297A Chapter 5

Hands On: Algebra • Ways to Make Numbers to 20

LESSON 5.8

Professional Development

Professional Development

Professional Development Videos

Progress to AlgebraIf Children AskChildren may ask how addition and subtraction facts can have the same sum or difference. This concept may be confusing since these number sentences are not related. Explain that not all number sentences are related.

For example, children may ask why 2 + 4 = 6 and 8 − 2 = 6 are both ways to make the number 6, but the sentences are not related. The parts and wholes are different.

As you work through the lesson, be sure that children realize they are to look for ways to make the given number. Remind them that the addition and subtraction expressions do not need to be related.

2 � 4 =6 8 � 2 = 6

LESSON AT A GLANCE

Progressto Algebra

Interactive Student Edition

Personal Math Trainer

Math on the Spot Video

Animated Math Models

iTools: Counters

HMH Mega Math

About the Math

Learning ObjectiveRepresent equivalent forms of numbers using sums and differences within 20.

Language ObjectiveTeams pick a number and then write as many different ways as they can to show how you can add and subtract to make the same number.

MaterialsMathBoard, red, blue, and yellow connecting cubes, red and blue crayons

F C R Focus:Common Core State Standards

1.OA.C.6 Add and subtract within 20, demonstrating fl uency 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).

MATHEMATICAL PRACTICES (See Mathematical Practices in GO Math! in the Planning Guide for full text.)MP5 Use appropriate tools strategically. MP7 Look for and make use of structure.

F C R Coherence:Standards Across the GradesBeforeK.OA.A.2

Grade 11.OA.C.6

After2.OA.B.2

F C R Rigor:Level 1: Understand Concepts....................Share and Show ( Checked Items)Level 2: Procedural Skills and Fluency.......On Your Own, Practice and HomeworkLevel 3: Applications..................................Think Smarter and Go Deeper

F C R For more about how GO Math! fosters Coherence within the Content Standards and Mathematical Progressions for this chapter, see page 251J.

FOCUS COHERENCE RIGOR

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Daily RoutinesCommon Core

ENGAGE1

1 23 4 Fluency BuilderMaterials red and blue connecting cubes

Number TrainsExplain that you can make a number in many different ways. Point out that a number can be named with both addition and subtraction. Write 8 + 9 = 17 and18 + 1 = 17 on the board. Have children use connecting cubes to build cube trains to show the two number sentences.

• Here are two ways to make 17. Can you think of other ways?

Have volunteers demonstrate their ways to make 17 with the connecting cubes. Write the number sentences on the board. Challenge the class to choose another number and list several ways to show that number.

Problem of the Day 5.8Word of the Day sum

Tell the sum for each fact below.

6 + 6 = 12 — 4 + 5 = 9 —

8 + 3 = 11 — 7 + 8 = 15 —

9 + 7 = 16 — 8 + 8 = 16 —

Children may find the sum using counters.

VocabularyInteractive Student EditionMultimedia Glossary e

with the Interactive Student Edition

Essential QuestionHow can you add and subtract in different ways to make the same number?

Making ConnectionsAsk children to tell what they know about related facts.

• What is another way to say 3 + 5 = 8? 5 + 3 = 8

• Why are these called related facts? Possible answer: Both addition sentences use the same numbers.

Learning ActivityWhat problem are children trying to solve? Connect the story to the problem. Ask the following questions.

• How can you use counters to show 12? Possible answer: I can count out 12 counters. I can place the counters in groups, such as one group of 10 and one group of 2 to show 12.

• How can you use two-color counters to show different ways to make 12? Possible answer: I can count out 12 counters. Then I can turn some counters over to show a different color. The two groups show the parts that make up 12.

Literacy and MathematicsChoose one of the following activities.

• Have children use counters to make all the combinations for 11. Talk with children about ways to make sure they have made all the combinations.

• Write a number on the board. Have a volunteer show one way to make that number. Continue until all ways have been identified. Repeat with other numbers.

Lesson 5.8 297B

1 23 4 Pages 120–121 in Strategies and Practice for Skills and Facts Fluency provide additional fluency support for this lesson.

How can you add and subtract in

different ways to make the same number?

