First Grade Unit 4: Operations and Algebraic Thinking―Addition and Subtraction9 weeksIn this unit, students will: Explore, understand, and apply the commutative and associative properties as strategies for solving addition problems. Share, discuss, and compare strategies as a class. Connect counting on to solving subtraction problems. For the problem “15 – 7 = ?” they think about the number they have to count on from 7 to get to 15. Work with sums and differences less than or equal to 20 using the numbers 0 to 20. Identify and then apply a pattern or structure in mathematics. For example, pose a string of addition and subtraction problems involving the same three

numbers chosen from the numbers 0 to 20, such as 4 + 13 = 17 and 13 + 4 = 17. Analyze number patterns and create conjectures or guesses. Choose other combinations of three numbers and explore to see if the patterns work for all numbers 0 to 20. Understand that addition and subtraction are related and that subtraction can be used to solve problems where the addend is unknown. Use the strategies of counting on and counting back to understand number relationships. Organize and record results using tallies and tables. Determine the initial and the change unknown.Unit ResourcesUnit 4 Overview Video Parent Letter Parent Standards Clarification Number Talks Vocabulary Cards Prerequisite Skills Assessment Sample Post Assessment Concept Map Student Friendly Standards Topic 1: Problems with Addition and Subtraction Big Ideas/Enduring Understandings: Students develop strategies for adding and subtracting whole numbers based on their prior work with small numbers. Students use a variety of models, including discrete objects and length-based models (e.g., cubes connected to form lengths), to model add-to, take-from,

put-together, take-apart, and compare situations. They will use these models to develop meaning for the operations of addition and subtraction, and to develop strategies to solve arithmetic problems with these operations.

Essential Questions: How can we represent a set of objects using numerals? What happens when we join two quantities or take one from another? How can we find the total when we join two quantities? How can we find what is left when we take one quantity from another? How can we find the difference when we compare one quantity to another? How can we represent problem situations?Content StandardsContent standards are interwoven and should be addressed throughout the year in as many different units and activities as possible in order to emphasize the natural connections that exist among mathematical topics.Represent and solve problems involving addition and subtraction.

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MGSE1.OA.1 (EM40Q) 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, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

MGSE1.OA.2 (EM80Q) Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Vertical Alignment Kindergarten StandardsUnderstand addition as putting together and adding to, and understand subtraction as taking apart and taking from. MGSEK.OA.1 Represent addition and subtraction with objects, fingers, mental

images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

MGSEK.OA.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Second Grade StandardsRepresent and solve problems involving addition and subtraction. MGSE2.OA.1 Use addition and subtraction within 100 to solve

one and two step word problems by using drawings and equations with a symbol for the unknown number to represent the problem. Problems include contexts that involve adding to, taking from, putting together/taking apart (part/part/whole) and comparing with unknowns in all positions.

Report Card Quarter 2 Standards-Based GradingThe report card is not able to assess students on all standards being taught in third grade. The following standards are the priority for mastery for this quarter: Solve word problems within 20 with unknowns Counts and represent numbers to 120 starting with any number Demonstrates the meaning of the equal sign Adds and subtracts within 20 using multiple strategies Represents the 2 digits of numbers 20-99 by composing and decomposing Organize, represent, and interpret data with up to 3 categoriesInstructional StrategiesAddition and Subtraction in Elementary School The strategies that students use to solve problems provide important information concerning number sense, and place value. It is important to look at more than the answers students get. The strategies used provide useful information about what problems to give the next day and

how to differentiate instruction. It is important to relate addition and subtraction. Student created strategies provide reinforcement of place value concepts. Traditional algorithms can actually confuse the understanding of place value. Student created strategies are built on a student’s actual understanding, instead of on what the book says or what we think/hope they know! Students make fewer errors with invented strategies because they are built on understanding rather than memorization. OA.1This standard builds on the work in Kindergarten by having students use a variety of mathematical representations (e.g., objects, drawings, and equations) during their work. The unknown symbols should include boxes or pictures, and not letters.

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Teachers should be aware of the three types of problems (see Table 1 below) and provide multiple experiences for their students solving ALL three types of problems. The three types of addition and subtraction problems: Result Unknown, Change Unknown, and Start Unknown. Use informal language (and, minus/subtract, the same as) to describe joining situations (putting together) and separating situations (breaking apart).

Use the addition symbol (+) to represent joining situations, the subtraction symbol (-) to represent separating situations, and the equal sign (=) to represent a relationship regarding quantity between one side of the equation and the other.

A helpful strategy is for students to recognize sets of objects in common patterned arrangements (0-10) to tell how many without counting (subitizing).

Contextual problems that are closely connected to students’ lives should be used to develop fluency with addition and subtraction. The table below describes the four different addition and subtraction situations and their relationship to the position of the unknown. Students use objects or drawings to represent the different situations.

Take From example: Avery has 9 balls. She gave 3 to Susan. How many balls does Avery have now? Compare example: Avery has 9 balls. Susan has 3 balls. How many more balls does Avery have than Susan? A student will use 9 objects to represent Avery’s 9

balls and 3 objects to represent Susan’s 3 balls. Then they will compare the 2 sets of objects.

Note that even though the modeling of the two problems above is different, the equation, 9 - 3 = ?, can represent both situations yet the compare example can also be represented by 3 + ? = 9 (How many more do I need to make 9?)

It is important to attend to the difficulty level of the problem situations in relation to the position of the unknown. Result Unknown, Total Unknown, and Both Addends Unknown problems are the least complex for students. The next level of difficulty includes Change Unknown, Addend Unknown, and Difference Unknown The most difficult are Start Unknown and versions of Bigger and Smaller Unknown (compare problems).

See Table 1 below for additional examples. The level of difficulty for these problems can be differentiated by using smaller numbers (up to 10) or larger numbers (up to 20).

Table 1: Common addition and subtraction situations

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Learning to mathematize (the process of seeing and focusing on the mathematical aspects and ignoring the nonmathematical aspects. Mathematizing in first grade: Solving problems, reasoning, and Communicating, Connecting, and Representing Ideas.

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Total Unknown Addend Unknown Both Addends Unknown

Put Together

Take Apart

Three red apples and two green apples are on the table. How many apples are on the table?

3 + 2 = ?

Five apples are on the table. Three are red and the rest are green. How many apples are green?

3 + ? = 5, 5 – 3 = ?

Grandma has five flowers. How many can she put in her red vase and how many in her blue vase?

5 = 0 + 5, 5 = 5 + 05 = 1 + 4, 5 = 4 + 15 = 2 + 3, 5 = 3 + 2

Result Unknown Change Unknown Start Unknown

Add to

Two bunnies sat on the grass. Three more bunnies hopped there. How many bunnies are on the grass now?

2 + 3 = ?

Two bunnies were sitting on the grass. Some more bunnies hopped there. Then there were five bunnies. How many bunnies hopped over to the first two?

2 + ? = 5

Some bunnies were sitting on the grass. Three more bunnies hopped there. Then there were five bunnies. How many bunnies were on the grass before?

? + 3 = 5

Take from

Five apples were on the table. I ate two apples. How many apples are on the table now?

5 – 2 = ?

Five apples were on the table. I ate some apples. Then there were three apples. How many apples did I eat?

5 – ? = 3

Some apples were on the table. I ate two apples. Then there were three apples. How many apples were on the table before?

? – 2 = 3

Difference Unknown Bigger Unknown Smaller Unknown

Compare

(“How many more?” version): Lucy has two apples. Julie has five apples. How many more apples does Julie have than Lucy?

(“How many fewer?” version): Lucy has two apples. Julie has five apples. How many fewer apples does Lucy have than Julie?

2 + ? = 5, 5 – 2 = ?

(Version with “more”): Julie has three more apples than Lucy. Lucy has two apples. How many apples does Julie have?

(Version with “fewer”): Lucy has 3 fewer apples than Julie. Lucy has two apples. How many apples does Julie have?

2 + 3 = ?, 3 + 2 = ?

(Version with “more”): Julie has three more apples than Lucy. Julie has five apples. How many apples does Lucy have?

