LESSON 5.6

Algebra • Use Related Facts

285A Chapter 5

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LESSON AT A GLANCE

Progressto Algebra

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16 − 9 = 9 + = 16

16

79

About the Math

Progress to AlgebraUsing Math TrianglesDraw the triangle model shown at the right on the board. Tell children that they can fi nd the unknown number from an addition or subtraction sentence by writing each given number in a box in the math triangle.

Have children write 16 − 9 _ on their MathBoards. Since they know the whole (16), and one part (9), they can use the inverse operation, addition, to fi nd the unknown number.

Have children write 9 + _ = 16 on their MathBoards. Ask, “How many more do I need to make 16?” Have children write the unknown addend in the bottom right-hand box and in the addition sentence.

Point out that these number sentences use the same three numbers, so inverse operations is a good strategy for solving this kind of unknown number problem.

Learning ObjectiveUse a related fact to subtract.

Language ObjectivePairs create a chart to show how you can use a related fact to fi nd a missing number.

MaterialsMathBoard, crayons

F C R Focus:Common Core State Standards

1.OA.D.8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.

MATHEMATICAL PRACTICES (See Mathematical Practices in GO Math! in the Planning Guide for full text.)MP2 Reason abstractly and quantitatively. MP4 Model with mathematics. MP7 Look for and make use of structure.

F C R Coherence:Standards Across the GradesBeforeK.OA.A.3

Grade 11.OA.D.8

After2.OA.A.1

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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ENGAGE1Daily Routines

Common Core

Problem of the Day 5.6Calendar Math Point to a date. Count back 1 or 2 days. Write the subtraction sentence. Then repeat. Answers will vary.

Once children have counted back, you might have them count on

the same number of days. Children should notice that counting on brings them back to the number they started with.

VocabularyInteractive Student EditionMultimedia Glossary e

Lesson 5.6 285B

ENGAGE1

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 use a related fact to f ind an

unknown number?

1 23 4 Fluency BuilderMaterials 2 sets of Numeral Cards labeled 1-9 (see eTeacher Resources)

Have children work in pairs. Give each pair two sets of cards.

Have partners mix the cards and place them in a pile face down. Have children take turns turning over two cards at a time and using the numbers to write two related facts. For example, if the numbers are 4 and 7, the related facts might be 4 +7 = 11 and 11 − 4 = 7.

Common Core Fluency Standard 1.OA.C.6

with the Interactive Student Edition

Essential QuestionHow can you use a related fact to find an unknown number?

Making ConnectionsInvite children to tell you what they know about related facts.

How are addition and subtraction related? Possible answer: you can use subtraction to find the missing number in an addition problem; subtraction is the opposite of addition because addition means to add to but subtraction means to take away.

Learning ActivityDirect children to think about how to find the unknown number in a number sentence.

• What is Avery trying to find? (the number of eggs in the bigger nest)

• What does Avery already know? (the number of eggs in the smaller nest and the total number of eggs)

• What addition sentence can you write to show the problem? (3 + ___ = 7)

• How can you find the missing number? (possible answers: subtract; find a related fact)

Literacy and Mathematics• Have children write a brief explanation about how to use

subtraction to find the answer to an addition problem.

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Listen and DrawListen and Draw

MATHEMATICAL PRACTICES 4MathTalk

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Chapter 5 two hundred eighty-fi ve 285

What number can you add to 8 to get 10? Draw a picture to solve. Write the unknown number.

Algebra • Use Related Facts Essential Question How can you use a related fact to find an unknown number?

8 + B2 = 10

Lesson 5.6

Operations and Algebraic Thinking—1.OA.D.8 Also 1.OA.C.6

MATHEMATICAL PRACTICESMP2, MP4, MP7

Model Describe how to solve this problem using cubes.

FOR THE TEACHER • Have children draw a picture and complete the number sentence to show the number that can be added to 8 to get 10.

Check children’s drawings.

