addition and facts between 11-20 and then 20-100
bull During this process students are taught addition and subtraction together to help relate one to the other
Progressionbull In order for first grade students to be able to
apply properties of operations and find relationships between addition and subtraction they must firstbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of properties of operations and find relationships between addition and subtraction they willbull 2NBT9 Explain why addition and subtraction strategies
work using place value and the properties of operations
Add and subtract within 20bull 1OA5 Relate counting to addition and subtraction
(eg by counting on 2 to add 2) bull 1OA6 Add and subtract within 20 demonstrating
fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
What does it look likebull Students use many different strategies to add and
subtract Strategies can includebull Counting onbull Using the number linebull Using counters to represent addition and subtraction
problemsbull Acting out problemsbull Using modelsbull Drawing picturesbull And many morehellip
What does it look likebull httpwwwbrainpopjrcommath
additionandsubtractioncountingon
What does it look like5+4=
Misconceptionsbull Students may struggle with the use of their
manipulativesbull Double hopping on the number linebull Losing track of countersbull Sloppy drawingsbull Etchellip
bull Students might confuse the + and ndash signbull Many times students are more apt to add rather
than subtract Because of this they will not look at the sign and assume addition
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
Progressionbull In order for first grade students to be able to
apply properties of operations and find relationships between addition and subtraction they must firstbull KOA1 Represent addition and subtraction with objects
fingers mental images drawings sounds (eg claps) acting out situations verbal explanations expressions or equationsbull KOA2 Solve addition and subtraction word problems
and add and subtract within 10 eg by using objects or drawings to represent the problem
Progressionbull Following first grade students will use their
understanding of properties of operations and find relationships between addition and subtraction they willbull 2NBT9 Explain why addition and subtraction strategies
work using place value and the properties of operations
Add and subtract within 20bull 1OA5 Relate counting to addition and subtraction
(eg by counting on 2 to add 2) bull 1OA6 Add and subtract within 20 demonstrating
fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
What does it look likebull Students use many different strategies to add and
subtract Strategies can includebull Counting onbull Using the number linebull Using counters to represent addition and subtraction
problemsbull Acting out problemsbull Using modelsbull Drawing picturesbull And many morehellip
What does it look likebull httpwwwbrainpopjrcommath
additionandsubtractioncountingon
What does it look like5+4=
Misconceptionsbull Students may struggle with the use of their
manipulativesbull Double hopping on the number linebull Losing track of countersbull Sloppy drawingsbull Etchellip
bull Students might confuse the + and ndash signbull Many times students are more apt to add rather
than subtract Because of this they will not look at the sign and assume addition
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
Progressionbull Following first grade students will use their
understanding of properties of operations and find relationships between addition and subtraction they willbull 2NBT9 Explain why addition and subtraction strategies
work using place value and the properties of operations
Add and subtract within 20bull 1OA5 Relate counting to addition and subtraction
(eg by counting on 2 to add 2) bull 1OA6 Add and subtract within 20 demonstrating
fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
What does it look likebull Students use many different strategies to add and
subtract Strategies can includebull Counting onbull Using the number linebull Using counters to represent addition and subtraction
problemsbull Acting out problemsbull Using modelsbull Drawing picturesbull And many morehellip
What does it look likebull httpwwwbrainpopjrcommath
additionandsubtractioncountingon
What does it look like5+4=
Misconceptionsbull Students may struggle with the use of their
manipulativesbull Double hopping on the number linebull Losing track of countersbull Sloppy drawingsbull Etchellip
bull Students might confuse the + and ndash signbull Many times students are more apt to add rather
than subtract Because of this they will not look at the sign and assume addition
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
Add and subtract within 20bull 1OA5 Relate counting to addition and subtraction
(eg by counting on 2 to add 2) bull 1OA6 Add and subtract within 20 demonstrating
fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
What does it look likebull Students use many different strategies to add and
subtract Strategies can includebull Counting onbull Using the number linebull Using counters to represent addition and subtraction
problemsbull Acting out problemsbull Using modelsbull Drawing picturesbull And many morehellip
What does it look likebull httpwwwbrainpopjrcommath
additionandsubtractioncountingon
What does it look like5+4=
Misconceptionsbull Students may struggle with the use of their
manipulativesbull Double hopping on the number linebull Losing track of countersbull Sloppy drawingsbull Etchellip
bull Students might confuse the + and ndash signbull Many times students are more apt to add rather
than subtract Because of this they will not look at the sign and assume addition
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
What does it look likebull Students use many different strategies to add and
subtract Strategies can includebull Counting onbull Using the number linebull Using counters to represent addition and subtraction
problemsbull Acting out problemsbull Using modelsbull Drawing picturesbull And many morehellip
What does it look likebull httpwwwbrainpopjrcommath
additionandsubtractioncountingon
What does it look like5+4=
Misconceptionsbull Students may struggle with the use of their
manipulativesbull Double hopping on the number linebull Losing track of countersbull Sloppy drawingsbull Etchellip
bull Students might confuse the + and ndash signbull Many times students are more apt to add rather
than subtract Because of this they will not look at the sign and assume addition