(Version with “fewer”): Lucy has 3 fewer apples than Julie. Julie has five apples. How many apples does Lucy have?

5 – 3 = ?, ? + 3 = 5

Modeling addition and subtraction situations with objects, fingers, and drawings is the foundation for algebraic problem solving. More difficult types of problems situations (change and collection situations) should be given from grade 1 on.

Provide opportunities for students to participate in shared problem-solving activities to solve word problems. Collaborate in small groups to develop problem-solving strategies using a variety of models such as drawings, words, and equations with symbols for the unknown numbers to find the solutions. Additionally students need the opportunity to explain, write and reflect on their problem-solving strategies.

The situations for the addition and subtraction story problems should involve sums and differences less than or equal to 20 using the numbers 0 to 20. They need to align with the 12 situations found in Table 1 above. Students need the opportunity of writing and solving story problems involving three addends with a sum that is less than or equal to 20. For example, each student writes or draws a problem in which three whole things are being combined. The students exchange their problems with other students, solving them individually and then discussing their models and solution strategies. Now both students work together to solve each problem using a different strategy. It is important to emphasize the most critical problem-solving strategy—understand the situation and represent the problem (e.g. use counters, cubes, or drawings). Key-word strategies in which children focus only on one or a few words will not work with algebraic problems. Teachers need to help all children move beyond such limiting strategies by emphasizing understanding & representing the situation.

Literature is an excellent way to incorporate problem-solving in a context that young students can understand. Many literature books that include mathematical ideas and concepts have been written in recent years.

For Grade 1, the incorporation of books that contain a problem situation involving addition and subtraction with numbers 0 to 20 should be included in the curriculum. Use the situations found in Table 1, in the Appendix for guidance in selecting appropriate books. As the teacher reads the story, students use a variety of manipulatives, drawings, or equations to model and find the solution to problems from the story.

Expect and support children’s ability to make meaning and mathematize the real world and create a nurturing and helpful math-talk community. OA.2This standard asks students to add (join) three numbers whose sum is less than or equal to 20, using a variety of mathematical representations. This objective does address multi-step word problems.Example:There are cookies on the plate. There are 4 oatmeal raisin cookies, 5 chocolate chip cookies, and 6 gingerbread cookies. How many cookies are there total?

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To further students’ understanding of the concept of addition, students create word problems with three addends. They can also increase their estimation skills by creating problems in which the sum is less than 5, 10 or 20. They use properties of operations and different strategies to find the sum of three whole numbers such as: Counting on and counting on again (e.g., to add 3+2+4 a student writes 3+2+4=? and thinks, “3, 4, 5, that’s 2 more, 6, 7, 8, 9 that’s 4 more so 3+2+4=9.” Making tens (e.g., 4+8+6=4+6+8=10+8=18) Using “plus 10, minus 1” to add 9 (e.g., 3+9+6 A student thinks, “9 is close to 10 so I am going to add 10 plus 3 plus 6 which gives me 19. Since I added 1 too

many, I need to take 1 away so the answer is 18). Decomposing numbers between 10 and 20 into 1 ten plus some ones to facilitate adding the ones Using doubles

Using near doubles (e.g.,5+6+3=5+5+1+3=10+4=14)

Students may use document cameras to display their combining strategies. This gives them the opportunity to communicate and justify their thinking.

Children need many opportunities to use a variety of models, including discrete objects, length-based models (e.g., lengths of connecting cubes), and number paths, to model “part-whole”, “adding to,” “taking away from”, and “comparing situations to develop an understanding of the meanings of addition and subtraction and strategies to solve such arithmetic problems. Children need to understand the connections between counting and the operations of addition and subtraction (e.g., adding two is the same as “counting on” two).

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“Number paths” were used in the examples rather than “number lines”. A great deal of confusion arises about what the term number line means. It is recommended that number lines not be used until grade 2 because they are conceptually too difficult for younger children.

In early childhood materials including Kindergarten, the term number line or mental number line often really means a number path, such as in the common early childhood games where numbers are put on squares and children move along such a numbered path. Such number paths are counting models in which things are counted. Each square is a thing that can be counted, so these are appropriate for children age two through grade 1.

A number path and a number line are shown below along with the meanings that children must understand and relate when using these models. A number line is a length model such as a ruler or a bar graph in which numbers are represented by the length from zero along a line segmented into equal lengths. Children need to count the length units on a number line, not the numbers.

Young children have difficulties with such a number line representation because they have difficulty seeing the units—they need to see things, so they focus on the numbers or the segmenting marks instead of on the lengths. Thus, they may count the starting point 0 and then be off by one, or they may focus on the spaces and be confused by the location of the numbers at the ends of the spaces.

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Consider also teaching subtraction as an unknown addend: students can always solve subtraction problems by a forward method that finds the unknown. The counting down or back is difficult and error-prone. Help children learn and use the more accurate forward methods.Common MisconceptionsAddition and subtraction can be divided into four categories: join problems, separate problems, part-whole problems, and compare problems (see Table 1). Within these four types of problems, most educators focus on addition and subtract when the result is unknown, this leads to the understanding that addition is “put together” and subtraction means to “take away”. This is a major misconception and limits the students’ understanding.

One way to prevent development of this misunderstanding is to provide problem based story problems in which the students are attempting to solve not only the result but also the change, and the initial. (Van De Walle, pages 67-71)

“What might a good lesson look like for second grade [first grade] that is built around word problems? The answer comes more naturally if you think about students not just solving the problems but also using words, pictures, and numbers to explain how they went about solving the problem and why they think they are correct. Children should be allowed to use whatever physical materials they feel they need to help them, or they can just simply draw pictures. Whatever they put on paper should explain what they did well enough to allow someone else to understand it. Allow at least a half page of space for a problem.” (VDW, page 71)

Once students have an understanding of numbers, they are then more prepared to perform and comprehend operations. A common misconception is that the commutative property applies to subtraction. After students have discovered and applied the commutative property for addition, ask them to investigate whether this property works for subtraction. Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction.

Many children misunderstand the meaning of the equal sign. The equal sign means “is the same as” or the left side of the equation balances or is the same as right side of the equal sign. However, most primary students believe the equal sign tells you that the “answer is coming up” to the right of the equal sign. This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right.

First graders need to see equations written multiple ways, for example 5+7=12 and 12=5+7.

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time. For example, they might assume that the word left always means that subtraction must be used to find a solution. Providing problems in which key words like this are used to represent different operations is essential. For example, the use of the word left in this problem does not indicate subtraction as a solution method: Jose took the 8 stickers he no longer wanted and gave them to Anna. Now Jose has 11 stickers left. How many stickers did Jose have to begin with?

Students need to analyze word problems and make sense of them, rather than look for “tricks” to help them decide which operation to use. Avoid teaching key 8

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words to solve problems, instead emphasize understanding the situation.DifferentiationIncrease the RigorOA.1 Gail and Bill found 12 seashells on the beach. Some of them were shaped like cones. The rest of them were shaped like half circles. How many could have

been shaped like cones? How many could have been shaped like half circles? Maria has eight more crayons than Brian. Maria has 10 crayons. How many crayons does Brian have? Use this answer to solve the next question. Ana has 4 crayons. If she puts her crayons with Brian and Maria’s crayons, will they have enough crayons to fill a box that holds 16 crayons? How do you

know? Jim had sixteen toy cars. He went to the toy store with his father. His father bought him some more cars. When Jim got home, he counted his cars and then

he had 20. How many cars did his father buy for him? On Monday, Cara made 5 cupcakes. On Tuesday, Cara made some more. She had 11 cupcakes altogether. How many cupcakes did Cara make on Tuesday?OA.2 Brady read for three days. At the end of the third day, Brady had read a total of 20 pages. How many pages could he have read on the first, second and third

days? What is another possibility? There are chickens, sheep and pigs in a barn. There are 18 animals total in the barn. How many chickens, sheep and pigs could be in the barn? Maria has 14 fish in her fishtank. Some are angelfish, goldfish, and neon fish. How many angelfish, goldfish, and neon fish could she have? John has a box of 18 donuts. There are three different types of donuts in the box, chocolate, sugar, and strawberry. John knows there are 8 chocolate donuts.

