303A Chapter 5

Algebra • Equal and Not Equal

LESSON 5.9

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Professional Development

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Progress to AlgebraTeaching for DepthThe concept of equality is an important foundation of algebraic understanding. For many children, however, the equal sign does not signify equality but represents a request for an answer.

To help children develop an algebraic understanding of equality, they need to understand that the equal sign tells them the quantities on both sides are equivalent in value. Guide them to think of the equal sign as meaning “is the same as” or “has the same value as.”

In their early work with number sentences, children need to see that 3 + 6 = 9 and 9 = 3 + 6 represent the same idea. Help them understand that 9 = 3 + 6 is not written backwards or incorrectly. It is just a different way to show that 9 is the same as 3 + 6. Make sure they do not change symbols to make the number sentence true. For example, children may want to write 9 = 3 + 6 as 9 − 3 = 6.

LESSON AT A GLANCE

Progressto Algebra

Interactive Student Edition

Personal Math Trainer

Math on the Spot Video

iTools: Counters

HMH Mega Math

About the Math

Learning ObjectiveDetermine if an equation is true or false.

Language ObjectiveChildren complete the sentence frame, The best way to decide if a number sentence is true or false is _____________.

MaterialsMathBoard, crayons

F C R Focus:Common Core State Standards

1.OA.D.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.

MATHEMATICAL PRACTICES (See Mathematical Practices in GO Math! in the Planning Guide for full text.)MP2 Reason abstractly and quantitatively. MP6 Attend to precision.MP7 Look for and make use of structure.

F C R Coherence:Standards Across the GradesBeforeK.OA.A.5

Grade 11.OA.D.7

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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ENGAGE1Daily Routines

Common Core

Lesson 5.9 303B

1 23 4 Fluency BuilderNumber RiddlesProvide children with these clues about a number. Then have children guess the number.

• I am thinking of a number. It is the sum of 3 + 5. It is the difference of 9 − 1. What is my number? 8

• What is another way to make 8? Possible answers: 0 + 8, 1 + 7, 2 + 6, 4 + 4, 17 – 9, 16 – 8, 15 – 7, 14 – 6, 13 – 5, 12 – 4, 11 – 3, 10 – 2, 8 – 0

Have children make up their own riddles to share with the class. Encourage children to write them down and solve them before sharing.

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 decide i f a number sentence

is true or false?

Problem of the Day 5.9Word of the Day equalMake two groups of cubes. Add or take away cubes to make the groups equal.

• How many cubes did you show in each group? Answers will vary.

Invite volunteers to explain how they made the two groups equal.

VocabularyInteractive Student EditionMultimedia Glossary e

Common Core Fluency Standard 1.OA.C.6

with the Interactive Student Edition

Essential QuestionHow can you decide if a number sentence is true or false?

Making ConnectionsAsk children to tell what they know about addition sentences.

• What does the = sign in 3 + 5 = 8 mean? Possible answer: It means that the numbers on each side of the equal sign mean the same thing.

• How can you show that 3 + 5 is the same as 8? Possible answer: I can count out three yellow counters and 5 red counters. Then I can count all the counters to show I have 8.

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

• How can you use counters to show the numbers on either side of the equal sign mean the same thing? Possible answer: I can set out counters to match the two numbers on one side of the equal sign. Then I can count all the counters to be sure they match the number on the other side.

• What should you do if the numbers do not mean the same thing? Check my work.

Literacy and Mathematics• Have one partner say a number to 15. Have the other partner

use counters to show that number. Have both children write the number sentence the counters show. Have children repeat by saying a different number.

• Say a number sentence, such as 1 + 3 = 5. Have children raise one arm if the number sentence is true. Have children raise both arms and make an X if the number sentence is false. Repeat with other number sentences.

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Enrich 5.9

LESSON 5.9

EXPLORE2

Name

Shape Number CodeDraw the shape to make each number sentence true.

♥

Shape Code

stands for 8 stands for 1

stands for 4 stands for 2

1. 9 + 3 = + 2. 12 = + +

3. 3 + = 7 - 0 4. - = 5 +

5. 16 = 6 + + 6. 7 + = 10 -

Writing and Reasoning Explain how you chose the shapes for Exercise 5.Possible answer: I know 16 = 6 + 10, so themissing shapes have to equal 10. I used atriangle and heart to make 8 + 2, or 10.

