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TRG Math Pacing Guide Grade 1 Page 1 of 2

TRG Math Pacing Guide Grade: 1 Trimester 1

September October November K.CC.A.1; K.CC.B.4; K.CC.B.5; K.CC.C.6; K.OA.A.1; K.OA.A.4

1.NBT. A.1 1.NBT.B.2; 1.NBT.B.2a;

1.NBT.B.2b; 1.NBT.B.2c

Individual School Improvement Standards

Individual Classroom Intervention Standards

Trimester 2 December January February 1.NBT.C.4; 1.NBT.C.5; 1.NBT.C.6;

1.OA.A.1; 1.OA.A.2; 1.OA.B.3;

1.OA.B.4; 1.OA.C.5; 1.OA.C.6;



Trimester 3 March April May June 1.OA.D.7; 1.OA.D.8;

1.G.A.1; 1.G.A.2; 1.G.A.3

1.MD.A.1; 1.MD.A.2;

1.MD.C.4; 1.MD.B.3;



TRG Math Pacing Guide Grade 1 Page 2 of 2

1

GRADE: 1st SUBJECT: Math STRAND: Operations and

Algebraic Thinking MONTH(S) TAUGHT:

Description: 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. ACT/Anchor Standard: Make sense of problems and persevere in solving them (MP.1), Reason abstractly and quantitatively (MP.2), Model with mathematics (MP.3)

CODE:

1.OA.A.1

Board Objective: I can represent and solve word problems using addition and subtraction in order to become a better problem-‐solver.

ASSESSMENTS: CONCEPT NOTES: STRATEGIES

Global Scholars (Performance Series) Teacher observations and class discussions (anecdotal notes) Have students write their own word problem and the solution. (If time allows, pair students up and allow them to exchange and solve each other’s word problems.)

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 use numbers within 20 and align with the twelve situations found in Table 1 of the Common Core State Standards (CCSS) for Mathematics located at http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf . Students need the opportunity of writing and solving story problems involving three addends whose sum is less than or equal to 20. For example, each student writes or draws a problem where three whole things are being combined. The students exchange their problems with another student, solving them individually and then discuss their models and solution strategies. Now both students work together to solve each problem using a different strategy. Literature is a wonderful way to incorporate problem solving in a context that young students can understand. Many literature books have been written over recent years that include mathematical ideas and concepts. For first grade the incorporation of books that contain a problem situation involving addition and subtraction within 20 should be included in the curriculum. Use the situations found in Table 1 of the CCSS 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 and. Connections First grade students build on their work solving addition and subtraction problems within 10 in Kindergarten. The mathematics in first-grade problems should connect to the grade level content in other domains and other subject areas. Second-grade students will build on their work with solving addition and subtraction word problems within 20 in First grade as they add and subtract within 100 solving one- and two-step word problems.

Concrete: Read the word problem as a class. Identify the key words that indicate whether subtraction or addition is necessary to solve the problem. Then, identify the different qualities that are be subtracted or added. Use connecting cubes to tangible illustrate this process. Cubes can be added together or cubes can be taken away from the whole to show the math processes that are taking place within the problem. Semi-‐Concrete (Pictorial): Distribute white boards and markers to each student. Next, read the word problem together as a class. Identify the key words that indicate whether subtraction or addition is necessary to solve the problem. Then, identify the different qualities that are to be subtracted or added. Use the white boards to draw images (simple is better) to represent each quality. If it is addition, draw both qualities and add the total to find the sum. If it is subtraction, draw the total and cross

2 Common Misconceptions Many children misunderstand the meaning of the equal sign. The equal sign means “is the same as” but most primary students believe the equal sign tells you that the “answer is coming up” to the right of the equal sign. A second misconception that many students have is to assume that a key word or phrase in a problem suggests the same operation will be used every time. For example, assuming that the word left always means that subtraction must be used to find a solution. Providing problems where key words like this are used to represent different operations is essential.

out the number that is being taken away or simply erase to find the difference. Abstract: Distribute highlighters to each student. As the students read the word problem, have them highlight the key words that indicate the quantities to be added or subtracted and the key words that indicate this correct mathematical process. Then, have the students create a number sentence that correlates to the word problem and solve.

RESOURCES: VOCABULARY: Common Core State Standards for Mathematics: Common addition and subtraction situations http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf Table 1 on page 88 in the Common Core State Standards (CCSS) for School for Mathematics illustrates twelve addition and subtraction problem situations. ORC # 2807 From the International Reading Association, National Council of Teachers of English and Verizon Thinkfinity: Giant story problems: Reading comprehension through math problem-solving http://www.readwritethink.org/classroom-resources/lesson-plans/giant-story-problems-reading-146.html (Using drawings, equations, and written responses, students work cooperatively in two class sessions to solve Giant Story Problems while they gain practice in reading for information.) Counters, flashcards, and connecting cubes Math Lessons: www.aaastudy.com Math Games: www.gamequarium.com, www.funbrain.com, www.arcademicskillbuilders.com, www.mathisfun.com Games and Worksheets: www.aplusmath.com Math Resources: www.svsu.edu/supo

ADDITION, SUBTRACTION, EQUAL SIGN, WORD PROBLEM VOCABULARY (“ADDING TO,” “TAKING FROM,” “PUTTING TOGETHER,” AND “TAKING APART”), SYMBOL

ESSENTIAL QUESTIONS:

WHAT IS THE DIFFERENCE BETWEEN ADDITION AND SUBTRACTION? WHAT ARE THE KEY WORDS THAT INDICATE WHETHER A STORY PROBLEMS USES ADDITION OR SUBTRACTION? WHAT IS

A WORD PROBLEM? WHAT STEPS DO I TAKE TO SOLVE A WORD PROBLEM?

3 GRADE: 1st SUBJECT: Math STRAND: Operations and


Description: 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. ACT/Anchor Standard: Make sense of problems and persevere in solving them (MP.1), Reason abstractly and quantitatively (MP.2), Model with mathematics (MP.3)

CODE:

1.OA.A.2 Board Objective: I can represent and solve word problems using three-‐digit addition in order to become a better problem-‐solver.


Global Scholars (Performance Series) Teacher observations and class discussions (anecdotal notes) Have students write their own word problem and the solution. (If time allows, pair students up and allow them to exchange and solve each other’s word problems.) Change problems, where the initial part is unknown or where the change amounts are unknown, are usually difficult for primary students. Providing opportunities for students to analyze,

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 use numbers within 20 and align with the twelve situations found in Table 1 of the Common Core State Standards (CCSS) for Mathematics located at http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf . Students need the opportunity of writing and solving story problems involving three addends whose sum is less than or equal to 20. For example, each student writes or draws a problem where three whole things are being combined. The students exchange their problems with another student, solving them individually and then discuss their models and solution strategies. Now both students work together to solve each problem using a different strategy. Literature is a wonderful way to incorporate problem solving in a context that young students can understand. Many literature books have been written over recent years that include mathematical ideas and concepts. For first grade the incorporation of books that contain a problem situation involving addition and subtraction within 20 should be included in the curriculum. Use the situations found in Table 1 of the CCSS 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 and. Connections First grade students build on their work solving addition and subtraction problems within 10 in Kindergarten. The mathematics in first-grade problems should connect to the grade level content in other domains and other subject areas. Second-grade students will build on their work with solving addition and subtraction word problems within 20 in First grade as they add and subtract within 100 solving one- and two-step word problems.

Concrete: Read the word problem as a class. Identify the key words that indicate whether subtraction or addition is necessary to solve the problem. Then, identify the different qualities that are be subtracted or added. Use connecting cubes to tangible illustrate this process. Cubes can be added together or cubes can be taken away from the whole to show the math processes that are taking place within the problem. Semi-‐Concrete (Pictorial): Distribute white boards and markers to each student. Next, read the word problem together as a class. Identify the key words that indicate whether subtraction or addition is necessary to solve the problem. Then, identify the different qualities that are to be subtracted or added. Use the white boards to draw images (simple is better) to represent each quality. If it is addition, draw both qualities and add the total to find the sum. If it is subtraction, draw the total and cross out the number that is being taken

4 model and solve problems by working backwards helps student visualize what is happening.

away or simply erase to find the difference. Abstract: Distribute highlighters to each student. As the students read the word problem, have them highlight the key words that indicate the quantities to be added or subtracted and the key words that indicate this correct mathematical process. Then, have the students create a number sentence that correlates to the word problem and solve.

RESOURCES: VOCABULARY: Common Core State Standards for Mathematics: Common addition and subtraction situations http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf Table 1 on page 88 in the Common Core State Standards (CCSS) for School for Mathematics illustrates twelve addition and subtraction problem situations. ORC # 2807 From the International Reading Association, National Council of Teachers of English and Verizon Thinkfinity: Giant story problems: Reading comprehension through math problem-solving http://www.readwritethink.org/classroom-resources/lesson-plans/giant-story-problems-reading-146.html (Using drawings, equations, and written responses, students work cooperatively in two class sessions to solve Giant Story Problems while they gain practice in reading for information.) Counters, flashcards, and connecting cubes Math Lessons: www.aaastudy.com Math Games: www.gamequarium.com, www.funbrain.com, www.arcademicskillbuilders.com, www.mathisfun.com Games and Worksheets: www.aplusmath.com Math Resources: www.svsu.edu/supo

ADDITION, EQUAL SIGN, SYMBOL, MANIPULATIVE, EQUATION, SUM, DIGIT


WHAT IS A WORD PROBLEM? WHAT STEPS DO I TAKE TO SOLVE A WORD PROBLEM?

5 GRADE: 1st SUBJECT: Math STRAND: Operations and


Description: Apply properties of operations as strategies to add and subtract.2 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.) ACT/Anchor Standard: Make sense of problems and persevere in solving them (MP.1), Reason abstractly and quantitatively (MP.2), Look for and make use of structure (MP.7)

CODE:

1.OA.B.3

Board Objective: I can understand and apply the properties of operations as strategies to add and subtract in order to become a better problem solver.