How many of sugar and strawberry donuts could John have? The carnival takes tickets for the following rides: ferris wheel is 6 tickets, the swings are 5 tickets and the magic carpet ride is 8 tickets. How many tickets will

Mark need to go on each ride once? There are 3 bananas, 4 apples, and 4 oranges in a fruit bowl. Are there more or less than 10 pieces of fruit in the bowl?Acceleration InterventionThe Intervention Table below provides links to interventions specific to this unit. The interventions support students and teachers in filling foundational gaps revealed as students work through the unit. All listed interventions are from New Zealand’s Numeracy Project.

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First Grade Focused Math Intervention Kit for EIP: Lesson 6: Addition Word Problems Page 101Lesson 11: Compare Addition: Bigger Unknown Page 141Lesson 12: Compare Subtraction Difference Unknown Page 149Lesson 13: Compare Subtraction: Smaller Unknown page 157Lesson 4: Three-Addend Addition Page 84

Evidence of Learning10

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Cluster of Standards Name of Intervention Snapshot of summary orStudent I can statement. . .

Materials Master

Represent and solve problems in Addition and Subtraction

MGSE1.OA.1MGSE1.OA.2MGSE1.OA.7MGSE1.OA.8

Make a Ten Further develop part/whole mental methods of making a ten

Using Ten Frames for the Strategy of Bridging to a ten

Mental math strategies of making a ten

A Square of Circles Recall basic addition facts

BridgesRecall addition and subtraction facts to 20

ComparisonsRecall addition and subtraction facts to 20

Number Cards Practice addition and subtraction facts

Pocket Facts Recall basic addition and subtraction facts

Adding and Subtracting with Counters

Solve addition problems to 20 by joining sets and counting all the objects.

What's Hidden Solve subtraction problems from 20 by counting all the objects in their head.

Imaging with Tens Frames

Solve addition and subtraction problems to 20 by counting all the objects in their head.

MM 4-6

Adding and Subtracting with Counters

Solve addition problems to 20 by joining sets and counting all the objects

The Garden Sort, count, objects in categories

By the completion of this lesson, students should be able to: Represent and solve problems involving addition and subtraction.Additional Assessments: Elementary Formative Assessment Lesson: MGSE1.OA.1 (Caterpillars and Leaves) Shared Assessments: See formative assessment folder.Purchased ResourcesMy Math:Chapter 1:1.1 Addition Stories1.2 Model Addition1.3 Addition Number Sentences1.5 Vertical Addition1.6 Problem – Solving Strategy: Write a Number SentenceChapter 2:2.1 Subtraction Stories2.2 Model Subtraction2.3 Subtraction Number Sentences2.5 Vertical Subtraction2.6 Problem – Solving Strategy: Draw a Diagram*These lessons are not to be completed consecutively as it is way too much material. They are designed to help support you as you teach your standards.

Hands On Standards Numbers & Operations Book:Understanding Addition and Subtraction: Lesson 1: Solve Add-To and Take-From Word Problems page 10Understanding Addition and Subtraction: Lesson 2: Solve Put-Together and Take-Apart Word ProblemsUsing Strategies to Add and Subtract Within 20: Lesson 1: Two for One Page 28Understanding Addition and Subtraction: Lesson 4: Solve Word Problems By Adding here Whole Numbers page 22

Purchased Online ResourcesMy Mathhttp://connected.mcgraw-hill.com/connected/login.doTeacher User ID: ccsde0(enumber)Password: cobbmath1Student User ID: ccsd(student ID)Password: cobbmath1

Exemplarshttp://www.exemplarslibrary.com/User: Cobb EmailPassword: cobbmath

Think Math (previous adoption):Chapter 2:2.10 Problem Solving Strategy and Test PrepChapter 4:4.6 Addition Stories4.7 Subtraction Stories4.8 Problem Solving Strategy and Test PrepChapter 5:5.6 Using the Number Line to Solve ProblemsChapter 6:6.6 Problem Solving Strategy and test Prep

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Web ResourcesK-5 Math teaching Resources: http://www.k-5mathteachingresources.com/1st-grade-number-activities.htmlOA.1Add To: Change Unknown Word ProblemsTake From: Change Unknown Word ProblemsBunk Bed ProblemDouble Decker Bus ProblemOA.2Three Addends Word ProblemsFind 3 CardsIllustrative Mathematics provides instructional and assessment tasks, lesson plans, and other resources: https://www.illustrativemathematics.org/OA.1School SuppliesAt the ParkBoys and Girls, Variation 1Maria’s MarblesSharing MarkersFinding a ChairBoys and Girls, Variation 2The Pet SnakeMeasuring BlocksGrowing Bean Plants20 TicketsField Day ScarcityPeyton’s BooksLink-Cube AdditionOA.2Daisies in the VasesThe Very Hungry CaterpillarHoward County Department of Education Wiki: https://hcpss.instructure.com/courses/9414/pages/grade-1-year-at-a-glanceEstimation 180 is a website of 180 days of estimation ideas that build number sense: http://www.estimation180.com/days.htmlInside Mathematics provides lessons: http://www.insidemathematics.orgGreg Tang Math Number Games: http://www.gregtang.com

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Suggested ManipulativesBase-ten blocksten framesdouble-ten framestwo-colored countersnumber linesdiceplaying cardshundred chartsnap cubesbear counters

Vocabulary additionsubtractiondifferenceequationsumsymbolequal signequaladdendsubtrahendminuend

Suggested Literature Animals on BoardSplash A Collection for Kate10 for dinnerMonster Musical ChairsA Mountain of TrashThe Crayon Counting BookGet up and GoReady, Set, Hop!Lights, Out!One is a SnailTen is a CrabTen Sly PiranhasTen Little FishCounting CrocodilesFive Little MonkeysElevator MagicDomino AdditionOne More BunnyRoll Over!Let’s Go Visiting

Task DescriptionsScaffolding Task Task that build up to the learning task.Constructing Task Task in which students are constructing understanding through deep/rich contextualized problem solving Practice Task Task that provide students opportunities to practice skills and concepts.Culminating Task Task designed to require students to use several concepts learned during the unit to answer a new or unique situation. Formative Assessment Lesson (FAL)

Lessons that support teachers in formative assessment which both reveal and develop students’ understanding of key mathematical ideas and applications.

3-Act Task Whole-group mathematical task consisting of 3 distinct parts: an engaging and perplexing Act One, an information and solution seeking Act Two, and a solution discussion and solution revealing Act Three.

State TasksTask Name Task Type Content

StandardContent Addressed Brief Description

Developing Constructing Task MGSE1.OA. Problem solving with the result Students will solve real world math 13

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Meaning Using Story Problems: Result Unknown

Whole Group, Small Group, Individual 1unknown problems using addition and

subtraction.

Meaning Using Story Problems:

Change Unknown

Constructing TaskWhole Group/ Small Group/ Individual

MGSE1.OA.1 Problem solving with the change

unknown

Students will solve real world math problems using addition and subtraction.

Developing Meaning Using Story Problems: Initial Unknown

Constructing Task Whole Group/ Small Group/ Individual

MGSE1.OA.1

Problem solving with the initial unknown

Students will solve real world math problems using addition and subtraction.

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First Grade Unit 4: Operations and Algebraic Thinking―Addition and SubtractionTopic 2: Relationship Between Addition and SubtractionBig Ideas/Enduring Understandings: Students understand connections between counting and addition/subtraction (e.g., adding two is the same as counting on two). Students use properties of addition to add whole numbers and to create and use increasingly sophisticated strategies based on these properties (e.g.,

“making tens”) to solve addition and subtraction problems within 20. By comparing a variety of solution strategies, students will build an understanding of the relationship between addition and subtraction. Essential Questions: What happens when we change the order of numbers when we add (or subtract)? Why? How are addition and subtraction related? Content StandardsContent standards are interwoven and should be addressed throughout the year in as many different units and activities as possible in order to emphasize the natural connections that exist among mathematical topics.Understand and apply properties of operations and the relationship between addition and subtraction. MGSE1.OA.3 (220Q) 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.)