Math Talk: Possible answer:Show 8 red cubes. Then add bluecubes until there are 10 in all.

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Listen and DrawMaterials crayonsRead the following question aloud to the class.

What number can you add to 8 to get 10?

Have children make a math drawing in the workspace to complete the activity. Ask the following questions to guide children through the solution process.• What number do you start with? 8• What number do you want to get to? 10

• What do you need to fi nd? I need to fi nd the number I can add to 8 that makes 10.

• How can you solve the problem using addition? Possible answer: I can draw 8 red lines and then draw more blue lines until there are 10 lines. The answer is the number of blue lines.

• How can you solve the problem using subtraction? Possible answer: I can draw 10 lines and circle and cross out 8 of them. The answer is the number of lines that are not crossed out.

• What number do you add to 8 to equal 10? 2

Have children say the answer: 8 + 2 = 10.

MathTalk

MP4 Model with mathematics. Then use Math Talk to focus on children’s understanding of how to solve problems with unknown addends using models and related number sentences.• How else could you solve this problem?

Possible answer: I could count up from 8 to 10. That’s 2

ELL Strategy: Illustrate Understanding

Children can make drawings to review vocabulary and illustrate understanding.Write 7 + ___ = 11 on the board.Ask children to draw a picture that shows the addition problem. If they need assistance, suggest that they draw 11 objects and then circle 7 of those objects to fi nd out how many objects are left out.Ask children to describe their drawings.Repeat with a different addition fact.

EXPLORE2

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Writing and Reasoning Choose two numbers. Use them to write a riddle like Exercise 1. Then write two related number sentences.

Addition and Subtraction RiddlesWrite the missing number to solve the riddle. Then write two related number sentences.

1. We have a sum of 6. We have a difference of 2. What numbers are we?

4 and 2 —

4 C+ 2 — C= 6

6 — C- 4 — C= 2 —

2. We have a sum of 9. We have a difference of 3. What numbers are we?

6 and 3 —

6 C+ 3 — C= 9 —

9 —

C- 6 —

C= 3 —

3. Together we make 12. Our difference is 0. What numbers are we?

6 and 6 —

6 —

C+ 6 C= 12

12 —

C- 6 —

C= 6 —

Lesson 5.6Enrich

Check children’s work.

Possible number sentences shown.

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5-16 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

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Name 

THINKStart with 6. How

many do I add to make 11?

Algebra • Use Related Facts

Find 11 – 6.

Use counters to help you.

6 + 5  — = 11

5

1 1

611 - 6 = 5  —

Use counters. Write the missing numbers.

1. Find 13 - 8.

8 + 5 — = 13

13 - 8 = 5 —

13

8 5

2. Find 12 - 3.

3 + 9 — = 12

12 - 3 = 9 —

9

12

3

Lesson 5.6Reteach

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5-15 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

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Enrich 5.6Reteach 5.6 DifferentiatedInstruction

Progressto Algebra

285 Chapter 5

1.OA.D.8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. Also 1.0A.C.6

LESSON 5.6

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COMMON ERRORS

Quick Check

If

Rt I RRR1

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Model and DrawModel and Draw

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Write the unknown numbers.

You can use an addition fact to fi nd a related subtraction fact.

I know that 3 + 7 = 10, so

10 − 3 = 7.

Find 10 − 3.

10

3 7

14

8 6

17

8 9

11

6 5

15

9 6

8 + 6 —

= 14

14 − 8 = 6 —

8 + 9 —

= 17

17 − 8 = 9 —

3. Find 11 − 6. 4. Find 15 − 9.

6 + 5 —

= 11

11 − 6 = 5 —

9 + 6 —

= 15

15 − 9 = 6 —

1. Find 14 − 8. 2. Find 17 − 8.

3 + 7

— = 10

10 − 3 = 7

—

Error Children may not know how to fill in the triangle diagram

Example For Exercise 1, 8 + — = 14 and 14 – 8 = — , children write 14 in the bottom box.Springboard to Learning Have children think of the triangle diagram as parts and wholes. The top box is the whole, so the greatest number goes there. The two bottom boxes are the parts, so the two lesser numbers go there. Have children write a small w in the top box and small p’s in the bottom two boxes to help them focus on the concept of parts and wholes.