Global Scholars (Performance Series) Teacher observations and class discussions (anecdotal notes) Create a Fact Family book using a Dominos. This is an independent task that can be used for assessment. Student pick dominos from a bag. Each domino represents two numbers, which can be added to get the biggest number. The easily foldable book, allows student to provide ample samples and record all the necessary information.

Provide investigations that require the identification and then application of a pattern or structure in mathematics. For example, pose a string of addition and subtraction problems involving the same three numbers students analyze structure patterns and create conjectures. (3, 8,11) These conjectures can then be proved with other groups of numbers resulting in an understanding of order and grouping properties of addition and subtraction. The focus of this strategy is to learn and understand the concepts of the commutative and associative properties not to learn the terminology. Expand the work to 3 or more addends to provide the opportunities to change order and/or groupings to make tens. This will allow the connections between place value models and the properties of operations for addition and subtraction to be seen. The concepts of the commutative and associative properties builds flexibility for computation and estimation, a key element of number sense. Continue to provide multiple opportunities to study the relationship between addition and subtraction in a variety of ways, including games, modeling and real-world situations. Common Misconceptions A common misconception with students at this grade is that commutative property applies to subtraction. This is partly due to the misconception that when subtracting one always finds the difference between the two numbers and that they are not dealing with negative numbers. “The larger number should always be placed first is a subtraction problem.” At this age we don’t what the teaching of negative numbers but students can still understand that I am taking away more than I have and that number is below zero or negative. Connections: Understanding and applying properties of operations and the relationship between addition and subtraction (1.OA.3, 1.OA.4) builds on students’ work with composing (K.OA.4) and decomposing (K.OA.3) numbers, solving addition and subtraction word problems (K.OA.2) and adding and subtracting within 5 (K.OA.5) in Kindergarten.

Concrete: To teach the commutative property of addition (which lends itself to a conversation about fact families), provide each student with a ten-‐frame set and ten counters, which should have a different color on each side, usually it is red on one side and yellow on the other. Explain to the students they are going to use these materials to solve some addition problems. Instruct the students to place three counters yellow-‐side up in the first three boxes of the ten-‐frame. Then, ask the students to place two red counters inside the ten-‐frame boxes next to the yellow counters. Ask the students how many counters are in the ten-‐frame total. As a class, work together to create an equation that represents the total by adding the yellow counters and then the red counters. Discuss that the counters or (numbers) can be added another way and the same answer will still be found. This time, as a class, add the red counters and then the yellow counters. Discuss how the two equations are similar and different. At this point, introduce the term

6 commutative property of addition. Continue to practice this property using the ten-‐frame materials. Semi-‐Concrete (Pictorial): The activity presented in the concrete instruction technique can easily be modified to a semi-‐concrete activity. Provide each student with a pre-‐printed ten-‐frame sheet, along with a yellow and red crayon and a pencil. Have the students draw in the two quantities into the ten-‐frame square, such as four yellow dots and 5 red dots. Then, have them write down two equations that represent the total quantity in their ten-‐frame. Abstract: At this point, the students are ready for some project based learning. This is a perfect time to introduce the term “fact families.” Provide each students with a template of a house. Give students three numbers and have them create four facts that use the commutative property of addition and subtraction.

RESOURCES: VOCABULARY: ORC # 3992 From the National Council of Teachers of Mathematics: Balancing equations http://illuminations.nctm.org/LessonDetail.aspx?ID=L77 In this lesson, students will imitate the action of a pan balance and record the modeled subtraction facts in equation form. ORC # 3978 From the National Council of Teachers of Mathematics: How many left? http://illuminations.nctm.org/LessonDetail.aspx?ID=L117 This lesson encourages the students to explore unknown-addend problems using the set model and the game Guess How Many? Counters, flashcards, and connecting cubes

ADDITION, SUBTRACTION, STRATEGY, COMMUTATIVE PROPERTY OF ADDITION, ASSOCIATIVE PROPERTY OF ADDITION, EQUATION, FACT FAMILY, NUMBER SENTENCE

7 Math Lessons: www.aaastudy.com Math Games: www.gamequarium.com, www.funbrain.com, www.arcademicskillbuilders.com, www.mathisfun.com Games and Worksheets: www.aplusmath.com Math Resources: www.svsu.edu/supo ESSENTIAL QUESTIONS:

WHAT IS THE COMMUTATIVE PROPERTY? WHAT IS THE ASSOCIATIVE PROPERTY? WHAT ARE FACT FAMILIES? WHY IS IT IMPORTANT TO TRY DIFFERENT STRATEGIES TO SOLVE ADDITION

AND SUBTRACTION PROBLEMS?



Description: Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8. ACT/Anchor Standard: Attend to precision (MP.6), Look for and make use of structure (MP.7)

CODE:

1.OA.B.4 Board Objective: I can solve a subtraction problems with the understanding that is an unknown-‐addend problem.


Global Scholars (Performance Series) Teacher observations and class discussions (anecdotal notes) Create a Fact Family book using a Dominos. This is an independent task that can be used for assessment. Student pick dominos from a bag. Each domino represents two numbers, which can be added to get the biggest number. The

Provide investigations that require the identification and then application of a pattern or structure in mathematics. For example, pose a string of addition and subtraction problems involving the same three numbers students analyze structure patterns and create conjectures. (3, 8,11) These conjectures can then be proved with other groups of numbers resulting in an understanding of order and grouping properties of addition and subtraction. The focus of this strategy is to learn and understand the concepts of the commutative and associative properties not to learn the terminology. Expand the work to 3 or more addends to provide the opportunities to change order and/or groupings to make tens. This will allow the connections between place value models and the properties of operations for addition and subtraction to be seen. The concepts of the commutative and associative properties builds flexibility for computation and estimation, a key element of number sense. Continue to provide multiple opportunities to study the relationship between addition and subtraction in a variety of ways, including games, modeling and real-world situations. Common Misconceptions A common misconception with students at this grade is that commutative property applies to subtraction. This is partly due to the misconception that when subtracting one always finds the difference between the two numbers and that they are not dealing with negative numbers. “The

Concrete: Provide each student with two ten-‐frame board and twenty counters. Present them with the following math problem: 15-‐9 = ? . Ask the students to put nine counters on the ten-‐frame board. (Using their understanding of the associative property), have the students place one more counter to make ten and discuss how many more are needed to make fifteen. Ask the students how many counters they had to add to the original nine to get to fifteen. The answer should be six, which is the answer to the subtraction problem. Semi-‐Concrete: The concrete process discussed above can be translated into a semi-‐concrete

8 easily foldable book, allows student to provide ample samples and record all the necessary information.

larger number should always be placed first is a subtraction problem.” At this age we don’t what the teaching of negative numbers but students can still understand that I am taking away more than I have and that number is below zero or negative. Connections: Understanding and applying properties of operations and the relationship between addition and subtraction (1.OA.3, 1.OA.4) builds on students’ work with composing (K.OA.4) and decomposing (K.OA.3) numbers, solving addition and subtraction word problems (K.OA.2) and adding and subtracting within 5 (K.OA.5) in Kindergarten.

process with students drawing dots to represent counters within ten-‐frame square when solving subtraction problems. Abstract: Present students with several different thinking strategies to solve subtraction problems using addition. The first method is called “Think Addition.” An example of “Think Addition” follows. Present the following problem to the class: 10 – 2 = ?. Model the following thought process: “2 and what make 10? I know that 8 and 2 make 10. So, 10 – 2 = 8.” The second method is call “Build Up Through 10.” An example of “Build Up Through Ten” follows. Present the following problem to the class: 15 – 9 = ?. Model the following thought process: “I’ll start with 9. I need one more to make 10. Then, I need 5 more to make 15. That’s 1 and 5-‐ so it’s 6. 15 – 9 = 6.”

RESOURCES: VOCABULARY: ORC # 3992 From the National Council of Teachers of Mathematics: Balancing equations http://illuminations.nctm.org/LessonDetail.aspx?ID=L77 In this lesson, students will imitate the action of a pan balance and record the modeled subtraction facts in equation form. ORC # 3978 From the National Council of Teachers of Mathematics: How many left? http://illuminations.nctm.org/LessonDetail.aspx?ID=L117 This lesson encourages the students to explore unknown-addend problems using the set model and the game Guess How Many? Counters, flashcards, and connecting cubes Math Lessons: www.aaastudy.com Math Games: www.gamequarium.com, www.funbrain.com, www.arcademicskillbuilders.com, www.mathisfun.com

SUBTRACTION, ADDEND, EQUATION, NUMBER SENTENCE

9 Games and Worksheets: www.aplusmath.com Math Resources: www.svsu.edu/supo


HOW CAN I USE ADDITION TO HELP ME SOLVE SUBTRACTION PROBLEMS? HOW ARE ADDITION AND SUBTRACTION RELATED? WHY IS IT IMPORTANT TO KNOW DIFFERENT PROBLEM-‐SOLVING STRATEGIES?



Description: Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

ACT/Anchor Standard: Make sense of problems and persevere in solving them (MP.1), Look for and make use of structure (MP.7), Look for and express regularity in reasoning (MP.8)

CODE:

1.OA.C.5 Board Objective: I can relate counting to addition and subtraction to become a better problem solver.


10 Global Scholars (Performance Series) Teacher observations and class discussions (anecdotal notes) Timed addition and subtraction tests Game: Around the World

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 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 students 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 them 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. Common Misconceptions Students ignore the need for regrouping when subtracting within 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. Showing these relationships for each step by using a mathematical drawing or base-ten blocks can build understanding of an efficient strategy for multi-digit subtraction. Connections: Addition, subtraction, composing and decomposing numbers within 10 in Kindergarten (K.OA.1, K.OA.2, K.OA.3) is foundational to the addition and subtraction within 20 in first grade (1.OA.5, 1.OA.6) and fluency in second grade (2.OA.2). Finding the number that makes ten in Kindergarten (K.OA.4) supports the development of addition and subtraction strategies within 20 in first grade (1.OA.6).