Common Core Fluency Standard 1.OA.C.6

DifferentiatedInstruction1

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Enrich 5.8

LESSON 5.8

EXPLORE2

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Writing and Reasoning Choose another number. Use the code to write all the ways to make that number.

Check children’s work.

Code FactsList all the ways to make the numbers using the code shapes shown here.

2 3 4 5 6 7 8 9 10 11 12

1.

— + — =

— + — =

— + — =

— - — =

— - — =

— - — =

— - — =

2.

— + — =

— + — =

— + — =

— + — =

— + — =

— + — =

— + — =

Lesson 5.8Enrich

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5-20 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

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Reteach 5.8

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14 - 0 = 14

4 + 4 + 6 = 147 + 7 = 14

Algebra • Ways to Make Numbers to 20

These are some ways to make the number 14.

Use to show each way. Cross out the way that does not make the number.

1. 7 8 - 1 3 + 4 2 + 3 + 1

2. 15 7 + 6 15 - 0 8 + 7

3. 13 4 + 4 + 5 9 - 4 6 + 7

4. 9 8 + 2 3 + 3 + 3 10 - 1

5. 18 9 + 9 9 - 9 18 - 0

Lesson 5.8Reteach

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5-19 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

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Progressto Algebra

Listen and DrawListen and Draw

MATHEMATICAL PRACTICES 5MathTalk

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Chapter 5 two hundred ninety-seven 297

Algebra • Ways to Make Numbers to 20Essential Question How can you add and subtract in different ways to make the same number?

Way One Way Two

Lesson 5.8HANDS ON

Use . Show two ways to make 10.Draw to show your work.

FOR THE TEACHER • Have children use connecting cubes to show two ways to make 10. Then have them draw to show the two ways.

HandsOn

Operations and Algebraic Thinking—1.OA.C.6

MATHEMATICAL PRACTICESMP5, MP7

Use Tools How do your models show two ways to make 10?

Math Talk: Possible answer: My models show adding 6 + 4 to make 10 and adding 2 + 8 to make 10.

Possible answers:

r r r r r r b b b b r r b b b b b b b b

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297 Chapter 5

1.OA.C.6 Add and subtract within 20, demonstrating fl uency 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 1 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Listen and Draw Materials red, blue, and yellow connecting cubes,red and blue crayonsHave children listen attentively as you read the following question aloud to the class.

Use red and blue connecting cubes. What are two different ways to make 10?

In the workspace, have children model two ways to make 10 and then draw pictures to show the ways.• How many cubes did you use for each way

to make 10? 10 cubes

• Can you make 10 with all red or all blue cubes? Explain. Possible answer: Yes. If I use all red cubes to make 10, the number of blue cubes is zero.

• What are some other ways to make 10? Possible answers: 0 red and 10 blue, 1 red and 9 blue, 2 red and 8 blue, 3 red and 7 blue, 4 red and 6 blue, 5 red and 5 blue, 6 red and 4 blue, 7 red and 3 blue, 8 red and 2 blue, 9 red and 1 blue

• What addition fact can you write for each way to make 10? Children’s answers should refl ect the number of cubes in each color added together equal 10.

• Why might someone have a different answer from you? Possible answer: There is more than one way to make 10.

• Why are 1 + 9 and 2 + 8 two correct ways to make 10? Possible answer: They both make the same sum, 10. They just have different parts.

MathTalk

MP5 Use appropriate tools strategically. Use Math Talk to help children focus on different ways to show 10 with connecting cubes.

• Are there other ways to make 10? I can turn my cube train around and fi nd another way.

ELL Strategy: Model Concepts

Children may understand concepts and directions if they are modeled.Model two ways to make 9 using connecting cubes. Make sure children understand each way you make 9.Give children connecting cubes in three colors. Have children use the cubes to show two different ways to make 9.Have children explain how they made 9.Repeat the activity to make 12.

HandsOn

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Model and DrawModel and Draw

Share and ShShare and ShShare and Show MATHBOARDMATHBOARD

12

6 — + 6 —

5 — + 4 — + 3 —

12 — − 0 —

298 two hundred ninety-eight

How can you make the number 12 in different ways?

Use . Write ways to make the number at the top.