EXPLAIN3

Then

a child misses the checked exercises

Differentiate Instruction with • Reteach 5.6

• Personal Math Trainer 1.OA.D.8

• RtI Tier 1 Activity (online)

Advanced Learners

Lesson 5.6 286

Model and Draw MATHEMATICAL PRACTICES

MP7 Look for and make use of structure.Work through the model with children.• What related addition and subtraction facts

are shown in the model? 3 + _ = 10 and 10 − 3 = _

• How does the triangle diagram show the parts and the whole? The number at the top is the whole; the numbers at the bottom are the parts.

• How can you use addition to solve the subtraction fact? Possible answer: I can start with 3 and put out a cube for each number I count until I get to 10.

Share and Show MATHBOARDMATHBOARDMBMMMBBBMATHABOARDMMMAAATHATHTHHAAAAAAAAATTAAAABOARDBOARDBOARD

For Exercises 1–4, have children find the unknown addend in the addition sentence and the difference in the related subtraction sentence.Use the checked exercises for Quick Check. Have children draw models on their MathBoards to explain their thinking.

7 � � 12

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Materials sets of Numeral Cards 1–12 and Sign Cards +, −, = (see eTeacher Resources)

• Have pairs use Numeral and Sign Cards to make related addition and subtraction sentences.

• While one child is turned away, have the partner turn over the card for one addend in the addition sentence so it is facedown. The partner uses the subtraction sentence to name the unknown addend.

• Have partners change roles and repeat with other related facts.

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Chapter 5 • Lesson 6 two hundred eighty-seven 287

Write the unknown numbers.

10

5

9

7

4 + 9 —

= 13

13 − 4 = 9 —

7. Find 12 − 7. 8. Find 15 − 8.

9. Find 11 − 5. 10. Find 13 − 6.

5. Find 20 − 10. 6. Find 13 − 4.

20

12

7

13

15

4

8

10

10 + 10 —

= 20

20 − 10 = 10 —

7 + 5 —

= 12

12 − 7 = 5 —

5 — + 6 — = 11 —

11 — − 5 — = 6 —

8 + 7 —

= 15

15 − 8 = 7 —

13 — = 7 — + 6 —

7 — = 13 — − 6 —

On Your OwnOn Your Own

DEEPER Write an addition sentence to help you fi nd the difference. Then write the related subtraction sentence to solve.

Also accept: 13 = 6 + 7Also accept: 6 + 5 = 11

4 ELABORATE

287 Chapter 5

On Your OwnMP2 Reason abstractly and quantitatively. If children answered Exercises 3 and 4 correctly, assign Exercises 5 − 10.

DEEPER

Exercises 9 and 10 require children to use higher order thinking skills. In each exercise, children must first identify a related addition fact to help them subtract. Then children use their addition fact to write and solve the subtraction fact. Suggest that children draw a triangle to help them write the related addition and subtraction facts if they need to. In Exercise 10, children should note the placement of the is equal to symbol.

DEEPER

MP4 Model with mathematics. To extend their thinking, have children write the other related addition and subtraction sentences for Exercises 9 and 10.• Look at the number sentences. Some have

one number on the left of the equal sign and some have two numbers. Why are both correct? Possible answer: The equal sign just means that the amount on either side is the same.

MATHEMATICAL PRACTICES

Math

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288 two hundred eighty-eight

11.

+ = − =

12. + = − =

13. SMARTER

+ = − =

MATHEMATICALPRACTICE 2 Reason Abstractly Look at the

shapes in the addition sentence. Draw shapes to show a related subtraction fact.

B + 5 = 12

5 + B = 12 12 − B = 5

12 − 5 = B

5 7 8 9● ● ● ●

TAKE HOME ACTIVITY • Give your child 5 small objects, such as paper clips. Then ask your child how many more objects he or she would need to have 12.