Concrete: For addition, write a sample problem on the board, such as 15 + 2 = ___. Then, the student counts out fifteen counters. The student adds two more counters. The student then counts all of the counters starting at 1 (1, 2, 3, 4,…14, 15, 16, 17) to find the total amount. For subtraction, write a sample problem on the board, such as 12 – 3 = ____. The student counts out twelve counters. The student then removes 3 of them. To determine the final amount, the student counts each one (1, 2, 3, 4, 5, 6, 7, 8, 9) to find out the final amount. Semi-‐Concrete: Given the same addition problem as above, the student uses simple pictures or tally marks to represent the addends and then counts to find the sum. Likewise, with subtraction the students uses simple pictures to represent the total quantity and crosses out the amount that is being subtracted, leaving the difference visually evident. Abstract: For addition and subtraction, it is a simple matter of fluently responding to addition or subtraction problems. For the addition problem 15 + 2, the student might hold the number 15 in her head and then hold up one finger and says 16, then hold up another finger and says 17. Resulting in the students knowing that 15 + 2 is 17, since she counted on 2 using her fingers. For the subtraction problem 12 – 3, the

11 student might keep 12 in his head and then counts backwards, “11” as he holds up one finger; says “10” as he holds up a second finger; says “9” as he holds up a third finger. Seeing that he has counted back 3 since he is holding up 3 fingers, the student can state that 12 – 3 = 9.

RESOURCES: VOCABULARY: ORC #4269 From the National Council of Teachers of Mathematics: More and more buttons http://illuminations.nctm.org/LessonDetail.aspx?ID=L26 Students use buttons to create, model, and record addition sentences in this lesson. A Sums to Ten chart is provided for students to use. ORC # 4312 From the National Council of Teachers of Mathematics: Balancing discoveries http://illuminations.nctm.org/LessonDetail.aspx?ID=L55 This lesson encourages students to explore another model of addition, the balance model. The exploration also involves recording the modeled addition facts in equation form. Students begin to memorize the addition facts by playing the Seven-Up game.

ADDITION, SUBTRACTION, SKIP-‐COUNTING, COUNTING ON

12 ORC # 4313 From the National Council of Teachers of Mathematics: Seeing doubles http://illuminations.nctm.org/LessonDetail.aspx?ID=L56 In this lesson, the students focus on dominoes with the same number of spots on each side and on the related addition facts. They make triangle-shaped flash cards for the doubles facts. Number lines, 120 chart, ten-frames and counters Math Lessons: www.aaastudy.com Math Games: www.gamequarium.com, www.funbrain.com, www.arcademicskillbuilders.com, www.mathisfun.com Games and Worksheets: www.aplusmath.com Math Resources: www.svsu.edu/supo ESSENTIAL QUESTIONS:

WHAT IS SKIP-‐COUNTING? HOW CAN I USE ADDITION TO HELP ME COUNT? HOW CAN I USE SUBTRACTION TO HELP ME COUNT? HOW CAN I FIND PATTERNS WHEN COUNTING BY USING

ADDITION OR SUBTRACTION? GRADE: 1st SUBJECT: Math STRAND: Operations and


Description: Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. 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). ACT/Anchor Standard: Make sense of problems and persevere in solving them (MP.1), Look for and make use of structure (MP.7), Look for and express regularity in reasoning (MP.8)

CODE:

1.OA.C.6

Board Objective: I can fluently add and subtract with 10, using a variety of strategies to help me become a better problem solver.



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 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 students 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 them 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. Common Misconceptions Students ignore the need for regrouping when subtracting within 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. Showing these relationships for each step by using a mathematical drawing or base-ten blocks can build understanding of an efficient strategy for multi-digit subtraction. Connections: Addition, subtraction, composing and decomposing numbers within 10 in Kindergarten (K.OA.1, K.OA.2, K.OA.3) is foundational to the addition and subtraction within 20 in first grade (1.OA.5, 1.OA.6) and fluency in second grade (2.OA.2). Finding the number that makes ten in Kindergarten (K.OA.4) supports the development of addition and subtraction strategies within 20 in first grade (1.OA.6).

Concrete: Present students with a world problem and materials manipulative materials. For example, a sample problem and set up might be: Find how amny balls Sara and Sam had all together if Sara had 9 red balls (show 9 red counters) and Sam had 7 yellow balls (show 7 yellow counters). Through a think aloud discussion, help the student decompose 7 yellow counters into 6 and 1 because they understand that 9 plus 1 is 10. First, add up 9 and 1 to get 10. Then, add the remaining 6 counters to get 16. Semi-‐Concrete: At this stage, present the same word problem from above, but instead of using manipulatives to solve and represent the quantities, have the student draw pictures or use tally marks. Abstract: After reading the same world problem above, the student breaks down the values in his head to add to get a group of ten and then adds the remaining numbers to find the answer.

RESOURCES: VOCABULARY: ORC #4269 From the National Council of Teachers of Mathematics: More and more buttons http://illuminations.nctm.org/LessonDetail.aspx?ID=L26 Students use buttons to create, model, and record addition sentences in this lesson. A Sums to Ten chart is provided for students to use. ORC # 4312 From the National Council of Teachers of Mathematics: Balancing discoveries http://illuminations.nctm.org/LessonDetail.aspx?ID=L55 This lesson encourages students to explore another model of addition,

ADDITION, SUBTRACTION, SUM, DIFFERENCE, “COUNTING ON,” “MAKING TEN,” DECOMPOSE, EQUIVALENT

14 the balance model. The exploration also involves recording the modeled addition facts in equation form. Students begin to memorize the addition facts by playing the Seven-Up game. ORC # 4313 From the National Council of Teachers of Mathematics: Seeing doubles http://illuminations.nctm.org/LessonDetail.aspx?ID=L56 In this lesson, the students focus on dominoes with the same number of spots on each side and on the related addition facts. They make triangle-shaped flash cards for the doubles facts. Number lines, 120 chart, ten-frames and counters, connecting cubes Math Lessons: www.aaastudy.com Math Games: www.gamequarium.com, www.funbrain.com, www.arcademicskillbuilders.com, www.mathisfun.com Games and Worksheets: www.aplusmath.com Math Resources: www.svsu.edu/supo ESSENTIAL QUESTIONS:

HOW CAN I USE THE STRATEGY OF COUNTING ON TO HELP ME FLUENTLY SUBTRACT OR ADD? HOW CAN I USE THE STRATEGY OF MAKING TEN OR DECOMPOSING A NUMBER LEADING TO

TEN TO HELP ME FLUENTLY SUBTRACT OR ADD? HOW CAN I CREATE EQUIVALENT SUMS TO HELP ME FLUENTLY SUBTRACT OR ADD? HOW CAN I USE THE RELATIONSHIP BETWEEN ADDITION

AND SUBTRACTION TO SOLVE PROBLEMS?



Description: 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. ACT/Anchor Standard: Reason abstractly and quantitatively (MP.2), Attend to precision (MP.6). Look for and make use of structure (MP.7)

CODE:

1.OA.D.7 Board Objective: I can determine if equations involve addition and subtraction because I understand the meaning of the equal sign.



Provide opportunities for students to use objects of equal weight and a number balance to model equations for addition and subtraction within 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 + 5 = 5 + 8 Commutative Property for Addition 3 + 7 + 4 = 10 + 4 Associative Property for Addition Ask students to determine whether the equations are true or false and to 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. As a class, students then discuss their thinking that supports their answers. Provide numerous experiences for students to compose and decompose numbers within 20 using a variety of manipulatives. Have students represent their work with drawings, words, and numbers. Ask students to share their work and thinking with their classmates. Then ask the class identify similarities and differences in the students’ representations. Connections: First graders build on decomposing numbers less than or equal to 10 (K.OA.3) and finding the number that makes 10 for a given number ( K.OA.4) in kindergarten to develop the concept of equality (1.OA.7) and determine the unknown whole number in an addition or subraction equation (1.OA.8). This work in Grade 1 prepares students to be fluent in adding and subtracting within 20 in Grade 2. Common Misconceptions Many 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 equals 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 – 5 = 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, give students experiences with the meaning of = sign as is the same as and equations with one number to the left.

Concrete: Use a bucket balance to show the purpose of the equal sign. Place a pronblem like 5 + 8 = 13. Explain to the students that equal sign means the amount has to be the same on both sides. Put 5 and 8 counter in one bucket and place 13 counters in the other bucket. The balance should equal just like the number sentence shows with the equal sign. Semi-‐Concrete: Using the same problem as above, the student draw 5 for the first addend and 8 for the second addend. Then, the students draws 13 on the other side of the equal sign to represent the sum. The student can count the number of images they drew on either side and see how the total is the same. Abstract: The student is able to add and subtract an equation whether the sum or difference is presented at the start or end of the problem.

RESOURCES: VOCABULARY: ORC # 4321 From the National Council of Teachers of Mathematics: Finding the Balance http://illuminations.nctm.org/LessonDetail.aspx?ID=L106 This lesson encourages students to explore another model of subtraction, the balance. Students will use real and virtual balances. Students also explore recording the modeled subtraction facts in

EQUAL SIGN, ADDITION, SUBTRACTION, EQUATION, TRUE, FALSE

16 equation form. Click on Pan Balance – Shapes to get to the online tool Pan Balance – Numbers. This virtual tool can be used to strengthen students’ understanding and computation of numerical expressions and equality. A variety of objects that can be used for modeling and solving addition and subtraction problems: Number balances, Five-frames, ten-frames and double ten-frames Number lines, 120 chart, ten-frames and counters, connecting cubes Math Lessons: www.aaastudy.com Math Games: www.gamequarium.com, www.funbrain.com, www.arcademicskillbuilders.com, www.mathisfun.com Games and Worksheets: www.aplusmath.com Math Resources: www.svsu.edu/supo ESSENTIAL QUESTIONS:

WHAT ARE THE PARTS OF A NUMBER SENTENCE OR EQUATION? WHAT DOES THE EQUAL SIGN MEAN?



Description: 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 = _ – 3, 6 + 6 = _. ACT/Anchor Standard: Reason abstractly and quantitatively (MP.2), Attend to precision (MP.6), Look for and make use of structure (MP.7)

CODE:

1.OA.D.8 Board Objective: I can determine the unknown whole number in an addition and subtraction equation because I understand the three parts of an equation.