1. 13

6 — + 7 —

13 — − 0 —

1 — + 9 — + 3 —

5 — + 8 — 9 — C + 4 —

2. 10

10 — − 0 — 4 — + 6 — 12 — − 2 —

5 — + 2 — + 3 —

7 — C + 3 —

You can add or subtract to

make 12.

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EXPLAIN3

Advanced LearnersCOMMON ERRORS

Quick Check

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Error Children may make a number with subtraction using the target number as the starting number.

Example For Exercise 2, children write a subtraction fact for 10 as 10 – 2 instead of 12 – 2.Springboard to Learning When subtracting to make 10, guide children to start with any number of cubes more than 10 in a cube train. Have them break off cubes until they have 10 as the difference.

Then

Lesson 5.8 298

a child misses the checked exercises

Differentiate Instruction with • Reteach 5.8

• Personal Math Trainer 1.OA.C.6

• RtI Tier 1 Activity (online)

Model and Draw MATHEMATICAL PRACTICES

MP7 Look for and make use of structure. Work through the model with children. • Do 6 + 6 and 5 + 4 + 3 make the same

number? How do you know by looking? I can see that both cube trains are the same length.

Share and Show MATHBOARDMATHBOARDMBMMMBBBMATHABOARDMMMAAATHATHTHHAAAAAAAAATTAAAABOARDBOARDBOARD

As children complete Exercises 1 and 2, they may draw models on their MathBoard.• How do you know what to write for the

last fact in Exercise 1? I can add or subtract any two numbers that make 13.

Discuss with children the different answers they might have for Exercises 1 and 2. Help children conclude that there are many ways to make a number.• How do you know which answers are

correct? Possible answer: I can make cube trains to check.

Use the checked exercises for Quick Check.

15

Materials connecting cubes in four colors, drawing paper

• Challenge children to find as many ways as they can to make 15 using three and four addends. Children can use the connecting cubes to model the addition and then record their work on paper.

• Suggest that children organize the ways to make 15 in some way.

• Have pairs compare their lists. Suggest that they work together to make one large list. Display the list in the classroom, and have children add to it as they find new combinations.

Visual / KinestheticIndividual / Partners

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Chapter 5 • Lesson 8 two hundred ninety-nine 299

MATHEMATICALPRACTICE 5 Use Appropriate Tools

Use . Write ways to make the number at the top.

3. 17

7 — + 3 — + 7 —

8 — + 9 —

17 — − 0 —

7 — C + 10 —

4. 14

5 — + 9 —

2 — + 8 — + 4 —

14 — − 0 —

7 — C + 7 —

5. 16

9 — + 7 —

5 — + 6 — + 5 —

16 — − 0 —

8 — C + 8 —

6. 18

18 — + 0 —

9 — + 9 —

4 — + 6 — + 8 —

10 — C + 8 —

7. 8.

On Your OwnOn Your Own

B SMARTER Choose a number less than 20. Write the number. Write two ways to make your number.

Possible answers are shown.

Answers will vary.

4 ELABORATE

Math on the Spot videos are in the Interactive Student Edition and at www.thinkcentral.com.

299 Chapter 5

On Your OwnMP5 Use appropriate tools strategically. If children answered Exercises 1 and 2 correctly, assign Exercises 3–8.

SMARTER

Exercises 7 and 8 require children to use higher order thinking skills. Have children write a number in the box. Then have them use what they learned in this lesson to show how to make this number in two different ways. They can use addition or subtraction and any number of parts.

DEEPER

MP7 Look for and make use of structure. To extend their thinking, have early finishers make their number using both addition and subtraction. For example, one way to show the number 8 is 10 − 5 + 3.You might also turn these exercises into a game. Invite children to the board to write both ways to make their number. After each way, have the class try to name the number. If a child names the number after the first way, he or she gets two points. If a child names the number after the second way, he or she gets one point. After all children have taken a turn at the board, the child with the most points wins the game.MP3 Construct viable arguments and critique the arguments of others.• When would 10 − 5 + 3 not be equal to 8?

Possible answer: If I add 5 + 3 first and then subtract that from 10.

Math on the Spot Video TutorUse this video to help children model and solve this type of Think Smarter problem.

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIES

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DEEPER Write numbers to make each line have the same sum.