14. SMARTER Which is the unknown number in these related facts?

Check children’s work.

Possible answer is shown.

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

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIESD

Lesson 5.6 288

Children practice naming related subtraction facts to 8.

GamesRelated Fact Race

LiteratureJuggling

Children read the book and practice addition and subtraction facts through 12.

ActivitiesNumber Tales

Children complete purple Activity Card 18 by exploring and modeling related facts.

Essential QuestionReflect Using the Language Objective Have children pair up and create a chart to answer the Essential Question.How can you use a related fact to find an unknown number? Children’s answers should show an understanding that addition and subtraction are inverse operations.

Math Journal Math

Draw pictures to show how to solve 14 − 7 = ___ and 7 + ___ = 14.

EVALUATE5 Formative Assessment

MATHEMATICAL PRACTICES

Exercises 11−14 may be solved using algebraic reasoning. If a + b = c, then c − a = b and c − b = a. After recording a subtraction sentence for each exercise, ask children to rearrange the same shapes to make another related subtraction sentence.

SMARTER

MP2 Reason abstractly and quantitatively. For Exercise 13, have children write both subtraction facts on their MathBoards.

SMARTER

Exercise 14 requires children to apply what they know about related facts. When they find the unknown number in any of the four given facts, they can use the same number to complete the others. Children may need to use counters to verify that all four unknown numbers are the same.

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

Problem Solving • Applications

COMMON CORECOMMCOMMCOMMCOMMON CON CON CON COREOREOREORE

PROFESSIONALDEVELOPMENT Math Talk in Action

Problem SolvingProblem Solving

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Chapter 5 two hundred eighty-nine 289

Algebra • Use Related Facts

Write the missing numbers.

1. Find 16 − 9.

9 + B 7 = 16

16 − 9 = B 7

2. Find 12 − 7.

7 + B 5 = 12

12 − 7 = B 5

3. Find 15 − 6.

6 + B 9 = 15

15 − 6 = B 9

4. Find 18 − 9.

9 + B 9 = 18

18 − 9 = B

9

Look at the shapes in the addition sentence.Draw a shape to show a related subtraction fact.

5.

6. Math Draw pictures to show how to solve 14 – 7 = ___ and 7 + ___ = 14.

B 9 B 7

B 16 B 12

B 7 B 5

B 15

B 6 B 9

B 18

B 9 B 9

COMMON CORE STANDARD—1.OA.D.8 Work with addition and subtraction equations.

Lesson 5.6Practice and Homework

Check children’s work.

Check children’s drawings.

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.

Some children may not understand how to find a related addition and subtraction fact. Have children look at Exercise 3.

Teacher: How do you find a related addition fact to help you solve 15 2 6?

Camille: I can use the numbers in 15 2 6. I know 15 is the whole and 6 is one part.

Teacher: How would you write your related addition fact?

Camille: I would write 6 1 a missing part 5 15.

Teacher: So what number do you add to 6 to get 15?

Camille: 9

Teacher: Yes! So what is the related addition sentence?

Camille: 6 1 9 5 15

Teacher: Great job! Now, how can you use the addition fact to write a related subtraction fact?

Bobby: I know the parts and the whole in 6 1 9 5 15. So I subtract 6 from 15 in the related subtraction fact to get 9.

Teacher: What is that number sentence?

Bobby: 15 2 6 5 9

Teacher: Great job!

289 Chapter 5

Personal Math Trainer

FOR MORE PRACTICE GO TO THE

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Lesson Check (1.OA.D.8)

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1. Write an addition fact that helps you solve 12 – 4.

8 — + 4 — = 12 —

2. Circle the greater addend. Count on to find the sum.

3. Draw to show the doubles fact.Write the sum.

9 + 3

]

12

Spiral Review (1.OA.C.5, 1.OA.C.6)

8 1 8

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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 5.6 290