Provide opportunities for students to use objects of equal weight and a number balance to model equations for addition and subtraction within 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 + 5 = 5 + 8 Commutative Property for Addition 3 + 7 + 4 = 10 + 4 Associative Property for Addition Ask students to determine whether the equations are true or false and to 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. As a class, students then discuss their thinking that supports their answers. Provide numerous experiences for students to compose and decompose numbers within 20 using a variety of manipulatives. Have students represent their work with drawings, words, and numbers. Ask students to share their work and thinking with their classmates. Then ask the class identify similarities and differences in the students’ representations. Connections: First graders build on decomposing numbers less than or equal to 10 (K.OA.3) and finding the number that makes 10 for a given number ( K.OA.4) in kindergarten to develop the concept of equality (1.OA.7) and determine the unknown whole number in an addition or subraction equation (1.OA.8). This work in Grade 1 prepares students to be fluent in adding and subtracting within 20 in Grade 2. Common Misconceptions Many 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 equals 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 – 5 = 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, give students experiences with the meaning of = sign as is the same as and equations with one number to the left.

Concrete: Read a simple word problem, such as: “There were five cookies. I ate some and now there were three left. How many did I eat?”. Set out three connecting cubes, acknowledging that there are three cookies left. Then, count on, attaching two more cubes to get to five, realizing the missing value is two. Semi-‐Concrete: Using the cookie word problem from above, sketch out three tally marks. Then, count and draw however many more tally marks it takes to get to five, realizing that the missing value is two. Abstract: Using the cookie word problem from above, the student asks himself what goes with three to make five. The student deduces that two plus three equals five and is able to solve the problem abstractly.

RESOURCES: VOCABULARY: ORC # 4321 From the National Council of Teachers of Mathematics: Finding the Balance http://illuminations.nctm.org/LessonDetail.aspx?ID=L106 This lesson encourages students to explore another model of subtraction, the balance. Students will use real and virtual balances. Students also explore recording the modeled subtraction facts in

EQUAL SIGN, ADDITION, SUBTRACTION, EQUATION, TRUE, FALSE

18 equation form. Click on Pan Balance – Shapes to get to the online tool Pan Balance – Numbers. This virtual tool can be used to strengthen students’ understanding and computation of numerical expressions and equality. A variety of objects that can be used for modeling and solving addition and subtraction problems: Number balances, Five-frames, ten-frames and double ten-frames Number lines, 120 chart, ten-frames and counters, connecting cubes Math Lessons: www.aaastudy.com Math Games: www.gamequarium.com, www.funbrain.com, www.arcademicskillbuilders.com, www.mathisfun.com Games and Worksheets: www.aplusmath.com Math Resources: www.svsu.edu/supo ESSENTIAL QUESTIONS:

WHAT ARE THE PARTS OF A NUMBER SENTENCE OR EQUATION? WHAT DOES THE EQUAL SIGN MEAN?

GRADE: 1st SUBJECT: Math STRAND: Numbers and

Operations in Base Ten MONTH(S) TAUGHT:

Description: Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. ACT/Anchor Standard: Use tools appropriately (MP.5), Attend to precision (MP.6), Look for and make use of structure (MP.7),

CODE:

1.NBT.A.1 Board Objective: I can count to 120, starting at any point before 120. I can read and write numerals within 120. I can represent a number of

objects within 120 with a written numeral.


19 Global Scholars (Performance Series) Teacher observations and class discussions (anecdotal notes) Oral skip count Count back with base-‐ten blocks Give each student a 120 chart with a limited amount of numbers inside and ask the students to complete the 120 chart.

Instructional Strategies In this grade, students build on their counting to 100 by ones and tens beginning with numbers other than 1 in Kindergarten. Students should use materials to count by ones and tens to build models for numbers. They can start at any number less than 120 and count to 120. Students learn to use numerals to represent numbers by relating their place-value notation to their models. They should build on their experiences with numbers 0 to 20 in Kindergarten to create models for 21 to 120 with groupable and pregroupable materials (see Resources/Tools). Students represent the models by placing numerals in labeled hundreds, tens and ones columns. They eventually move to representing the numbers in standard form, where the group of hundred, tens then singles shown in the model matches the left-to-right order of digits in numbers. As first graders learn to understand that the position of each digit in a number impacts the quantity of the number, they become more aware of the order of the digits when they write numbers. For example, a student may write “17” and mean “71”. Through teacher demonstration, opportunities to “find mistakes”, and questioning by the teacher (“I am reading this and it says seventeen. Did you mean seventeen or seventy-one? How can you change the number so that it reads seventy-one?”), students become precise as they write numbers to 120. Post the number words in the classroom to help students read and write them. Connections: K.CC.1; K.CC.2; K.CC.3; K.NBT.1

Concrete: Use manipulatives, such as connecting cubes or base-‐ten blocks to count. Semi-‐Concrete: Students can use tally marks or simple drawings to represent numerals that they read or trying to recognize. Abstract: Student count and recognize numerals on a 120 chart.

RESOURCES: VOCABULARY: Groupable models Beans and a small cup for 10 beans Linking cubes Plastic chain links Pregrouped materials Strips (ten connected squares) and squares Base-ten blocks Beans and beans sticks (10 beans glued on a craft stick) Ten-frame Place value mat or chart Graph paper with numbers from 1 to 120 in rows Math Lessons: www.aaastudy.com Math Games: www.gamequarium.com, www.funbrain.com, www.arcademicskillbuilders.com, www.mathisfun.com Games and Worksheets: www.aplusmath.com Math Resources: www.svsu.edu/supo

NUMERAL, COUNTING, PLACE-‐VALUE, TENS, ONES, HUNDREDS, DIGIT

20 ESSENTIAL QUESTIONS:

WHY IS IT IMPORTANT TO COUNT IN ORDER? WHY IS IT IMPORTANT TO READ AND WRITE NUMBERS CORRECTLY?



Description: Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:

a. 10 can be thought of as a bundle of ten ones — called a “ten.” b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

ACT/Anchor Standard: Reason abstractly and quantitatively (MP.2), Model for mathematics (MP.4), Use appropriate tools strategically (MP.5), Look for and express regularity in repeated reasoning (MP.8)

CODE:

1.NBT.B2

Board Objective: I can express a two digit number as an amount of tens and ones.


Global Scholars (Performance Series) Teacher observations and class discussions (anecdotal notes) Counting and representing numbers with base-‐ten blocks

First Grade students are introduced to the idea that a bundle of ten ones is called “a ten”. This is known as unitizing. When First Grade students unitize a group of ten ones as a whole unit (“a ten”), they are able to count groups as though they were individual objects. For example, 4 trains of ten cubes each have a value of 10 and would be counted as 40 rather than as 4. This is a monumental shift in thinking, and can often be challenging for young children to consider a group of something as “one” when all previous experiences have been counting single objects. This is the foundation of the place value system and requires time and rich experiences with concrete manipulatives to develop. A student’s ability to conserve number is an important aspect of this standard. It is not obvious to young children that 42 cubes is the same amount as 4 tens and 2 left-overs. It is also not obvious that 42 could also be composed of 2 groups of 10 and 22 leftovers. Therefore, first graders require ample time grouping proportional objects (e.g.,cubes, beans, beads, ten-frames) to make groups of ten, rather than using pre-grouped materials (e.g., base ten blocks, pre-made bean sticks) that have to be “traded” or are non-proportional (e.g., money). First Grade students extend their work from Kindergarten when they composed and decomposed numbers from 11 to 19 into ten ones and some further ones. In Kindergarten, everything was thought of as individual units: “ones”. In First Grade, students are asked to unitize those ten individual ones as a whole unit: “one ten”. Students in first grade explore the idea that the teen numbers (11 to 19) can be expressed as one ten and some leftover ones. Ample experiences with a variety of groupable materials that are proportional (e.g., cubes, links, beans, beads) and ten frames help students develop this concept. Ample experiences with a

Concrete: There are a variety of manipulatives that students can use to represent place value. Groupable objects verses pre-‐grouped objects are preferred. Using connecting cubes, have the students express the number 24. There are a variety of ways that the cubes can be grouped. Discussing place value, lead the children to group their cubes into two groups of two and four ones to match the place value of each numeral in the number 24. Semi-‐Concrete: At this stage in the learning process, use a place value mat that has the ones and tens places labeled. Have students draw images that are representative of the base-‐ten blocks to show the value of a given number. For example, if the student is asked to

21 variety of groupable materials that are proportional (e.g., cubes, links, beans, beads) and ten frames allow students opportunities to create tens and break apart tens, rather than “trade” one for another. Since students first learning about place value concepts primarily rely on counting, the physical opportunity to build tens helps them to “see” that a “ten stick” has “ten items” within it. Pre-grouped materials (e.g., base ten blocks, bean sticks) are not introduced or used until a student has a firm understanding of composing and decomposing tens. (Van de Walle & Lovin, 2006)

represent the number 42 with place-‐value blocks, the student would draw four groups of ten and two ones in the respective areas of the place value mat. Abstract: At this stage in learning, students should be able to immediately recognize the place-‐value of each number in a given numeral and identify the quantity of tens and ones that are in the number. For example, if the student is asked about the place value of the number 85, the students should be able to explain that the five is in the ones place so that means there are five ones and the eight is the tens place so that means there are eight groups of ten or eighty ones. To extend this learning, the students can express the number 85 using expanded notation, which would look like 80 + 5 = 85.

RESOURCES: VOCABULARY: Base Ten Blocks Sticks and other counters Coins (penny and dime replicas) Ten Frames Number line National Library of virtual manipulatives Base Ten Block.(Adjust the application to only deal with ones and tens) http://nlvm.usu.edu/en/nav/frames_asid_152_g_1_t_1.html?from=category_g_1_t_1.html Math Lessons: www.aaastudy.com Math Games: www.gamequarium.com, www.funbrain.com, www.arcademicskillbuilders.com, www.mathisfun.com Games and Worksheets: www.aplusmath.com Math Resources: www.svsu.edu/supo

ONES, TENS, PLACE-‐VALUE, EXPANDED NOTATION

22 ESSENTIAL QUESTIONS:

WHAT IS A GROUP OF TEN? HOW MANY ONES MAKE A GROUP OF TEN? WHY IS IT IMPORTANT TO UNDERSTAND PLACE-‐VALUE?