Lesson 5.9Enrich

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Reteach 5.9

Name 

THINK3 + 2 = 5 and 5 - 2 = 3.

Is 5 the same as 3?

no  —

It is false.

THINK3 + 3 = 6 and 6 - 0 = 6.

Is 6 the same as 6?

yes  —

It is true.

Algebra • Equal and Not Equal

An equal sign means both sides are the same.

3 + 3 = 6 - 0 3 + 2 = 5 - 2

Which is true? Circle your answer. Which is false? Cross out your answer.

1. 7 – 5 = 5 – 2

8 – 8 = 6 – 6

2. 1 + 8 = 18

2 + 8 = 8 + 2

3. 4 + 3 = 5 + 2

7 + 3 = 4 + 5

4. 9 – 2 = 9 + 2

9 = 10 – 1

Lesson 5.9Reteach

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Color the cards that make the same number.

Lesson 5.9Algebra • Equal and Not EqualEssential Question How can you decide if a number sentence is true or false?

Chapter 5 three hundred three 303

Listen and DrawListen and Draw

FOR THE TEACHER • Have children color the cards that make the same number.

Operations and Algebraic Thinking—1.OA.D.7 Also 1.OA.C.6

MATHEMATICAL PRACTICESMP2, MP6, MP7

Reasoning Why can you use two of the cards you color and an equal sign to make a number sentence?

2 + 6 12 − 6

11 − 2

10 + 6

5 + 2 + 53 + 4

3 + 2 + 2

3 + 3 + 1

4 + 3

6 + 1

16 − 9

13 − 6

Math Talk: Possible answer: Each card I color has a sum or difference of 7. I can put an equal sign between two of the cards to make a number sentence because 7 is equal to 7.

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303 Chapter 5

Listen and DrawMaterials crayonsRead the following aloud.

Color the cards that make the same number.

Have children fi nd and record the value of each card.• What number is made on more than one

card? 7• Which two cards use the same numbers?

3 + 4 and 4 + 3 How are the cards different? The numbers are in a different order.

• How can different number sentences have the same sum or difference? Both sentences can mean the same amount.

MathTalk

MP2 Attend to precision. Use Math Talk to focus on children’s understanding of ways to show the same number and the meaning of the equal sign. Write an equal sign on the board. Ask children what it means. Elicit responses to show that it means “is the same as.”

Ask a volunteer to choose two cards that have the same value. As the child tells which two cards they are, draw one card on each side of an equal sign so that the number sentence looks like the following example: 6 + 1 = 13 − 6.• What does this sentence mean? Possible

answers: 6 plus 1 equals 13 minus 6; 6 plus 1 is the same as 13 minus 6; 7 is equal to 7

• What does the equal sign mean? Possible answer: When you do the addition or subtraction you get the same number on both sides.

ELL Strategy: Scaffold Language

Children can practice using the words equal and not equal with both words and symbols.Draw two squares on the board. In one square, draw 3 red circles and 2 blue circles. In the other square, draw 4 red circles and 1 blue circle.• Are the numbers of circles the same or

different? They are the same. Are the numbers of circles equal or not equal? They are equal.

Repeat with an example of not equal, such as 4 red and 7 blue circles in one square, and 5 red and 5 blue circles in the other square.

1.OA.D.7 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. Also 1.OA.C.6

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Model and DrawModel and Draw

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1. 7 = 8 – 1

1 + 2 = 3 – 2

2. 4 + 1 = 5 + 2

6 − 6 = 7 − 7

3. 7 + 2 = 6 + 3

8 − 2 = 6 + 4

4. 5 − 4 = 4 − 3

10 = 1 + 0

Which is true? Circle your answer.Which is false? Cross out your answer.

The equal sign means that both sides are the same.

Write a number to make each true.

4 + 5 = 5 + 5 is not true. It is false.

THINK Are both sides

equal?

4 + 5 = 9 — 4 + 5 = 5 — + 49 = 9 —

++ 2 == 33 22+ 2 = 3 2==

EXPLAIN3

Advanced Learners

Quick Check

If

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COMMON ERRORS

Lesson 5.9 304

a child misses the checked exercises

Differentiate Instruction with• Reteach 5.9

• Personal Math Trainer 1.OA.D.7

• RtI Tier 1 Activity (online)

Error Children may not use the correct operation.