MGSE1.OA.4 (EM80Q) Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8.

Vertical AlignmentKindergarten StandardsUnderstand addition as putting together and adding to, and understand subtraction as taking apart and taking from. MGSEK.OA.1 Represent addition and subtraction with objects, fingers,

mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

Second Grade Standards MGSE2.NBT.5 Fluently add and subtract within 100 using strategies

based on place value, properties of operations, and/or the relationship between addition and subtraction.

MGSE2.NBT.6 Add up to four two-digit numbers using strategies based on place value and properties of operations.

MGSE2.NBT.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method.

Report Card Quarter 2 Standards-Based GradingThe report card is not able to assess students on all standards being taught in third grade. The following standards are the priority for mastery for this quarter: Solve word problems within 20 with unknowns Counts and represent numbers to 120 starting with any number Demonstrates the meaning of the equal sign

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Adds and subtracts within 20 using multiple strategies Represents the 2 digits of numbers 20-99 by composing and decomposing Organize, represent, and interpret data with up to 3 categoriesInstructional StrategiesOne focus in this cluster is for students to discover and apply the commutative and associative properties as strategies for solving addition problems. Students do not need to learn the names for these properties. It is important for students to share, discuss, and compare their strategies as a class. The second focus is using the relationship between addition and subtraction as a strategy to solve unknown addend problems. Students should connect counting on to solving subtraction problems. For the problem “15 – 7 = ?” they think about the number they have to count on from 7 to get to 15. First graders should be working with sums and differences less than or equal to 20 using the numbers 0 to 20. OA.3This standard asks students to apply properties of operations as strategies to add and subtract. Students do not need to use formal terms for these properties. Students should use mathematical tools, such as cubes and counters, and representations such as the number path and a 100 chart to model these ideas.

Students use properties of addition (commutativity and associativity) to add whole numbers, and they create and use increasingly sophisticated strategies based on these properties (e.g., ”making tens”) to solve addition and subtraction problems involving basic facts. By comparing a variety of solution strategies, children relate addition and subtraction as inverse operations.

Example:Students can build a tower of 8 green cubes and 3 yellow cubes and another tower of 3 yellow and 8 green cubes to show that order does not change the result in the operation of addition. Students can also use cubes of 3 different colors to prove that (2+6)+4 is equivalent to 2+(6+4) and then to prove 2+6+4=2+10. Students should understand the important ideas of the following properties: Identity property of addition (e.g., 6=6+0) Identity property of subtraction (e.g., 9−0=9) Commutative property of addition--Order does not matter when you add numbers. (e.g. 4+5=5+4) Associative property of addition--When adding a string of numbers you can add any two numbers first. (e.g., 3+9+1=3+10=13) Student 1: Using a number balance to investigate the commutative property. If I put a weight on 8 first and then 2, I think that it will balance if I put a weight on 2 first this time then on 8.

Students need several experiences investigating whether the commutative property works with subtraction. The intent is not for students to experiment with negative numbers but only to recognize that taking 5 from 8 is not the same as taking 8 from 5. Students should recognize that they will be working with numbers later on that will allow them to subtract larger numbers from smaller numbers. However, in first grade students do not work with negative numbers.

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Instruction needs to focus on lessons that help students to discover and apply the commutative and associative properties as strategies for solving addition problems. It is not necessary for students to learn the names for these properties. It is important for students to represent, share, discuss, and compare their strategies as a class.

The second focus is using the relationship between addition and subtraction as a strategy to solve unknown-addend problems. Students naturally connect counting on to solving subtraction problems. For the problem “15−7=?” they think about the number they have to add to 7 to get to 15. First graders should be working with sums and differences less than or equal to 20 using the numbers 0 to 20.

Instruction needs to focus on lessons that help students to discover and apply the commutative and associative properties as strategies for solving addition problems. It is not necessary for students to learn the names for these properties. It is important for students to represent, share, discuss, and compare their strategies as a class.

Provide investigations that require students to identify and then apply a pattern or structure of mathematics. For example, pose a string of addition and subtraction problems involving the same three numbers chosen from the numbers 0 to 20, like 4+13=17 and 13+4=17. Students analyze number patterns and create conjectures or guesses. Have students choose other combinations of three numbers and explore to see if

the patterns work for all numbers 0 to 20. Students then share and discuss their reasoning. Be sure to highlight students’ uses of the commutative and associative properties and the relationship

between addition and subtraction.

Expand the student work to three or more addends to provide the opportunities to change the order and/or groupings to make tens. This will allow the connections between place-value models and the properties of operations for addition to be seen. Understanding the commutative and associative properties builds flexibility for computation and estimation, a key element of number sense.

Provide multiple opportunities for students to study the relationship between addition and subtraction in a variety of ways, including games, modeling and real-world situations. Students need to understand that addition and subtraction are related, and that subtraction can be used to solve problems where the addend is unknown.OA.4This standard asks for students to use subtraction in the context of unknown addend problems. When determining the answer to a subtraction problem, 12−5, students think, “If I have 5, how many more do I need to make 12?” Encouraging students to record this symbolically, 5+?=12, will develop their understanding of the relationship between addition and subtraction.

Some strategies they may use are counting objects, creating drawings, counting up, using number path or 10 frames to determine an answer. Refer to Table 1 listed under the instructional strategies in topic one to consider the level of difficulty of this standard.Example:

17First Grade Unit 4 8/4/2016

12−5=? could be expressed as 5+?=12. Students should use cubes and counters, and representations such as the number path and the100 chart, to model and solve problems involving the inverse relationship between addition and subtraction.

Common MisconceptionsA common misconception is that the commutative property applies to subtraction. After students have discovered and applied the commutative property for addition, ask them to investigate whether this property works for subtraction. Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction.

First graders might have informally encountered negative numbers in their lives, so they think they can take away more than the number of items in a given set, resulting in a negative number( below zero). Provide many problems situations where students take away all objects from a set, e.g. 19 - 19 = 0 and focus on the meaning of 0 objects and 0 as a number. Ask students to discuss whether they can take away more objects than what they have.DifferentiationIncrease the RigorOA.3 How would you describe the commutative property to someone from another planet? Show me 2 different examples that proves the commutative property. Why does the total stay the same, even though you are adding in a different order? (example 6+5=11 and 5+6=11) Use drawings and/or models to help

explain. Would you get the same sum if you had two blue buttons and three red buttons as you would if you had three blue buttons and two red buttons? Can you

write the addition sentences that show that? Laura had 5 fish. Her mother gave her 1 more. Laura’s brother Frank had 1 fish. Their mother gave Frank 5 more. Laura cried, “That’s not fair! He has more

fish than I do!” Frank doesn’t agree. Who is correct? How you know?

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I own a pet store. There are 9 dogs, 1 cat and 3 fish in the store. How many pets are in the store? What number sentence could you write to match this story problem? Where is 10 in this number sentence? What new number sentence could we write to match what we did?

Laura solved the following problem: 7 + 2 + 3 = 12 How do you decide which numbers to add together first? What “friendly” number combinations do you see? Will we get the same number if we solve it different ways?

OA.4 Sarah picked three apples from the tree. Sarah needs 15 apples in all. How many more apples does Sarah need to pick? There were 12 children on the swim team. Four of them were boys and some were girls. How many girls were on the swim team? The zoo keeper gave some bananas to the monkeys for lunch. The monkeys ate 7 bananas and the zoo keeper counted 8 left. How many bananas did the

zoo keeper start with? Marty has 9 books in his library. He wants to have 18. How many more books does Marty need to get? Ms. Smith has 17 stamps left in her book of 20. How many stickers did she use?

Acceleration InterventionThe Intervention Table below provides links to interventions specific to this unit. The interventions support students and teachers in filling foundational gaps revealed as students work through the unit. All listed interventions are from New Zealand’s Numeracy Project.