Description: Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, 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 and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. ACT/Anchor Standard: Make sense of problems and persevere in solving them (MP.1), Reason abstractly and quantitatively (MP.2), Model with mathematics (MP.3), Attend to precision (MP. 6), Look for and make use of structure (MP.7),

CODE:

1.NBT.C4

Board Objective: I can add a one-‐digit number and a two-‐digit number within 100 using drawings, models or strategies to help me become a better problem solver. I can add two two-‐digit numbers within 100 using drawings, models, or strategies to help me become a better problem solver.


Global Scholars (Performance Series) Teacher observations and class discussions (anecdotal notes) Counting and representing numbers with base-‐ten blocks Game: Around the World Timed Tests

First Grade students use concrete materials, models, drawings and place value strategies to add within 100. They do so by being flexible with numbers as they use the base-ten system to solve problems. The standard algorithm of carrying or borrowing is neither an expectation nor a focus in First Grade. Students use strategies for addition and subtraction in Grades K-3. By the end of Third Grade students use a range of algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction to fluently add and subtract within 1000. Students are expected to fluently add and subtract multi-digit whole numbers using the standard algorithm by the end of Grade 4. 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. Students will solve problems using concrete models and drawings to support and record solutions strategies. Then students will typically use base-ten concepts, properties of operations, and the relationship between addition and subtraction to invent their own strategies. Student-invented strategies do not use physical objects and counting by ones; some will be done mentally. Help students share, explore, and record their strategies. Encourage students to try strategies invented by their classmates. Have students connect a hundreds chart to their invented strategy for finding ten more and ten less than a given number. Ask them to record their strategy and explain their reasoning.

Concrete: Base-‐ten blocks or ten-‐frames can be used to concretely demonstrate the process of addition. For example, present the students with a word problem, such as the following: “24 red apples and 8 green apples are on the table. How many apples are on the table?”. Guide the students through the process of solving the word problem using ten-‐frames. Instruct the students to put 24 chips in 3 ten-‐frames and then count out 8 more chips. Six of them fill up the third ten-‐frame, which means there are 2 left over, resulting in an answer of 3 tens and 2 ones or 32. Semi-‐Concrete: Present the students with a word problem, such as the following: “24 red apples and 8 green apples are on the table. How

23 many apples are on the table?”. Using an open number line, model for students how to solve the problem. Decompose 8 into 6 and 2 and make six jumps to get to 30 and then two more to get to 32, mimicking the similar process done with the concrete strategy. Abstract: Present the students with a word problem, such as the following: “24 red apples and 8 green apples are on the table. How many apples are on the table?”. Using the relationship between addition and subtraction, model how to solve the following word problem, which asks students to find the sum of 24 and 8. Explain to the students that, you will turn 8 into 10 by adding 2 because 24 plus 10 is much easier to add. Then, you will take your answer from 24 plus 10 and subtract 2 to because you added 2 extra to start, giving you a final answer of 32.

RESOURCES: VOCABULARY: Groupable models Beans and a small cup for 10 beans Linking cubes Plastic chain links Pregrouped materials Strips (ten connected squares) and squares Base-ten blocks Beans and beans sticks (10 beans glued on a craft stick) Ten-frame Place value mat or chart Graph paper with numbers from 1 to 120 in rows Hundreds chart Math Lessons: www.aaastudy.com Math Games: www.gamequarium.com, www.funbrain.com,

TENS, ONES, ONE-‐DIGIT, TWO-‐DIGIT, ADDITION, COMPOSE, DECOMPOSE

24 www.arcademicskillbuilders.com, www.mathisfun.com Games and Worksheets: www.aplusmath.com Math Resources: www.svsu.edu/supo


HOW DO NUMBERS GO TOGETHER? HOW DO NUMBERS CHANGE? HOW CAN I USE MY UNDERSTANDING OF PLACE-‐VALUE TO SOLVE AN ADDITION PROBLEM WITH TWO-‐DIGIT NUMBERS?



Description: Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. ACT/Anchor Standard: Reason abstractly and quantitatively (MP.2), Construct viable arguments and critique the reasoning of others (MP.3), Look for and express regularity in repeated reasoning (MP.8)

CODE:

1.NBT.C5 Board Objective: I can mentally find 10 more or 10 less of a given two-‐digit number, explaining my problem-‐solving strategy.



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. Students will solve problems using concrete models and drawings to support and record solutions strategies. Then students will typically use base-ten concepts, properties of operations, and the relationship between addition and subtraction to invent their own strategies. Student-invented strategies do not use physical objects and counting by ones; some will be done mentally. Help students share, explore, and record their strategies. Encourage students to try strategies invented by their classmates. First Graders build on their county by tens work in Kindergarten by mentally adding ten more and ten less than any number less than 100. First graders are not expected to compute differences of two-digit numbers other than multiples of ten. Ample experiences with ten frames and the number line provide students with opportunities to think about groups of ten, moving them beyond simply rote counting by tens on and off the decade. Such representations lead to solving such problems mentally.

Concrete: Using base-‐ten blocks or ten-‐frames are appropriate manipulatives for demonstrating how to add and subtract 10 more or less mentally. To use base-‐ten blocks, begin with a given quantity represented on a place-‐value mat. Students can remove or add groups of ten to and visually see how the number changes by adding ten more or ten less. Likewise, ten-‐frames can be filled and or emptied to show how a number changes by adding ten more or subtracting ten less from the original quantity. Semi-‐Concrete: Students can use a 120 chart and their knowledge of number patterns to determine ten more or ten less than a number. For example, if the given problem is 63

25 +10, model for the students how to jump down one row to the answer 73, explaining that by jumping down one row you understand that means you moved down ten spaces. Likewise, if the given problem is 63 + 20, jump down one row to 73 and explain that you understand that means you moved down ten spaces. However, jump down one more row to 83, explaining that you knew you needed to move down ten more spaces in order to correctly add 20 to the number 63. Abstract: If a student is given the same problem of 63 + 20, model how to reason that ten more than 63 is 73 and ten more than 73 is 83, which is the answer.

RESOURCES: VOCABULARY: Groupable models Beans and a small cup for 10 beans Linking cubes Plastic chain links Pregrouped materials Strips (ten connected squares) and squares Base-ten blocks Beans and beans sticks (10 beans glued on a craft stick) Ten-frame Place value mat or chart Graph paper with numbers from 1 to 120 in rows Hundreds chart Math Lessons: www.aaastudy.com Math Games: www.gamequarium.com, www.funbrain.com, www.arcademicskillbuilders.com, www.mathisfun.com Games and Worksheets: www.aplusmath.com Math Resources: www.svsu.edu/supo

ADDITION, SUBTRACTION, MORE, LESS, MENTALLY


HOW DO NUMBERS CHANGE? HOW ARE PATTERNS AND COUNTING RELATED?

26



Description: Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), 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 and explain the reasoning used. ACT/Anchor Standard: Make sense of problems and persevere in solving them (MP.1), Reason abstractly and quantitatively (MP.2), Construct viable arguments and critique the reasoning of others (MP.3), Use appropriate tools strategically (MP.5), Attend to precision (MP. 6)

CODE:

1.NBT.C6

Board Objective: I can subtract multiples of 10, using models, drawing and strategies to become a better problem solver. I can subtract multiples of 10 and explain my problem-‐solving method with in writing or with words.



First Graders build on their county by tens work in Kindergarten by mentally adding ten more and ten less than any number less than 100. First graders are not expected to compute differences of two-digit numbers other than multiples of ten. Ample experiences with ten frames and the number line provide students with opportunities to think about groups of ten, moving them beyond simply rote counting by tens on and off the decade. Such representations lead to solving such problems mentally. 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. Students will solve problems using concrete models and drawings to support and record solutions strategies. Then students will typically use base-ten concepts, properties of operations, and the relationship between addition and subtraction to invent their own strategies. Student-invented strategies do not use physical objects and counting by ones; some will be done mentally. Help students share, explore, and record their strategies. Encourage students to try strategies invented by their classmates.

Concrete: Present the students with a word problem or similar word problem to the frame the lesson conversation: “There are 60 students in the gym. 30 students leave. How many students are still in the gym?”. Using ten-‐frames, build 6 ten-‐frames to represent 60 and then remove 3 ten-‐frames, explaining to the students that this shows the 30 students that left. The remaining 3 ten-‐frames that were not removed represents the answer. Semi-‐Concrete: Present the students with a word problem or similar word problem to the frame the lesson conversation: “There are 60 students in the gym. 30 students leave. How many students are still in the gym?”. Using a number line, model how to start on 60 and move back 3 jumps of 10 to get 30, finding the solution to the word problem. Abstract: Present the students with a word problem or similar word problem to the frame the lesson

27 conversation: “There are 60 students in the gym. 30 students leave. How many students are still in the gym?”. Model how to use the relationship between addition and subtraction to find the solution. For example, think out-‐loud “30 and what makes 60? I know that 3 and 3 is 6. So, 30 and 30 must be 60, which means the answer to the problem is 30 students still in the gym.”

RESOURCES: VOCABULARY: Groupable models Beans and a small cup for 10 beans Linking cubes Plastic chain links Pregrouped materials Strips (ten connected squares) and squares Base-ten blocks Beans and beans sticks (10 beans glued on a craft stick) Ten-frame Place value mat or chart Graph paper with numbers from 1 to 120 in rows Hundreds chart Math Lessons: www.aaastudy.com Math Games: www.gamequarium.com, www.funbrain.com, www.arcademicskillbuilders.com, www.mathisfun.com Games and Worksheets: www.aplusmath.com Math Resources: www.svsu.edu/supo

SUBTRACTION, TENS, ADDITION, MODEL, PLACE-‐VALUE, ONES


HOW DO NUMBERS CHANGE? HOW CAN I USE MY UNDERSTANDING OF PLACE-‐VALUE TO SOLVE A SUBTRACTION PROBLEM?