TAKE HOME ACTIVITY • Have your child explain three different ways to make 15. Encourage him or her to use addition and subtraction, including addition of three numbers.

12. SMARTER Choose all the ways that make 13.

● 10 + 3

● 9 + 3 + 1

● 8 + 2 + 2

11. DEEPER Choose a number from 14 to 20 to be the sum. Write numbers to make each line have your sum.

sum for each line B

Check children’s work.

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIESD

MATHEMATICAL PRACTICES

Lesson 5.8 300

Children complete blue Activity Card 11 by expressing the same number as a sum or difference.

Children complete purple Activity Card 16 by determining that there are many ways to make the same sum.

Children find missing numbers in addition and subtraction sentences.

GamesBasic Facts Race

ActivitiesThe Sum Is the Same

ActivitiesAny Way You Cut It

Essential QuestionReflect Using the Language Objective Have child teams pick a number and write as many different ways as they can to show the answer to the Essential Question. How can you add and subtract in different ways to make the same number? I can put different numbers together or take different numbers apart and still end up with the same number.

Math Journal Math

Use numbers and pictures to show two ways to make the number 12.

EVALUATE5 Formative Assessment

Have children read Exercises 9 and 10. Make sure children understand that when the three numbers in each line are added, they have the same sum.

DEEPER

MP2 Reason abstractly and quantitatively. Since many different answers are possible for Exercise 11, have children share their diagrams with the class.

SMARTER

Exercise 12 requires children to demonstrate how to add and subtract in different ways to make the same number. Children who choose incorrectly may need additional practice using connecting cubes to model the addition. If children select the third combination, encourage them to make a ten and then add the remaining number to verify that the total is not 13.

Problem Solving • Applications

Cross-Curricular

Problem SolvingProblem Solving

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3. Write numbers to make each line have the same sum.

Algebra • Ways to Make Numbers to 20

Use . Write ways to make the number at the top.

1. 10

2 — 1 7 — 1 1 —

5 — 1 5 —

10 — 2 0 —

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2. 13

6 — 1 3 — 1 4 —

6 — 1 7 —

13 — 2 0 —

4 — C

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Lesson 5.8

COMMON CORE STANDARD—1.OA.C.6 Add and subtract within 20.

4. Math Use numbers and pictures to show two ways to make the number 12.

Practice and Homework

Possible answers:

Check children’s work.

Check children’s work.

Practice and HomeworkUse the Practice and Homework pages to provide children with more practice of the concepts and skills presented in this lesson. Children master their understanding as they complete practice items and then challenge their critical thinking skills with Problem Solving. Use the Write Math section to determine children’s understanding of content for this lesson. Encourage children to use their Math Journals to record their answers.

301 Chapter 5

SOCIAL STUDIES

Materials set of dominoes

• Tell children that dominoes is a game that originated in China.

• Explain that it is played using rectangular tiles called “bones” and that each bone has two sets of dots.

• Pick one domino and add the two sets of dots.• Then have children find other ways to make

that sum.

• Discuss tree rings with children.• Explain that every year a tree lives, its trunk grows

another ring of sapwood.• Present problems for children to solve such as the

following: The tree in my yard is 11 years old. Write 5 ways to make the number 11.

• Have children share their ways. Write the ways on the board. Then challenge children to find more ways, if any, to make the number 11.

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Lesson Check (1.OA.C.6)

302 three hundred two

1. Write ways to make 18.

18

8 — + 2 — + 8 —

10 — + 8 —

20 — − 2 —

9 — C

+ 9 —

2. Write ways to make 9.

9

4 — + 4 — + 1 —

5 — + 4 —

10 — − 1 —

8 — C

+ 1 —

Spiral Review (1.OA.B.4, 1.OA.C.6)

3. Write the doubles plus one fact for 7 + 7.

7 —

1 8 — 5 15 —

4. Write the doubles minus one fact for 4 + 4.

4 —

1 3 — 5 7 —

5. Think of an addition fact to help you subtract.

14 − 9

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5

9 + B

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14

5

Possible answers are shown.

Continue concepts and skills practice with Lesson Check. Use Spiral Review to engage children in previously taught concepts and to promote content retention. Common Core standards are correlated to each section.

Lesson 5.8 302