Example In Exercise 2, children subtract to rewrite the first number sentence as 3 = 3.Springboard to Learning Have children circle the plus and minus signs. Remind them to use those signs to see if the number sentence is true but not change the signs to make it true.

Model and Draw MATHEMATICAL PRACTICES

MP6 Attend to precision. Emphasize that false is the opposite of true. Explain that a number sentence is false if the values on both sides of the equal sign are not the same.• Why is 4 + 5 = 5 + 5 not true? The sums on

both sides of the equal sign are not the same. 4 + 5 = 9 and 5 + 5 = 10. 9 is not equal to 10.

• How did you find the number to make the number sentence true? I saw a 4 and a 5 on one side, so I put a 5 with the 4 on the other side.

Share and Show MATHBOARDMATHBOARDMBMMMBBBMATHABOARDMMMAAATHATHTHHAAAAAAAAATTAAAABOARDBOARDBOARD

Remind children to add or subtract before they decide if the number sentence is true or false.• For Exercise 2, what is 4 + 1? 5 + 2? 5; 7

• How can you use 5 and 7 to tell if the number sentence is true or false? I can compare 5 and 7. They are not the same, so the number sentence is false.

• How do you know which number sentences are true? Possible answer: The value on each side of the equal sign is the same.

Use the checked exercises for Quick Check.

Materials Numeral Cards 1–12 (see eTeacher Resources), index cards, crayons

• Give individuals or partners Numeral Cards and five index cards. Have children write an equal sign on one index card, plus signs on two index cards, and minus signs on the remaining two index cards.

• Have children shuffle the Numeral Cards and choose five cards without looking. Ask them to try to make a true number sentence using at least three of the Numeral Cards and the appropriate index cards.

• Once children have created a true number sentence or have decided that it is not possible, have them return the cards, reshuffle them, and repeat the activity.

Logical / MathematicalIndividual / Partners

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Chapter 5 • Lesson 9 three hundred fi ve 305

Write numbers to make sentences that are true.

MATHEMATICALPRACTICE 6 Attend to Precision

Which are true? Circle your answers. Which are false? Cross out your answers. 5.

1 + 9 = 9 – 1 8 + 1 = 2 + 7 19 = 19

6. 9 + 7 = 16 16 − 9 = 9 + 7 9 − 7 = 7 + 9

7. SMARTER Lyle writes the false number sentence 2 + 10 = 8. Complete the number sentence to make the sentence true. 2 + 6 — = 8

8. 2 + 10 = 7 + 5 —

9. 9

— = 2 + 3 + 4

10. 0 + 9 = 18 — – 9

11. 6

— + 7 = 7 + 6

On Your OwnOn Your Own

12. SMARTER Write numbers to show expressions of equal value.

— +

— =

— +

—

Answers will vary.

4 ELABORATE

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

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On Your OwnMP6 Attend to precision. If children answered Exercises 3 and 4 correctly, assign Exercises 5–12.

SMARTER

Exercise 12 requires children to go beyond investigating number sentences and write original number sentences that are true.

DEEPER

MP7 Look for and make use of structure. To extend children’s thinking, have them decide how to change a number sentence that is false to make it true. • In Exercise 5, which number sentence is

false? What would you change to make it true? 1 + 9 = 9 − 1 is false. I would change the − to a +.

• In Exercise 6, how could you change the second number sentence so that it is true? Possible answers: 16 − 0 = 9 + 7; 16 − 9 = 0 + 7

MP8 Look for and express regularity in repeated reasoning.• How can you tell if a number sentence is

true or false? Possible answer: When I figure out what each side equals, then I can see if the numbers are the same.

SMARTER

Exercise 7 is more challenging because it requires children to determine why the number sentence Lyle wrote is false and correct his error to make the number sentence true.

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

MathMath

Personal Math TrainerPersonal Math Trainer

MATHEMATICAL PRACTICES

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13. Which are true? Use to color.

7 + 8 = 15

8 — = 15 — C − 7 —

TAKE HOME ACTIVITY • Write 10 = 7 − 3 and 10 = 7 + 3 on a sheet of paper. Ask your child to explain which is true.