28

GRADE: 1st SUBJECT: Math STRAND: Numbers and Operations in Base Ten

MONTH(S) TAUGHT:

Description: Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. ACT/Anchor Standard: Reason abstractly and quantitatively (MP.2), Model with mathematics (MP.4),

CODE:

1.NBT.B3 Board Objective: I can compare two two-‐digit numbers based on the meanings of tens and ones digits, using appropriate math symbols.


Global Scholars (Performance Series) Teacher observations and class discussions (anecdotal notes) Counting and representing numbers with base-‐ten blocks

First Grade students use their understanding of groups and order of digits to compare two numbers by examining the amount of tens and ones in each number. After numerous experiences verbally comparing two sets of objects using comparison vocabulary (e.g., 42 is more than 31. 23 is less than 52, 61 is the same amount as 61.), first grade students connect the vocabulary to the symbols: greater than (>), less than (<), equal to (=). Common Misconceptions Often when students learn to use an aid (Pac Man, bird, alligator,…etc) for knowing which comparison sign (<,>,= ) to use, the students never associate the real meaning and name with the sign. The use of the learning aids must be accompanied by the connection to the names: <Less Than, > Greater Than, and = equal to. More importantly, students need to begin to develop the understanding of what it means for one number to be greater than another. At first grade, it means that this number has more tens, or the same number of tens, but with more ones, making it greater. Additionally, the symbols are shortcuts for writing down this relationship. Finally, students need to begin understanding that both symbols (<,>) can create true statements about any two numbers where one is greater/smaller than the other, (15 < 28 and 28 >15).

Concrete: Give students two numbers to compare. Have the students represent each number using base-‐ten blocks. Look at the number carefully and first count how many tens each number has. The number with the greater number of tens is the bigger number. However, if the number of tens is the same, then the students need to compare the number of ones each number has. The number, in this case, with the greater number of ones is the bigger number. After students have examined the numbers carefully, place the appropriate symbol between the numbers to create a true statement. Semi-‐Concrete: Using a similar process as the concrete instructional method, students should draw the value of the two numbers being compared and have the same discussions about the number of tens and if needed, the number of ones, in the numerals being compared. After the students have examined the numbers carefully, they should place the appropriate

29 symbol between the numbers to create a true statement. Abstract: Students should use mental reasoning and think-‐alouds, as they compare two numbers. For example, if students are asked to compare the number 42 and 45. A student think-‐aloud might sound like the following: “42 has 4 tens and 2 ones. 45 have 4 tens and 5 ones. They have the same number of tens, but 45 has more ones than 42. So, 42 is less than 45.”

RESOURCES: VOCABULARY: Base Ten Blocks Sticks and other counters Coins (penny and dime replicas) Ten Frames Number line National Library of virtual manipulatives Base Ten Block.(Adjust the application to only deal with ones and tens) http://nlvm.usu.edu/en/nav/frames_asid_152_g_1_t_1.html?from=category_g_1_t_1.html Math Lessons: www.aaastudy.com Math Games: www.gamequarium.com, www.funbrain.com, www.arcademicskillbuilders.com, www.mathisfun.com Games and Worksheets: www.aplusmath.com Math Resources: www.svsu.edu/supo

TENS, ONES, COMPARE, GREATER THAN SYMBOL, LESS THAN SYMBOL, TWO-‐DIGIT NUMBER, ONE-‐DIGIT NUMBER


WHAT ARE NUMBERS? HOW DO WE GROUP NUMBERS? HOW DO WE COMPARE NUMBERS?

GRADE: 1st SUBJECT: Math STRAND: Measurement and

Data MONTH(S) TAUGHT:

CODE: Description: Order three objects by length; compare the lengths of two objects indirectly by using a third object.

30 ACT/Anchor Standard: Use appropriate tools strategically (MP.5), Attend to precision (MP.6)

1.MD.A.1 Board Objective: I can order three objects by length. I can order three objects by length, comparing the lengths of two objects indirectly by using a third object.


Global Scholars (Performance Series) Teacher observations and class discussions (anecdotal notes) Kid-‐Steps (Non-‐standard Unit of Measurement Comparison Assessment Task): Place various strips of masking tape around the classroom. Letter each piece of tape A-‐H. Then, have the students go around and practice measuring each piece of tape using 'kid steps'. Have the students record their findings on their record sheet and compare the pieces of tape. When they finish, come together as a class and shared our measurements.

The measure of an attribute is a count of how many units are needed to fill, cover or match the attribute of the object being measured. Students need to understand what a unit of measure is and how it is used to find a measurement. They need to predict the measurement, find the measurement and then discuss the estimates, errors and the measuring process. It is important for students to measure the same attribute of an object with different-‐sized units. It is beneficial to use informal units for beginning measurement activities at all grade levels because they allow students to focus on the attributes being measured. The numbers for the measurements can be kept manageable by simply adjusting the size of the units and experiences with informal units promote the need for measuring with standard units. Measurement units share the attribute being measured. Students need to use as many copies of the length unit as necessary to match the length being measured. For instance, use large footprints with the same size as length units. Place the footprints end to end, without gaps or overlaps, to measure the length of a room to the nearest whole footprint. Use language that reflects the approximate nature of measurement, such as the length of the room is about 19 footprints. Students need to also measure the lengths of curves and other distances that are not straight lines. Students need to make their own measuring tools. For instance, they can place paper clips end to end along a piece of cardboard, make marks at the endpoints of the clips and color in the spaces. Students can now see that the spaces represent the unit of measure, not the marks or numbers on a ruler. Eventually they write numbers in the center of the spaces. Encourage students not to use the end of the ruler as a starting point. Compare and discuss two measurements of the same distance, one found by using a ruler and one found by aligning the actual units end to end, as in a chain of paper clips. Students should also measure lengths that are longer than a ruler. When students use reasoning to compare measurements indirectly. To order the lengths Objects A, B and C, examine then compare the lengths of Object A and Object B and the lengths of Object B and Object C. The results of these two comparisons allow students to use reasoning to determine how the length of Object A compares to the length of Object C. For example, to order three objects by their lengths, reason that if Object A is smaller than Object B and Object B is smaller than Object C, then Object A has to be smaller than Object C. The

Concrete: If students are asked to compare the lengths of a given set of objects, cut pieces of yarn to the length of each object and allow the student to manipulate the pieces of yarn, arranging them longest to shortest or shortest to longest, depending on the nature of the problem. Semi-‐Concrete: Frame the lesson conversation with the following word problem: “The snake handler is trying to put the snakes in order-‐ from shortest to longest. She knows that the red snake is longer than the green snake. She also knows that the green snake is longer than the blue snake. What order should she put the snakes?” Using colored pencils to match the color of the snacks, sketch out the length of each snake, one-‐by-‐one, using comparison and indirect measurement, while reading the problem. After all the snakes have been sketched, the student can visually determine the order of the snakes. Abstract: Frame the lesson conversation with the following word problem: “The snake handler is trying to put the snakes in order-‐ from shortest to longest. She knows that the red snake is longer than the green snake. She also knows that the

31 order of objects by their length from smallest to largest would be Object A -‐ Object B -‐ Object C.

green snake is longer than the blue snake. What order should she put the snakes?” Using a think-‐aloud process or think-‐pair-‐share, allow students to mentally reason the order of the snakes. A think-‐aloud might look like the following: “Ok. I know that the red snake is longer than the green snake and the blue snake because. Since it’s longer than the green, that means that it’s also longer than the blue snake. So the longest snake is the red snake. I also know that the green snake and red snake are both longer than the blue snake. So, the blue snake is the shortest snake. That means that the green snake is the medium sized snake.”

RESOURCES: VOCABULARY: ORC # 4329 From the National Council of Teachers of Mathematics: The Length of My Feet http://illuminations.nctm.org/LessonDetail.aspx?ID=L124 This lesson focuses students’ attention on the attributes of length and develops their knowledge of and skill in using nonstandard units of measurement. ORC # 1485 From the American Association for the Advancement of Science: Estimation and Measurement http://www.sciencenetlinks.com/lessons.php?DocID=243 In this lesson students will use nonstandard units to estimate and measure distances. In this lesson students will use nonstandard units to estimate and measure distances. Clothesline rope Yarn Toothpicks Straws Paper clips

LENGTH, MEASURE, COMPARE, INDIRECTLY, (ORDINAL NUMBERS-‐FIRST, SECOND, THIRD WHEN

USED IN REFERENCE TO MEASUREMENT PROBLEM-‐SOLVING), OBJECT, LINE, STRAIGHT, ADD, COUNT, SHORTER, LONGER

32 Connecting cubes Cuisenaire rods A variety of common two- and three-dimensional objects Strips of tagboard or cardboard Math Lessons: www.aaastudy.com Math Games: www.gamequarium.com, www.funbrain.com, www.arcademicskillbuilders.com, www.mathisfun.com Games and Worksheets: www.aplusmath.com Math Resources: www.svsu.edu/supo ESSENTIAL QUESTIONS:

WHAT IS MEASUREMENT? WHAT CAN WE MEASURE? WHAT ARE NON-‐STANDARD UNITS OF MEASUREMENT? WHAT ARE STANDARD UNITS OF MEASUREMENT?



Description: Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps. ACT/Anchor Standard: Use appropriate tools strategically (MP.5), Attend to precision (MP.6)

CODE:

1.MD.A.2

Board Objective: I can correctly measure the length of an object and express the length of the object as a whole number of length units.


33 Global Scholars (Performance Series) Teacher observations and class discussions (anecdotal notes) Create and Write Measurement Assessment Task: Have each student trace and cut out their own foot print. Then, using small, lightweight objects and food items that can easily be glued, such as Fruit Loops, marshmallows, Corn Chex, or even small stickers, have them measure the length of their foot. (The students can write about their measurements and the mathematical process in writing.)