First Grade Focused Math Intervention Kit for EIP: Lesson 3: Adding with the Commutative Property Page 77Lesson 5: Adding with the Associative Property Page 93Lesson 10: Subtract Using a Missing Addend Page 133 Evidence of LearningBy the completion of this lesson, students should be able to: Understand and apply properties of operations and the relationship between addition and subtraction.Additional Assessments:

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Cluster of Standards Name of Intervention

Snapshot of summary orStudent I can statement. . . Materials Master

Understand and apply properties of addition

and subtractionMGSE1.OA.3MGSE1.OA.4MGSE1.OA.5MGSE1.OA.6

Take Two

Use problem solving strategies to solve addition and subtraction problems

Elementary Formative Assessment Lesson: MGSE1.OA.1 (Caterpillars and Leaves) Shared Assessments: See formative assessment folder.Purchased ResourcesMy MathChapter 4:4.6 Use Related Facts to Add and Subtract4.7 Fact Families

Hands on Standards:Understanding Addition and Subtraction: Lesson 2: Grouping to Add page 32Understanding Addition and Subtraction: Lesson 3: They’re Related page 36

Purchased Online ResourcesMy Mathhttp://connected.mcgraw-hill.com/connected/login.doTeacher User ID: ccsde0(enumber)Password: cobbmath1Student User ID: ccsd(student ID)Password: cobbmath1

Exemplarshttp://www.exemplarslibrary.com/User: Cobb EmailPassword: cobbmath Bug Watching (OA.4) Clay Pots (OA.4) Field Trip (OA.4) License Plates (OA.4) Number Cube Game (OA.4) Snow Play (OA.4) Buttons for Snowman (OA.4) Riding at the Playground (OA.4) Sharing Sleds (OA.4) Someone’s Eating My Porridge (OA.4)

Think Math (previous adoption)Chapter 2:2.4 Relating Addition and Subtraction

Web ResourcesK-5 Math teaching Resources: http://www.k-5mathteachingresources.com/1st-grade-number-activities.htmlOA.3Turn Around TrainsTurn Around DominoesOA.4Subtract From 10Illustrative Mathematics provides instructional and assessment tasks, lesson plans, and other resources: https://www.illustrativemathematics.org/OA.3Domino AdditionDoubles?

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OA.4Cave Game SubtractionHoward County Department of Education Wiki: https://hcpss.instructure.com/courses/9414/pages/grade-1-year-at-a-glanceEstimation 180 is a website of 180 days of estimation ideas that build number sense: http://www.estimation180.com/days.htmlInside Mathematics provides lessons: http://www.insidemathematics.orgGreg Tang Math Number Games: http://www.gregtang.comSuggested ManipulativesBase-ten blocksten framesdouble-ten framestwo-colored countersnumber linesdiceplaying cardshundred chartsnap cubes OA.3snap cubes OA.4bear counters

Vocabulary additionsubtractiondifferenceequationsumsymbolequal signequaladdendsubtrahendminuend

Suggested Literature Animals on BoardSplash A Collection for Kate10 for dinnerMonster Musical ChairsA Mountain of TrashThe Crayon Counting BookGet up and GoReady, Set, Hop!Lights, Out!One is a SnailTen is a CrabTen Sly PiranhasTen Little FishCounting CrocodilesFive Little MonkeysElevator MagicDomino AdditionOne More BunnyRoll Over!Let’s Go Visiting

VideosGA DOE Video MGSE1.OA.4

First Grade Unit 4: Operations and Algebraic Thinking―Addition and SubtractionTopic 3: Add and Subtract Within 20Big Ideas/Enduring Understandings: Understand connections between counting and addition and subtraction (e.g., adding two is the same as counting on two).

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Use properties of addition to add whole numbers and to create and use increasingly sophisticated strategies based on these properties (e.g., ―making tens) to solve addition and subtraction problems within 20.

Essential Questions: What strategies can you use to solve addition and subtraction facts within 20? How can the relationship between addition and subtraction help you find the solution to related facts?Content StandardsContent standards are interwoven and should be addressed throughout the year in as many different units and activities as possible in order to emphasize the natural connections that exist among mathematical topics.Add and subtract within 20 MGSE1.OA.5 (EM40Q) Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). MGSE1.OA.6 (80Q) Add and subtract within 20.

a. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

b. Fluently add and subtract within 10.Vertical Alignment

Kindergarten StandardsUnderstand addition as putting together and adding to, and understand subtraction as taking apart and taking from. MGSEK.OA.3 Decompose numbers less than or equal to 10 into pairs in

more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation. (Drawings need not include an equation).

MGSEK.OA.5 Fluently add and subtract within 5.

Second Grade StandardsAdd and subtract within 20. MGSE2.OA.2 Fluently add and subtract within 20 using mental strategies.

By end of Grade 2, know from memory all sums of two one-digit numbers.

Report Card Quarter 2 Standards-Based GradingThe report card is not able to assess students on all standards being taught in third grade. The following standards are the priority for mastery for this quarter: Solve word problems within 20 with unknowns Counts and represent numbers to 120 starting with any number Demonstrates the meaning of the equal sign Adds and subtracts within 20 using multiple strategies Represents the 2 digits of numbers 20-99 by composing and decomposing Organize, represent, and interpret data with up to 3 categoriesInstructional StrategiesOA.5

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This standard asks for students to make a connection between counting and adding and subtraction. Students use various counting strategies, including counting all and counting on with numbers up to 20. This standard calls for students to move beyond counting all and become comfortable at counting on. The counting all strategy requires students to count an entire set. The counting and counting back strategies occur when students are able to hold the “start number” in their head and count on from that number. Students’ multiple experiences with counting may hinder their understanding of counting on as connected to addition and subtraction. To help them make these connections when students count on 3 from 4, they should write this as 4+3=7. When students count on for subtraction (3) from 7, they should connect this to 7−3=4. Students write 7−3=? and think I count on 3+?=7.Additional Example: 𝟓+𝟑=?

Provide many experiences for students to construct strategies to solve the different problem types illustrated in Table 1 (see instructional strategies under topic one). These experiences should help students combine their procedural and conceptual understandings.

Have students invent and refine their strategies for solving problems involving sums and differences less than or equal to 20 using the numbers 0 to 20. Ask them to explain and compare their strategies as a class.

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Note: Many children attempt to count down for subtraction, but counting down is difficult and error-prone. Children are much more successful when counting; it makes subtraction as easy as addition. The use of “touch points or touch math” should be avoided since it encourages students to stay at Level 1.

Provide multiple and varied experiences that will help students develop a strong sense of numbers based on comprehension – not rules and procedures. Number sense is a blend of comprehension of numbers and operations and fluency with numbers and operations. Students gain computational fluency (using efficient and accurate methods for computing) as they come to understand the role and meaning of arithmetic operations in number systems.

Primary students should come to understand addition and subtraction as they connect counting and number sequence to these operations. Addition and subtraction also involve part to whole relationships. Students’ understanding that the whole is made up of parts is connected to decomposing and composing numbers.

Provide numerous opportunities for students to use the counting on strategy for solving addition and subtraction problems. For example, provide a ten frame showing 5 colored dots in one row. Students add 3 dots of a different color to the next row and write 5+3. Ask students to count on from 5 to find the total number of dots. Then have them add an equal sign and the number eight to 5+3 to form the equation 5+3=8.

Ask students to verbally explain how counting on helps to add one part to another part to find a sum. Discourage students from inventing a counting back strategy for subtraction because it is difficult and leads to errors.OA.6This standard is strongly connected to all the standards in this domain. It focuses on students being able to fluently add and subtract numbers to 10 and having experiences adding and subtracting within 20.

Fluency means: accuracy (correct answer) efficiency (within 4-5 seconds) flexibility (using strategies such as making 5 or making 10)

The standards in this unit call for fluency as well as requiring students to use a variety of strategies when adding and subtracting numbers within 20. Students should have ample experiences modeling these operations before working on fluency. Teacher could differentiate using smaller numbers. By studying patterns and relationships in addition facts and relating addition and subtraction, students build a foundation for fluency with addition and subtraction facts. Adding and subtracting fluently refers to knowledge of procedures, knowledge of when and how to use them appropriately, and skill in performing them flexibly (use of different strategies), accurately, and efficiently.