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
What does it look likebull httpwwwbrainpopjrcommath
additionandsubtractioncountingon
What does it look like5+4=
Misconceptionsbull Students may struggle with the use of their
manipulativesbull Double hopping on the number linebull Losing track of countersbull Sloppy drawingsbull Etchellip
bull Students might confuse the + and ndash signbull Many times students are more apt to add rather
than subtract Because of this they will not look at the sign and assume addition
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
What does it look like5+4=
Misconceptionsbull Students may struggle with the use of their
manipulativesbull Double hopping on the number linebull Losing track of countersbull Sloppy drawingsbull Etchellip
bull Students might confuse the + and ndash signbull Many times students are more apt to add rather
than subtract Because of this they will not look at the sign and assume addition
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
Misconceptionsbull Students may struggle with the use of their
manipulativesbull Double hopping on the number linebull Losing track of countersbull Sloppy drawingsbull Etchellip
bull Students might confuse the + and ndash signbull Many times students are more apt to add rather
than subtract Because of this they will not look at the sign and assume addition
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
Progressionbull In order for first grade students to be able add and
subtract within 20 they must first be able to
bull KCC4c Understand that each successive number name refers to a quantity that is one larger
bull KOA1 Represent addition and subtraction with objects fingers mental images drawings2 sounds (eg claps) acting out situations verbal explanations expressions or equations
bull KOA2 Solve addition and subtraction word problems and add and subtract within 10 eg by using objects or drawings to represent the problem
bull KOA3 Decompose numbers less than or equal to 10 into pairs in more than one way eg by using objects or drawings and record each decomposition by a drawing or equation (eg 5 = 2 + 3 and 5 = 4 + 1)
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
Progressionbull Following first grade students will use their
understanding of adding and subtracting within 20 tobull 2OA2 Fluently add and subtract within 20 using mental
strategies2 By end of Grade 2 know from memory all sums of two one-digit numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
Work With Addition and Subtraction Equationsbull 1OA7 Understand the meaning of the equal
sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
bull 1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
What does it look like1OA7Compare the number of circles in each box If they are equal write a number sentence
4+3=5+1+1
Example from illustrative mathematics
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
1OA8Find the missing number in each of the following equations
9minus3= 8+=15
16minus=5 =7minus2
13=+7 6=14minus
Example from Illustrative Mathematics
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
Misconceptions
bull httpwwwyoutubecomwatchv=eO3OQI9Jwts
224-end
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
Progressionbull In order for first grade students to be able to work with
addition and subtraction equations they must be able to
bull 1OA1 Use addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem
bull 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
Progressionbull Following first grade students will use their
understanding of working with addition and subtraction equations they must be able tobull 2OA3 Determine whether a group of objects (up to 20)
has an odd or even number of members eg by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends bull 2OA4 Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and up to 5 columns write an equation to express the total as a sum of equal addends
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
Assessment
bull httpwwwsolonschoolsorgMRASasp (last video)
bull httpwwwsolonschoolsorgMRASVidasp (right)
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
Resourcesbull University of Arizona Progression Documentsbull Zimba Chartbull Illustrative Mathematicsbull NCTM Illuminationsbull NCTMbull CCSSbull Algebra and the Elementary Classroom by Maria
L Blantonbull Math Workstations by Debbie Diller
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
Lesson 1bull You will need a recording sheet and a set of
cards
bull Find your shoulder buddy
bull With your partner use the deck of cards to make as many sets of 12 as you can
bull Write the different ways you found on the paper
bull Be ready to share1OA3 Apply properties of operations as strategies to add and subtract
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
bull Now try 3 cards
bull How many ways can you make 12 with 3 cards
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
bull What was a pair that someone foundbull Did anyone find a different pairbull What strategies did you use to find the pairsbull Did anyone use a different strategybull Did you notice any patterns when finding pairs of
numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
bull What prior knowledge would the students need in order to be successful in this lessonbull How was this lesson cognitively
demandingbull How does this lesson apply to
algebraic thinkingreasoning
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
bull Differentiation optionsbull During lesson the sums can be altered to make it easier or
to add a challenge for studentsbull If students are able to master the three card pairs easily
you may add a fourth card and find patterns within the addition sentences with four addends bull Students can create story problems to go along with the
number sentences that they created
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
Lesson 2bull You will need 1 game mat for you and your partner and 1 set
of cards
bull Each player will use one side of the game mat (player 1 or player 2)
bull Take turns turning over a card bull Decide if the number on the card will fit in one of the blank
spaces in the number problems on your side of the game matbull If it does write the number in the blank space that it belongsbull If it doesnrsquot put the card face up in the discard pile The next
player can choose this card if they want or pick a new card bull Keep going until one player fills in every answer on their side
of the game mat1OA8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