The measure of an attribute is a count of how many units are needed to fill, cover or match the attribute of the object being measured. Students need to understand what a unit of measure is and how it is used to find a measurement. They need to predict the measurement, find the measurement and then discuss the estimates, errors and the measuring process. It is important for students to measure the same attribute of an object with different-‐sized units. It is beneficial to use informal units for beginning measurement activities at all grade levels because they allow students to focus on the attributes being measured. The numbers for the measurements can be kept manageable by simply adjusting the size of the units and experiences with informal units promote the need for measuring with standard units. Measurement units share the attribute being measured. Students need to use as many copies of the length unit as necessary to match the length being measured. For instance, use large footprints with the same size as length units. Place the footprints end to end, without gaps or overlaps, to measure the length of a room to the nearest whole footprint. Use language that reflects the approximate nature of measurement, such as the length of the room is about 19 footprints. Students need to also measure the lengths of curves and other distances that are not straight lines. Students need to make their own measuring tools. For instance, they can place paper clips end to end along a piece of cardboard, make marks at the endpoints of the clips and color in the spaces. Students can now see that the spaces represent the unit of measure, not the marks or numbers on a ruler. Eventually they write numbers in the center of the spaces. Encourage students not to use the end of the ruler as a starting point. Compare and discuss two measurements of the same distance, one found by using a ruler and one found by aligning the actual units end to end, as in a chain of paper clips. Students should also measure lengths that are longer than a ruler. When students use reasoning to compare measurements indirectly. To order the lengths Objects A, B and C, examine then compare the lengths of Object A and Object B and the lengths of Object B and Object C. The results of these two comparisons allow students to use reasoning to determine how the length of Object A compares to the length of Object C. For example, to order three objects by their lengths, reason that if Object A is smaller than Object B and Object B is smaller than Object C, then Object A has to be smaller than Object C. The order of objects by their length from smallest to largest would be Object A -‐ Object B -‐ Object C.

Concrete: If students are asked to determine the length of an object or which is object in a group is longest/shortest, use tiles, paperclips or other small non-‐standard units of measurements to measure and compare with. Semi-‐Concrete and Concrete: If students are asked to determine the length of an object or which object in a group is longest/shortest, provide each student with an inch rules and compare the number of inches (the numerical value) long each object is.

RESOURCES: VOCABULARY:

34 ORC # 4329 From the National Council of Teachers of Mathematics: The Length of My Feet http://illuminations.nctm.org/LessonDetail.aspx?ID=L124 This lesson focuses students’ attention on the attributes of length and develops their knowledge of and skill in using nonstandard units of measurement. ORC # 1485 From the American Association for the Advancement of Science: Estimation and Measurement http://www.sciencenetlinks.com/lessons.php?DocID=243 In this lesson students will use nonstandard units to estimate and measure distances. In this lesson students will use nonstandard units to estimate and measure distances. Clothesline rope Yarn Toothpicks Straws Paper clips Connecting cubes Cuisenaire rods A variety of common two- and three-dimensional objects Strips of tagboard or cardboard Math Lessons: www.aaastudy.com Math Games: www.gamequarium.com, www.funbrain.com, www.arcademicskillbuilders.com, www.mathisfun.com Games and Worksheets: www.aplusmath.com Math Resources: www.svsu.edu/supo

LENGTH, MEASURE, COMPARE, INDIRECTLY, (ORDINAL NUMBERS-‐FIRST, SECOND, THIRD WHEN

USED IN REFERENCE TO MEASUREMENT PROBLEM-‐SOLVING), OBJECT, LINE, STRAIGHT, ADD, COUNT, SHORTER, LONGER


WHAT IS MEASUREMENT? WHAT CAN WE MEASURE? WHAT ARE NON-‐STANDARD UNITS OF MEASUREMENT? WHAT ARE STANDARD UNITS OF MEASUREMENT?



CODE: Description: Tell and write time in hours and half-hours using analog and digital clocks.

35 ACT/Anchor Standard: Use appropriate tools strategically (MP.5), Attend to precision (MP.6)

1.MD.B.3 Board Objective: I can tell and write time in hours using analog and digital clocks. I can tell and write time in half-‐hours using analog and digital clocks.


Global Scholars (Performance Series) Teacher observations and class discussions (anecdotal notes) Orally tell time when prompted with pictures or digital or analog clocks Tests or quizzes with pictures of analog and digital clocks

Students should use informal units to help them understand standard units of time. For instance, they can use the duration of a pendulum swing as a unit. A pendulum can be made by attaching a tennis ball to a long string and suspending it from the ceiling. Students need to gain a sense of elapsed time. They can make a water timer using two, two-‐liter plastic bottles. Cut the neck with the cap off of one bottle. Pierce a small hole in the cap of the other bottle. Put water inside the bottle with the cap and place it upside down inside the bottle with the neck removed. The level of water in the bottom bottle indicates the beginning and end of the time period. Students compare the duration of an event by marking the water level on the bottle. The water timer is continuous with no units to count. Students are likely to experience some difficulties learning about time. On an analog clock, the little hand indicates approximate time to the nearest hour and the focus is on where it is pointing. The big hand shows minutes before and after an hour and the focus is on distance that it has gone around the clock or the distance yet to go for the hand to get back to the top. It is easier for students to read times on digit clocks but they do not relate times very well. To understand the display 4:53, students to know that it is about 5:00, that there are 60 minutes in a hour, 53 is close to 60 and 8 minutes is not a very long time. Students need to experience a progression of activities for learning how to tell time. Begin by using a one-‐handed clock to tell times in hour and half-‐hour intervals then discuss what is happening to the unseen big hand. Next use two real clocks, one with the minute hand removed, and compare the hands on the clocks. Students can predict the position of the missing big hand to the nearest hour or half-‐hour and check their prediction using the two-‐handed clock. They can also predict the display on a digital clock given a time on a one-‐ or two-‐handed analog clock and vice versa. Have students measure the duration of time for events in their everyday lives to the nearest hour or half-‐hour. It is helpful to compare durations for events that start at different times.

Concrete: Have each student create their own analog clock, labeling the clock face, the hour and minute hand, as well as the location for the minute hand when time is told to the hour and half-‐hour. Have the students then manipulate the clock to reflect the desired time. Likewise, have students manipulate real digital clocks to get the desired hour and minutes as asked by the teacher. Instruct the students what number should be in the minute location on the digital clock when it is a half-‐hour time and an hour time. Connect this understanding to the numbers on the analog clock. Semi-‐Concrete: Provide each student with a 8 ½ ‘’ x 11’’ paper that contains a pre-‐printed analogy clock (with no hands) on top and an empty digital clock on the bottom. Slip the pages into plastic page protectors and provide each student with a dry erase marker. Give students different times to write in their digital and analog clocks. Abstract: Show students pictures of digital or analog clocks and have them recall the time the image shows, explaining their reasoning as it relates to the position of the minute and hour hand or the numbers in the digital clock face.

36 RESOURCES: VOCABULARY: ORC # 4328 From the National Council of Teachers of Mathematics: Grouchy Lessons of Time http://illuminations.nctm.org/LessonDetail.aspx?ID=L126 This lesson provides an introduction to and practice with the concept of time and hours. Variety of models of analogy clocks with time marked in the half-‐hours and hour and the hour and minute hand clearly labeled. Models of digital clocks with the location for minute and time clearly marked. Math Lessons: www.aaastudy.com Math Games: www.gamequarium.com, www.funbrain.com, www.arcademicskillbuilders.com, www.mathisfun.com Games and Worksheets: www.aplusmath.com Math Resources: www.svsu.edu/supo

ANALOGY CLOCK, DIGITAL CLOCK, HOUR, MINUTES, HALF-‐HOUR, TIME, MINUTE HAND, HOUR HAND, CLOCK FACE


WHAT IS TIME? WHAT IS THE DIFFERENCE BETWEEN AN ANALOGY CLOCK AND A DIGITAL CLOCK? WHY IS IT IMPORTANT TO KNOW HOW TO TELL TIME?



Description: Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. ACT/Anchor Standard: Make sense of problems and persevere in solving them (MP.1), Reason abstractly and quantitatively (MP.2), Construct viable arguments and critique reasoning of others (MP.3)

CODE:

1.MD.C.4 Board Objective: I can organize and represent data. I can ask and answer questions in order to interpret data.


37 Global Scholars (Performance Series) Teacher observations and class discussions (anecdotal notes) Make graphs from class data (e.g. shirt color, favorite sports, number of letters in first name, etc.) and then interpret data from graphs. Have students generate questions about the data within the graph.

The focus of data analysis is classifying, organizing, representing, and using information to ask and answer questions. When moving to collecting data, children should make decisions about what to collect based on interests, keeping data as concrete and interesting as possible. First graders should follow these steps in their study of data analysis: 1) Formulate a question, 2) Collect data, 3) Analyze data, and 4) Interpret results. Teachers and students should pose interesting questions. The questions should be limited to the classroom level, such attributes of the students in the class. At first grade, two or three categories can be used to answer the question. Students can create a cluster graph when they sort objects by an attribute. A cluster graph is two or more labeled loops or regions (categories) related to the question in which students write or place items that fit in the category. Items that do not fit in a category are placed outside of the loops or regions. To make the data collection manageable, have students contribute only one fact to be placed in a category. Compare the total number of items shown in the cluster graph and the number of items in each category to answer the initial question and make generalizations and predictions. First graders should have experiences with the connectives and, or, and not for the names of the categories, such as Not Blue and Triangle and Red. The attributes for the same kind of object can vary. This will cause equal values in an object graph to appear unequal. For example, when making bars for an object graph using shoes for boys and girls, five adjacent boy shoes would likely appear longer than five adjacent girl shoes. To standardize the objects, place the objects on the same-sized construction paper, then make the object graph.

Concrete: Give each student a bar graph template and a cup of Fruit Loops. Label the graph with titles and category headings. Then, have the students sort the Fruit Loops by color into the correct categories, building up horizontally to create their graph. Students can glue the cereal down when they have finished and answer analysis questions about their graph. Semi-‐Concrete: Give each student a bar graph template and a set of objects to sort or data to graph (potentially from a teacher-‐directed or student-‐directed class survey). Have the students color in a bar to represent each piece of data. Abstract: Present students with a variety of pre-‐made graphs. Have the students analyze the data presented within the different graphs and discuss the different styles of graphic representation.