The use of objects, diagrams, or interactive whiteboards and various strategies will help students develop fluency. It is important for students to be able to use a variety of strategies when adding and subtracting numbers within 20. Students should have ample experiences modeling these operations before working on fluency.

Algebraic ideas underlie what students are doing when they create equivalent expressions in order to solve a problem or when they use addition

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combinations they know to solve more difficult problems. Students begin to consider the relationship between the parts. For example, students notice that the whole remains the same, as one part increases the other part decreases. 5+2=4+3The use of objects, diagrams, or interactive whiteboards and various strategies will help students develop fluency. It is important for students to be able to use a variety of strategies when adding and subtracting numbers within 20. Students should have ample experiences modeling these operations before working on fluency.

Teacher could differentiate using smaller numbers. Also, it is important to move beyond the strategy of counting on, which is considered a less important skill than the ones here in 1.OA.6. Many times teachers think that counting on is all a child needs, when it is really not much better skill than counting all and can becomes a hindrance when working with larger numbers.Example: 8 + 7 = ?

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Common MisconceptionsStudents ignore the need for regrouping when subtracting with numbers 0 to 20 and think that they should always subtract a smaller number from a larger number. For example, students solve 15 – 7 by subtracting 5 from 7 and 0 (0 tens) from 1 to get 12 as the incorrect answer. Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction. They need to show these relationships for each step using mathematical drawings, ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction.Differentiation

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Increase the RigorOA.5 When Austin solved his math problem on the number line, he was counting up. He started at a certain number, and he counted up 4 more. When he

stopped, he was at a number greater than 20. What three different numbers could he have started at? How are addition and subtraction related? What strategy do you use when solving 34 + 2 = and 75 - 2 = ? Explain your thinking.OA.6 How is 9+2 related to 29+2, 49+2, and 79+2? How does the make-ten fact, 4+6 help you find the sum of 34+6 or 54+6? Does the doubles strategy work with numbers greater than 10? When we subtract 2 we can think of counting back. Does this work with two-digit numbers? How are 61-2, 31-2, and 11-2 related? How could you use doubles to help you find the sum of 7 + 6? Julie picked out three different dominoes out of a pile of dominoes. If she added the dots on each domino, the sum of each domino was 10. What could

the three different addition sentences be for the three dominoes she picked?Acceleration InterventionThe Intervention Table below provides links to interventions specific to this unit. The interventions support students and teachers in filling foundational gaps revealed as students work through the unit. All listed interventions are from New Zealand’s Numeracy Project.

First Grade Focused Math Intervention Kit for EIP: Lesson 1: Counting to Add and Subtract Page 61Lesson 9: Subtraction Equations with an Unknown Page 125

First Grade Math Triumphs Intervention (came with the My Math adoption):3.1: Count On to the Next Ten3.2:Use Ones to Add

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Cluster of Standards Name of Intervention

Snapshot of summary orStudent I can statement. . . Materials Master

Understand and apply properties of addition

and subtractionMGSE1.OA.3MGSE1.OA.4MGSE1.OA.5MGSE1.OA.6

Take Two

Use problem solving strategies to solve addition and subtraction problems

3.5: Count Back to the Previous Ten3.6: Subtract Using the Ones Place1.4: Sums of 11 to 151.5: Sums of 16 to 201.6: Doubles3.3: Use Tens to Add3.4: Use Tens and Ones to Add3.7: Subtract Using the Tens PlaceEvidence of LearningBy the completion of this lesson, students should be able to: Add and subtract within 20.Additional Assessments: Elementary Formative Assessment Lesson: MGSE1.OA.1 (Caterpillars and Leaves) Shared Assessments: See formativd assessment folder.Purchased ResourcesMy MathChapter 1:1.4 Add 01.7 Ways to Make 4 and 51.8 Ways to Make 6 and 71.9 Ways to Make 81.10 Ways to Make 91.11 Ways to Make 10Chapter 2:2.4 Subtract 0 and All2.8 Subtract from 4 and 52.9 Subtract from 6 and 72.10 Subtract from 82.11 Subtract from 92.12 Subtract from 10Chapter 3:3.1 Count on 1, 2, or 33.2 Count on Using Pennies3.3 Use a Number Line to Add3.4 Use Doubles to Add3.5 Use Near Doubles to Add

Purchased Online ResourcesMy Mathhttp://connected.mcgraw-hill.com/connected/login.doTeacher User ID: ccsde0(enumber)Password: cobbmath1Student User ID: ccsd(student ID)Password: cobbmath1

Exemplarshttp://www.exemplarslibrary.com/User: Cobb EmailPassword: cobbmath Bug Watching (OA.6) Clay Pots (OA.6) Field Trip (OA.6) License Plates (OA.6) Number Cube Game (OA.6) Snow Play (OA.6)

Think Math (previous adoption)Chapter 2:2.2 Jumping on the Number Line2.3 Recording Jumps as Addition and SubtractionChapter 4:4.1 Introducing the Cross Number Puzzle4.2 Using Cross Number Puzzles to Add4.5 Sums of 10Chapter 5:5.1 Ten and Some More5.2 Lots of Tens and Some More

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3.6 Problem-Solving Strategy: Act it Out3.7 Make 10 to Add3.8 Add in Any Order3.9 Add Three NumbersChapter 4:4.1 Count Back 1, 2, or 34.2 Use a Number Line to Subtract4.3 Use Doubles to Subtract4.4 Problem-Solving Strategy: Write a Number Sentence4.5 Make 10 to Subtract

Hands on Standards Number & Operations Book:Understanding Addition and Subtraction: Lesson 4: Put It In Your Pocket Page 40Understanding Addition and Subtraction: Lesson 5: Make 10 to Add page 44Using Strategies to Add and Subtract Within 20 Lesson 6: Double the Fun: Page 50Web ResourcesK-5 Math teaching Resources: http://www.k-5mathteachingresources.com/1st-grade-number-activities.htmlOA.5Show One MoreShow One LessOA.6Count On One (ver.1)Count On One (ver.2)Count On Two (ver.1)Count On Three (ver.1)Doubles Cover Up (ver.2)Find TenMaking Ten (ver.1)Four in a Row SubtractionDomino AdditionPart Part Whole CardsIllustrative Mathematics provides instructional and assessment tasks, lesson plans, and other resources: https://www.illustrativemathematics.org/OA.5

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The Very Hungry CaterpillarOA.6$20 Dot MapMaking a TenHoward County Department of Education Wiki: https://hcpss.instructure.com/courses/9414/pages/grade-1-year-at-a-glanceEstimation 180 is a website of 180 days of estimation ideas that build number sense: http://www.estimation180.com/days.htmlInside Mathematics provides lessons: http://www.insidemathematics.orgGreg Tang Math Number Games: http://www.gregtang.comSuggested ManipulativesBase-ten blocksten framesdouble-ten framestwo-colored countersnumber linesdiceplaying cardshundred chartsnap cubesbear counters

Vocabulary additionsubtractiondifferenceequationsumsymbolequal signequaladdendsubtrahendminuend

Suggested Literature Animals on BoardSplash A Collection for Kate10 for dinnerMonster Musical ChairsA Mountain of TrashThe Crayon Counting BookGet up and GoReady, Set, Hop!Lights, Out!One is a SnailTen is a CrabTen Sly PiranhasTen Little FishCounting CrocodilesFive Little MonkeysElevator MagicDomino AdditionOne More BunnyRoll Over!Let’s Go Visiting

VideosGA DOE Video MGSE1.OA.6Task Descriptions

Scaffolding Task Task that build up to the learning task.Constructing Task Task in which students are constructing understanding through deep/rich contextualized problem solving

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Practice Task Task that provide students opportunities to practice skills and concepts.Culminating Task Task designed to require students to use several concepts learned during the unit to answer a new or unique situation. Formative Assessment Lesson (FAL)

Lessons that support teachers in formative assessment which both reveal and develop students’ understanding of key mathematical ideas and applications.