20 = 20 9 + 1 + 1 = 11 8 – 0 = 8

12 = 1 + 2 10 + 1 = 1 + 10 7 = 14 + 7

6 = 2 + 2 + 2

11 – 5 = 1 + 5

1 + 2 + 3 = 4 + 5

● Yes ● No

● Yes ● No

● Yes ● No

15. SMARTER Is the math sentence true? Choose Yes or No.

5 − 4 = 9 − 8

13 = 5 + 7

6 + 2 = 2 + 6

14. SMARTER Use the same numbers. Write a different number sentence that is true.

Possible answer shown.

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIESD

MATHEMATICAL PRACTICES

Lesson 5.9 306

EVALUATE5 Formative Assessment

Children find unknown numbers in addition and subtraction sentences.

GamesBasic Facts Race

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

LiteratureJuggling

Children complete blue Activity Card 18 by modeling subtraction facts to find an unknown number.

ActivitiesThe Missing Piece

Essential QuestionReflect Using the Language Objective Have children complete the sentence frame, The best way to decide if a number sentence is true or false is _____________, to answer to Essential Question.How can you decide if a number sentence is true or false? Possible answer: I can add or subtract to solve each side of the equal sign. Then I can compare the numbers to see if they have the same value.

Math Journal Math

Write 5 + = 6 + 8. Write a number to make the sentence true. Draw a quick picture to explain.

For Exercise 13, remind children to find the value on both sides of the equal sign before they decide if the number sentence is true.

SMARTER

MP6 Attend to precision. Exercise 14 requires children to use higher order thinking skills to write a related fact that is true.

Personal Math Trainer SMARTER

Be sure to assign Exercise 15 to children in the Personal Math Trainer. It features an animation to help them model and answer the problem. Exercise 15 requires children to determine if a number sentence is true. Some children who choose incorrectly may not use the correct operation. Some may need to use models to compare each side of the equations.

Problem Solving • Applications

Extend the Math Activity

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1. 6 + 4 = 5 + 5 2. 10 = 6 − 4 3. 8 + 8 = 16 − 8

4. 14 = 1 + 4 5. 8 − 0 = 12 − 4 6. 17 = 9 + 8

Algebra • Equal and Not Equal

Which are true? Circle your answers. Which are false? Cross out your answers.

7. Which are true? Use a to color.

15 = 15 12 = 2 3 = 8 − 5

15 = 1 + 5 9 + 2 = 2 + 9 9 + 2 = 14

1 + 2 + 3 = 3 + 3 5 − 3 = 5 + 3 13 = 8 + 5

8. Math Write 5 + = 6 + 8.Write a number to make the sentence true. Draw a quick picture to explain.

COMMON CORE STANDARD—1.OA.D.7Work with addition and subtraction equations.

Lesson 5.9Practice and Homework

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.

307 Chapter 5

True or False?Materials index cards, Sign Cards (See eTeacher Resources)

Investigate Write the numbers 5, 10, and 13 on the board. Have children choose one of the numbers and write a way to make that number on an index card. For example, children may choose the number 5, and write 8 – 3 on an index card. Invite two children to come to the board to copy what they have written on their index cards. They should write their facts side by side on the board and draw an equal sign between them. Explain that this number sentence may be true or false. Next, have the class work together to decide if the number sentence is true or false. If the number sentence is true, ask a child to write true next to it. If it is false, ask a child to draw a line through it.

Math Talk Use the following questions to guide the activity.

• How do you know whether a number sentence is true or false? I can see whether the value of each side of the equal sign is the same.

• When a number sentence is false, how can you change it to make it true? Possible answer: I can change the numbers or the plus and minus sign on one side of the equal sign.

Summarize Children analyze number sentences to decide whether they are true or false and then justify their reasoning.

Personal Math Trainer

FOR MORE PRACTICE GO TO THE

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Lesson Check (1.OA.D.7)

1. Circle the number sentences that are true. Cross out the ones that are false.

4 + 3 = 9 − 2 4 + 3 = 9 + 2

4 + 3 = 4 − 3 4 + 3 = 6 + 1

Spiral Review (1.OA.A.2, 1.OA.C.6)

2. Use 5, 6 and 11 to write related addition and subtraction sentences.

5 — 6 — 11 —

6 — 5 — 11 —

11 — 5 — 6 —

11 — 6 — 5 —

3. Solve. Draw or write to show your work. Leah has 4 green toys, 5 pink toys, and 2 blue toys. How many toys does Leah have?

Possible answer: 4 + 5 + 2 = 11

4 — 5 — 2 — 11 —

+

+

+ +

−

−

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11 — toys

Drawings may vary.

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.

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