RESOURCES: VOCABULARY: ORC # 5777 From the Charles A. Dana Center, University of Texas at Austin: Buttons, Buttons, Everywhere! http://www.utdanacenter.org/mathtoolkit/instruction/lessons/k_buttons.php In this lesson students use attributes such as shape, color, size, etc. to describe, compare, and sort buttons. Yarn or large paper for loops A variety of objects to sort Graph paper Interactive Bar Graph: http://www.amblesideprimary.com/amb leweb/mentalmaths/grapher.html Math Lessons: www.aaastudy.com Math Games: www.gamequarium.com, www.funbrain.com, www.arcademicskillbuilders.com, www.mathisfun.com

Legend, Pictograph, Bar graph, Pie chart, More, Less, Horizontal, Vertical, Key, Symbol, Symbolize, Scale, Data points, Category

38 Games and Worksheets: www.aplusmath.com Math Resources: www.svsu.edu/supo ESSENTIAL QUESTIONS:

WHAT IS DATA? WHAT IS GRAPH? GRADE: 1st SUBJECT: Math STRAND: Geometry MONTH(S) TAUGHT:

Description: Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes ACT/Anchor Standard: Construct viable arguments and critique the reasoning of others (MP.3), Look for and make use of structure (MP.7)

CODE:

1.G.A.1 Board Objective: I can build and draw shapes to possess defining attributes to become better problem solvers.


39 Global Scholars (Performance Series) Teacher observations and class discussions (anecdotal notes) Shape Poetry: Have students select a plane figure or solid figure of their choice and compose a five-‐line poem describing the attributes of the shape and objects that look like that shape. To complete the task, have students decorate the page with their poetry with magazine pictures of the shapes or their own unique drawings of the shapes.

Students can easily form shapes on geoboards using colored rubber bands to represent the sides of a shape. Ask students to create a shape with four sides on their geoboard then copy the shape on dot paper. Students can share and describe their shapes as a class while the teacher records the different defining attributes mentioned by the students. Pattern block pieces can be used to model defining attributes for shapes. Ask students to create their own rule for sorting pattern blocks. Students take turns sharing their sorting rules with their classmates and showing examples that support their rule. The classmates then draw a new shape that fits this same rule after it is shared. Students can use a variety of manipulatives and real-‐world objects to build larger shapes. The manipulatives can include paper shapes, pattern blocks, color tiles, triangles cut from squares (isosceles right triangles), tangrams, canned food (right circular cylinders) and gift boxes (cubes or right rectangular prisms). Folding shapes made from paper enables students to physically feel the shape and form the equal shares. Ask students to fold circles and rectangles first into halves and then into fourths. They should observe and then discuss the change in the size of the parts.

Concrete: Build different shapes using geoboards and using sticky labels to identify the sides and vertices. Provide students with a bag of pattern blocks and ask students to sort the shapes based on specific attributes. Semi-‐Concrete: Draw shapes using rulers and stencils. Then, with a pencil and highlighters label attributes, like angles, sides, vertices and other qualities. Abstract: With their knowledge of shape attributes, show students a group of five or six shapes and have them determine the different ways that the shapes can be sorted.

RESOURCES: VOCABULARY: Shape blocks and pieces Fraction pieces Tangrams Geo-‐boards Shape stencils and rulers ORC # 1481 From the Math Forum: Introduction to fractions for primary students http://mathforum.org/varnelle/knum1.html http://mathforum.org/varnelle/knum2.html http://mathforum.org/varnelle/knum5.html This four-lesson unit introduces young children to fractions. Students learn to recognize equal parts of a whole as halves, thirds and fourths. NRICH # 2487 From NRICH: The development of spatial and geometric thinking: the importance of instruction

Rectangle, Squares, Trapezoid, Triangles, Half-circles, Quarter-circles, Cubes, Prisms, Cones, Attribute, Angle, Vertices, Side, Plane figure, Solid figure

40 http://nrich.maths.org/2487 The van Hiele mosaic puzzle can be found at the end of this article. Math Lessons: www.aaastudy.com Math Games: www.gamequarium.com, www.funbrain.com, www.arcademicskillbuilders.com, www.mathisfun.com Games and Worksheets: www.aplusmath.com Math Resources: www.svsu.edu/supo ESSENTIAL QUESTIONS:

WHAT ARE SHAPES? WHAT ARE ATTRIBUTES? WHAT ARE SIDES? WHAT ARE ANGLES? WHAT ARE VERTICES? WHAT IS THE DIFFERENCE BETWEEN A SOLID FIGURE AND A PLANE FIGURE? GRADE: SUBJECT: STRAND: MONTH(S) TAUGHT:

Description: Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.1 ACT/Anchor Standard: Reason abstractly and quantitatively (MP.2), Model with mathematics (MP.4), Look for and make use of structure (MP.7)

CODE:

1.G.A.2

Board Objective: I can compose two-‐dimensional shapes or three-‐dimensional shapes to create a composite shape. I can compose new shapes from a composite shape made of two-‐dimensional shapes or three-‐dimensional shapes.


41 Global Scholars (Performance Series) Teacher observations and class discussions (anecdotal notes) Observe students building shapes using pattern blocks. Draw shapes or sort blocks by attributes. Construct shapes using geoboards.


Concrete: Provide students with a set of tanagram pieces. Guide students through the process of composing a composite shape with the pieces and then decomposing the composite shape into the separate shape pieces. Semi-‐Concrete: Draw several shapes on the board and ask the students to compose a figure out the shapes with drawings. For example, draw two rectangles on the board and ask the students to create a square or draw two triangles on the board and ask the students to draw a rhombus with the shapes. Abstract: Show the students a figure and ask them to look at the figure and determine the shapes that make up the composite figure.

RESOURCES: VOCABULARY: Shape blocks and pieces Fraction pieces Tanagrams Geo-‐boards Shape stencils and rulers ORC # 1481 From the Math Forum: Introduction to fractions for primary students http://mathforum.org/varnelle/knum1.html http://mathforum.org/varnelle/knum2.html http://mathforum.org/varnelle/knum5.html This four-lesson unit introduces young children to fractions. Students learn to recognize equal parts of a whole as halves, thirds and fourths. NRICH # 2487 From NRICH: The development of spatial and geometric thinking: the importance of instruction

Rectangle, Squares, Trapezoid, Triangles, Half-‐circles, Quarter-‐circles, Cubes, Prisms, Cones, Attribute, Angle, Vertices, Side, Plane figure, Solid figure, Compose, Decompose, Composite shape, Three-‐dimensional, Two-‐dimensional

42 http://nrich.maths.org/2487 The van Hiele mosaic puzzle can be found at the end of this article. Math Lessons: www.aaastudy.com Math Games: www.gamequarium.com, www.funbrain.com, www.arcademicskillbuilders.com, www.mathisfun.com Games and Worksheets: www.aplusmath.com Math Resources: www.svsu.edu/supo ESSENTIAL QUESTIONS:

WHAT ARE SHAPES? WHAT ARE ATTRIBUTES? WHAT ARE SIDES? WHAT ARE ANGLES? WHAT ARE VERTICES? WHAT IS THE DIFFERENCE BETWEEN A SOLID FIGURE AND A PLANE FIGURE? WHAT DO DECOMPOSE MEAN? WHAT DOES COMPOSE MEAN? GRADE: 1st SUBJECT: Math STRAND: Geometry MONTH(S) TAUGHT:

Description: Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. ACT/Anchor Standard: Construct viable arguments and critique the reasoning of others (MP.3), Model with mathematics (MP.4) Use appropriate tools strategically (MP.5),

CODE:

1.G.A.3

Board Objective: I can partition circles and rectangles in to two equal shares. I can partition circles and rectangles into four equal shares. I can describe shares using words such as halves, fourths and quarters. I can describe shares using phrases such as half of, fourth of, and quarter of.


43 Global Scholars (Performance Series) Teacher observations and class discussions (anecdotal notes) Observe students building shapes using pattern blocks. Draw shapes or sort blocks by attributes. Construct shapes using geo-‐boards. Tests and quizzes with shapes.


Concrete: Provide student with paper cut-‐outs of circles. Cut the shapes into halves and label the pieces using the appropriate key phrases. Cut another set of paper cut-‐outs into fourths and label the pieces using the appropriate key phrases. Lay the pieces of the circle cut into halves over a whole circle; lay the pieces of the circle cut into fourths over the pieces of the circle cut into halves. This allows students to see the progression of the shape being decomposed into smaller and smaller pieces. (This process can be repeated and should be repeated with rectangular shapes.) Semi-‐Concrete: Examine large drawings of rectangles and circles. Using a ruler, have the students draw lines that divide the circles and rectangles into fourths and halves. Abstract: Show students a picture of a rectangle or a circle that has been divided in fourths and halves, but do not tell them which is which. Ask the students to evaluate which picture was divided into fourths and halves. (Modify this activity and divide the circles and shapes into different quantities or incorrectly to challenge the students.)

44 RESOURCES: VOCABULARY: Shape blocks and pieces Fraction pieces Tanagrams ORC # 1481 From the Math Forum: Introduction to fractions for primary students http://mathforum.org/varnelle/knum1.html http://mathforum.org/varnelle/knum2.html http://mathforum.org/varnelle/knum5.html This four-lesson unit introduces young children to fractions. Students learn to recognize equal parts of a whole as halves, thirds and fourths. NRICH # 2487 From NRICH: The development of spatial and geometric thinking: the importance of instruction http://nrich.maths.org/2487 The van Hiele mosaic puzzle can be found at the end of this article. Math Lessons: www.aaastudy.com Math Games: www.gamequarium.com, www.funbrain.com, www.arcademicskillbuilders.com, www.mathisfun.com Games and Worksheets: www.aplusmath.com Math Resources: www.svsu.edu/supo

RECTANGLE, CIRCLE, QUARTER, FOURTH, QUARTER OF, HALF OF, HALVES, FOURTHS, FRACTION, PARTITION, DECOMPOSE, COMPOSE, EQUAL

, ESSENTIAL QUESTIONS:

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