3-Act Task Whole-group mathematical task consisting of 3 distinct parts: an engaging and perplexing Act One, an information and solution seeking Act Two, and a solution discussion and solution revealing Act Three.

State TasksTask Name Task Type Content

StandardContent Addressed Brief Description

Lots of Dots

Scaffolding TaskSmall Group/ Partners/ Individual

MGSE1.OA.3-6Composing and decomposing of

numbers

Students will practice finding sums, creating equations, expressions and the commutative property.

What Numbers Can You Make?

Constructing Task Small Group/ Partners/ Individual

MGSE1.OA.3-6MGSE1.MD.4 Composing and Decomposing of

numbers

Students will practice finding number combinations with like sums.

Wheel ShopPerformance Task

Small Group/ Partners/ IndividualMGSE1.OA.2MGSE.1.OA.5 Problem solving Students will find combinations

of numbers with a given sum.

I Want Candy!3 Act Task

Large Group, IndividualMGSE1.OA.1MGSE.1.OA.5MGSE1.MD.4

Problem Solving, Composing and Decomposing of numbers

Students will solve real world problem.

Digging Dinosaurs

Performance Task Small Group/ Partners/ Individual

MGSE1.OA.1-2MGSE.1.OA.5 Problem solving Students will practice flexibility

of numbers.

Fact Families to Ten

Scaffolding Task Whole Group/ Small Group/ Individual

MGSE1.OA.3-6 Relating addition to subtraction Students will practice fact families with cubes and number sentences.

Domino Fact Family

Practice TaskIndividual

MGSE1.OA.6 Relating addition to subtraction Practice with Fact Families using Dominoes.

Candy Practice TaskWhole Group/ Small Group/ Partners

MGSE.1.OA.5MGSE1.MD.4 Graphing Students will create a graph and

use terms most and least.

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First Grade Unit 4: Operations and Algebraic Thinking―Addition and SubtractionTopic 4: Addition and Subtraction EquationsBig Ideas/Enduring Understandings: Recognize that any given group of objects can be separated into sub groups in multiple ways and remain equivalent in amount to the original group (Ex: A

set of 6 cubes can be separated into a set of 2 cubes and a set of 4 cubes and remain 6 total cubes). Apply the relationship between addition and subtraction to determine the unknown in an addition or subtraction equation.Essential Questions: How can we show that addition and subtraction are related through fact families? How can we use different combinations of numbers and operations to represent the same quantity? How can we represent a number in a variety of ways?Content StandardsContent standards are interwoven and should be addressed throughout the year in as many different units and activities as possible in order to emphasize the natural connections that exist among mathematical topics.Work with addition and subtraction equations MGSE1.OA.7 (EM150Q) 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 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. The equal sign describes a special relationship between two quantities. In the case of a true equation, the quantities are the same.

MGSE1.OA.8 (20Q) Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = □ – 3, 6 + 6 = Δ.

Vertical AlignmentKindergarten StandardsUnderstand addition as putting together and adding to, and understand subtraction as taking apart and taking from. MGSEK.OA.3 Decompose numbers less than or equal to 10 into pairs in

more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation. (drawings need not include an equation).

MGSEK.OA.4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.

Second Grade Standards MGSE2.NBT.5 Fluently add and subtract within 100 using strategies

based on place value, properties of operations, and/or the relationship between addition and subtraction.

MGSE2.NBT.6 Add up to four two-digit numbers using strategies based on place value and properties of operations.

MGSE2.NBT.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method.

Report Card Quarter 2 Standards-Based GradingThe report card is not able to assess students on all standards being taught in third grade. The following standards are the priority for mastery for this quarter: Solve word problems within 20 with unknowns Counts and represent numbers to 120 starting with any number

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Demonstrates the meaning of the equal sign Adds and subtracts within 20 using multiple strategies Represents the 2 digits of numbers 20-99 by composing and decomposing Organize, represent, and interpret data with up to 3 categoriesInstructional StrategiesOA.7This standard calls for students to work with the concept of equality by identifying whether equations are true or false. Therefore, students need to understand that the equal sign does not mean “answer comes next”, but rather that the equal sign signifies a relationship between the left and right side of the equation. Interchanging the language of “equal to” and “the same as” as well as “not equal to” and “not the same as” will help students grasp the meaning of the equal sign. Students should understand that “equality” means “the same quantity as”. In order for students to avoid the common pitfall that the equal sign means “to do something” or that the equal sign means “the answer is,” they need to be able to: Express their understanding of the meaning of the equal sign Accept sentences other than a + b = c as true (𝑎=𝑎, 𝑐=𝑎+𝑏, 𝑎=𝑎+0, 𝑎+𝑏=𝑏+𝑎) Know that the equal sign represents a relationship between two equal quantities Compare expressions without calculating

The number sentence 4+5=9 can be read as, “Four plus five is the same amount as nine.” In addition, Students should be exposed to various representations of equations, such as: an operation on the left side of the equal sign and the answer on the right side (5+8=13) “Compose” an operation on the right side of the equal sign and the answer on the left side (13=5+8) “Decompose” numbers on both sides of the equal sign (6=6) operations on both sides of the equal sign (5+2=4+3).

Students need many opportunities to model equations using cubes, counters, drawings, etc. These key skills are hierarchical in nature and need to be developed over time.

Experiences determining if equations are true or false help student develop these skills. Initially, students develop an understanding of the meaning of equality using models. However, the goal is for students to reason at a more abstract level. At all times students should justify their answers, make conjectures (e.g., if you add a number and then subtract that same number, you always get zero), and make estimations. Once students have a solid foundation of the key skills listed above, they can begin to rewrite true/false statements using the symbols, < and >.Examples of true and false statements: 7=8−1 8=8 1+1+3=7 4+3=3+4 6−1=1−6

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12+2−2=12 9+3=10 5+3=10−2 3+4+5=3+5+4 3+4+5=7+5 13=10+4 19+9+1=19

Provide opportunities for students use objects of equal weight and a number balance to model equations for sums and differences less than or equal to 20 using the numbers 0 to 20. Give students equations in a variety of forms that are true and false. Include equations that show the identity property, commutative property of addition, and associative property of addition.

Students need not use formal terms for these properties. 13=13 Identity Property 8+6=6+8 Commutative Property for Addition 3+7+4=10+4 Associative Property for Addition

When asking students to determine whether the equations are true or false have them record their work with drawings. Students then compare their answers as a class and discuss their reasoning. Present equations recorded in a nontraditional way, like 13=16−3 and 9+4=18−5, then ask, “Is this true?.” Have students decide if the equation is true or false. Then as a class, students discuss their thinking that supports their answers.

Provide situations relevant to first graders for these problem types illustrated in Table 1 in the Appendix: Add to / Result Unknown, Take from / Start Unknown, and Add to / Result Unknown.

Demonstrate how students can use graphic organizers such as the Math Mountain (shown below) to help them think about problems. The Math Mountain shows a sum with diagonal lines going down to connect with the two addends, forming a triangular shape.

It shows two known quantities and one unknown quantity. Use various symbols, such as a square, to represent an unknown sum or addend in a horizontal equation. For example, here is a Take from / Start Unknown problem situation such as: Some markers were in a box. Matt took 3 markers to use. There are now 6 markers in the box. How many markers were in the box before? The teacher draws a square to represent the unknown sum and diagonal lines to the numbers 3 and 6.

Have students practice using the Math Mountain to organize their solutions to problems involving sums and differences less than or equal to 20 with the numbers 0 to 20. Then ask them to share their reactions to using the Math Mountain.

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Provide numerous experiences for students to compose and decompose numbers less than or equal to 20 using a variety of manipulatives. Have them represent their work with drawings, words, and numbers. Ask students to share their work and thinking with their classmates. Then ask the class to identify similarities and differences in the students’ representations.OA.8This standard extends the work that students do in 1.OA.4 by relating addition and subtraction as related operations for situations with an unknown. This standard builds upon the “think addition” for subtraction problems as explained by Student 2 in 1.OA.6 (see topic three above).

Students need to understand the meaning of the equal sign and know that the quantity on one side of the equal sign must be the same quantity on the other side of the equal sign. They should be exposed to problems with the unknown in different positions. Having students create word problems for given equations will help them make sense of the equation and develop strategic thinking.

Examples of possible student “think-throughs”: 8+?=11: “8 and some number is the same as 11. 8 and 2 is 10 and 1 more makes 11. So the answer is 3.” 5=?−3: “This equation means I had some cookies and I ate 3 of them. Now I have 5. How many cookies did I have to start with? Since I have 5 left and I ate

3, I know I started with 8 because I count on from 5. . . 6, 7, 8.” All students need to show a representation of the problem and communicate and justify their thinking.Common MisconceptionsMany students think that the equals sign means that an operation must be performed on the numbers on the left and the result of this operation is written on the right. They think that the equal sign is like an arrow that means becomes and one number cannot be alone on the left. Students often ignore the equal sign in equations that are written in a nontraditional way.

For instance, students find the incorrect value for the unknown in the equation 9=Δ−5 by thinking 9−4=4. It is important to provide equations with a single number on the left as in 18=10+8. Showing pairs of equations such as 11=7+4 and 7+4=11 gives students experiences with the meaning of the equal sign as is the same as and equations with one number to the left.DifferentiationIncrease the RigorOA.7 This balance shows that 4+2=5+1 (See page 125 for balance picture in Good Question Book)- need to insert image. How could you move the blocks to

show other equations that are true? Sally said 1+4=5+3. Sam says she is wrong. Who is correct? Use numbers, pictures and/or words to show your thinking.

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Consider this problem: 3+7=10. What does the equal sign mean? Trisha said 11=13 - 4 is not true. How could Trisha fix this problem to make it true?OA.8 I am thinking of two numbers on the number line that have a difference of 5. What could the two numbers be? How do you know? If the sum of two numbers is 13, what could the two addends be? How do you know? Use the digits 3, 4, 5, 6 & 7 to make the following equations true. Each digit may be used only once. (_ + 6 = 12, 5 - _ = 2, 4 = _ - 3, 6 = 2 + _13 - ___ = 8) A ribbon is 14 inches long. Jan used some ribbon to wrap a gift. How much ribbon could be left?. How many inches of ribbon did Jan use? Write a number

sentence show how you solved the problem. Acceleration InterventionThe Intervention Table below provides links to interventions specific to this unit. The interventions support students and teachers in filling foundational gaps revealed as students work through the unit. All listed interventions are from New Zealand’s Numeracy Project.

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First Grade Focused Math Intervention Kit for EIP: Lesson 2:

Understanding the Equal Sign Page 69Lesson 7: Addition Equations with an Unknown Page 109

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Cluster of Standards Name of Intervention Snapshot of summary orStudent I can statement. . .

Materials Master

Represent and solve problems in Addition and

Subtraction

MGSE1.OA.1MGSE1.OA.2MGSE1.OA.7MGSE1.OA.8

Make a Ten Further develop part/whole mental methods of making a ten

Using Ten Frames for the Strategy of Bridging to a ten Mental math strategies of making a ten

A Square of Circles Recall basic addition facts

Bridges Recall addition and subtraction facts to 20

Comparisons Recall addition and subtraction facts to 20

Number Cards Practice addition and subtraction facts

Pocket Facts Recall basic addition and subtraction facts

Adding and Subtracting with Counters

Solve addition problems to 20 by joining sets and counting all the objects.

What's Hidden Solve subtraction problems from 20 by counting all the objects in their head.

Imaging with Tens Frames Solve addition and subtraction problems to 20 by counting all the objects in their head.

MM 4-6

Adding and Subtracting with Counters

Solve addition problems to 20 by joining sets and counting all the objects

I Like Trucks Collect, analyze and report information about favorites

Not Enough Drawers Sort and analyze categories of clothesThe Garden Sort, count, objects in categories

Lesson 9: Subtraction Equations with an Unknown page 125Evidence of LearningBy the completion of this lesson, students should be able to: Work with addition and subtraction equations.Additional Assessments: Elementary Formative Assessment Lesson: MGSE1.OA.1 (Caterpillars and Leaves) Shared Assessments: See formative assessment folder.Purchased ResourcesMy Math1.12 Find Missing Parts of 102.7 Compare Groups2.13 Relate to Addition and Subtraction2.14 True and False Statements4.8 Missing Addends

Hands on Standards:Using Strategies to Add and Subtract Within 20ExplorAction 1 Fair and Square Page 48

Purchased Online ResourcesMy Mathhttp://connected.mcgraw-hill.com/connected/login.doTeacher User ID: ccsde0(enumber)Password: cobbmath1Student User ID: ccsd(student ID)Password: cobbmath1

Exemplarshttp://www.exemplarslibrary.com/User: Cobb EmailPassword: cobbmath

Think Math (previous adoption)Chapter 2:2.4 Relating Addition and SubtractionChapter 4:4.3 Exploring Missing AddendsChapter 9:9.2 Recording Addition Sentences

Web ResourcesK-5 Math teaching Resources: http://www.k-5mathteachingresources.com/1st-grade-number-activities.htmlOA.7True or False?OA.8Find the Missing NumberIllustrative Mathematics provides instructional and assessment tasks, lesson plans, and other resources: https://www.illustrativemathematics.org/OA.7Valid EqualitiesEquality Number SentencesUsing Lengths to Represent EqualityThe Very Hungry Caterpillar20 TicketsOA.8Find the Missing Number

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Kiri’s Mathematics Match GameHoward County Department of Education Wiki: https://hcpss.instructure.com/courses/9414/pages/grade-1-year-at-a-glanceEstimation 180 is a website of 180 days of estimation ideas that build number sense: http://www.estimation180.com/days.htmlInside Mathematics provides lessons: http://www.insidemathematics.orgGreg Tang Math Number Games: http://www.gregtang.comSuggested ManipulativesBase-ten blocksten framesdouble-ten framestwo colored counters OA.7two-colored counters OA.8number linesdiceplaying cardshundred chartsnap cubesbear counters

Vocabulary additionsubtractiondifferenceequationsumsymbolequal signequaladdendsubtrahendminuend

Suggested Literature Animals on BoardSplash A Collection for Kate10 for dinnerMonster Musical ChairsA Mountain of TrashThe Crayon Counting BookGet up and GoReady, Set, Hop!Lights, Out!One is a SnailTen is a CrabTen Sly PiranhasTen Little FishCounting CrocodilesFive Little MonkeysElevator MagicDomino AdditionOne More BunnyRoll Over!Let’s Go Visiting

VideosGA DOE Video MGSE1.OA.7GA DOE Video MGSE1 .OA.8 Task Descriptions

Scaffolding Task Task that build up to the learning task.Constructing Task Task in which students are constructing understanding through deep/rich contextualized problem solving Practice Task Task that provide students opportunities to practice skills and concepts.Culminating Task Task designed to require students to use several concepts learned during the unit to answer a new or unique situation.

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Formative Assessment Lesson (FAL)

Lessons that support teachers in formative assessment which both reveal and develop students’ understanding of key mathematical ideas and applications.

3-Act Task Whole-group mathematical task consisting of 3 distinct parts: an engaging and perplexing Act One, an information and solution seeking Act Two, and a solution discussion and solution revealing Act Three.

State TasksTask Name Task Type Content Standard Content Addressed Brief Description

Task 7:Shape Pounds

Constructing TaskWhole Group/ Small Group/ Individual

MGSE1.OA.7MGSE1.OA.8

Writing numbers sentences with a shape representing

an unknown

Students will work with equality and understanding of equal sign.

Culminating Task : Atlanta

Zoo

Culminating TaskIndividual

MGSE1.OA.1MGSE.1.OA.5MGSE1.OA.7MGSE1.OA.8MGSE1.MD.4

Problem solving, working with unknowns, writing

number sentences

Students will solve real world math problem with finding combinations of numbers with a given sum.

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