correctionkey=d lesson 7.1 hands on: algebra • …...lesson 7.1 reteach do not edit--changes must...

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LESSON AT A GLANCE

Progressto Algebra

About the MathProfessional DevelopmentAbout the MathProfessional Development

Professional Development Videos

399A Chapter 7

LESSON 7.1

Hands On: Algebra • Greater Than

Learning ObjectiveModel and compare two-digit numbers to determine which is greater.

Language ObjectiveChildren use comparison words to rephrase how they can compare two numbers to fi nd which is greater.

MaterialsMathBoard, base-ten blocks, connecting cubes

F C R Focus:Common Core State Standards

1.NBT.B.3 Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

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.CC.C.6K.CC.C.7

Grade 11.NBT.B.3

After 2.NBT.A.4

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 395H.

FOCUS COHERENCE RIGOR

Progress to AlgebraCompare with Base-Ten BlocksWhen two whole numbers have a different number of digits, the number with more digits is greater. When two whole numbers have the same number of digits, compare the digits in the greatest place fi rst.

When the number in the greatest place is the same, compare the ones. In this case, 36 has more ones. Therefore, 36 is greater than 31.

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ENGAGE1Daily Routines

Common Core

1 23 4 Pages 90–91 in Strategies and Practice for Skills and Facts Fluency provide additional fluency support for this lesson.

Lesson 7.1 399B

How can you compare two numbers to f ind

which is greater?

with the Interactive Student Edition

Essential QuestionHow can you compare two numbers to find which is greater?

Making ConnectionsInvite children to tell you what they know about comparing. Ask the children the following questions:

How do you compare two cube trains to tell which has more cubes? Answers will vary. Possible answer: Lay the cube trains next to each other. How do you know which cube train has more cubes? Answers will vary. Possible answer: The cube train that is longer has more cubes.

Learning ActivityHave children use cubes to model the numbers shown in the problem. Discuss the models with the children.

• What number do you know in the problem? The number of acorns in one pile.

• What do you need to know? The number of acorns in the other pile.

• What are some models you can use to show numbers? Answers will vary.

Literacy and MathematicsView the lesson opener with the children. Then, choose one or both of the following activities.

• Help children write sentences that compare two numbers using greater than.

• Write a class story that compares two amounts of items.

Problem of the Day 7.1Calendar Math Find three numbers on the calendar that have more tens than ones.

, ,

Possible answers depending on month: 10, 20, 21, 30, 31

Have volunteers share their answers.

Vocabulary is greater than >

1 23 4 Fluency BuilderFind the Unknown NumberExplain that you will say an addition fact with one number missing. Children should solve for the unknown number and show the unknown number with their fingers.

• 8 plus what is 15? 7 7 plus what is 10? 3

• 5 plus what is 12? 7 7 plus what is 11? 4

Continue with other examples as time allows.

Name That Number

Literature ConnectionFrom the Grab-and-Go™ Differentiated Centers Kit

Children read the book and compare numbers to complete a hundred chart.

Interactive Student EditionMultimedia Glossary e

Common Core Fluency Standard 1.OA.C.6

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> 66

72 >

> 91 > 33

21 >

59 81

75 63

86 9834 22

31 13

33 43

34 >

Which Makes It True?Circle the number that makes the number sentence true.

1. 2.

3. 4.

5. 6.

Writing and Reasoning Write a number that is greater than 98.Possible answer: 99

Lesson 7.1Enrich

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7-6 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

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Algebra • Greater Than

You can compare numbers to find which is greater.

48 — is greater than 24 —.

48 — > 24 —


65 — > 62 —

Draw lines to match. Write the numbers to compare.

1.


55 — > 43 —

2.


51 — > 34 —

Lesson 7.1Reteach

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7-5 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

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3 DifferentiatedInstruction

Listen and DrawListen and DrawHands

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MATHEMATICAL PRACTICES 5MathTalk

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Chapter 7 three hundred ninety-nine 399

Use or an iTool to solve. Draw quick pictures to show your work.

Algebra • Greater ThanEssential Question How can you compare two numbers to find which is greater?

Lesson 7.1HANDS ON

Tens Ones

How did you use tools to decide which number is greater?FOR THE TEACHER • Read the problem. Which

number is greater, 65 or 56? Have children use base-ten blocks and draw quick pictures to solve.

Number and Operations in Base Ten—1.NBT.B.3

MATHEMATICAL PRACTICESMP5, MP7

Math Talk: Possible answer: I used base-ten blocks and quick pictures to show the tens and ones. Then, I compared the tens first. 65 has more tens than 56, so 65 is the greater number. I do not need to compare the ones.

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1_MNLESE341913_C07L01.indd 399 3/1/14 11:21 AM

Progressto Algebra

EXPLORE2

399 Chapter 7

Listen and DrawMaterials base-ten blocks, connecting cubes

Have children recall what they know about the terms more and greater.• I have a bowl with 15 cubes and a bowl

with 20 cubes. Which bowl has more cubes? 20 cubes is more than 15 cubes. Which number is greater, 15 or 20? 20

• Name another number greater than 15. Possible answer: 16

Read the following problem aloud. Then have children use base-ten blocks or an iTool to model the two numbers on the place-value chart. Remind children that 1 ten is the same as 10 ones. iTools can be found at www.thinkcentral.com.

Which number is greater, 65 or 56?

• Both numbers have a 5 and a 6. How are the models different? 65 has 6 tens and 5 ones. 56 has 5 tens and 6 ones.

Children should then draw quick pictures on the page to represent their models.• How can you use the drawings to compare

the numbers? I can match the tens to see which number has more tens. The number with more tens is the greater number.

• Do you need to compare the ones? Explain. No, because the amount of tens is different and that already tells me which number is greater.

MathTalk MP5 Use appropriate tools

strategically. Use Math Talk to focus on children’s understanding of using tools and tens and ones to compare numbers.

ELL Strategy: Rephrase

Children demonstrate their understanding by rephrasing what they heard about the greater number. Have children model the numbers 17 and 23 using base-ten blocks. • To fi nd the greater number, I look at the

tens. 23 has two tens and 17 has one ten. 2 is greater than 1. 23 is greater than 17.

Have children rephrase the steps to fi nd the greater number. Repeat, modeling two different numbers.

LESSON 7.1

HandsOn

Enrich 7.1Reteach 7.1

1.NBT.B.3 Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

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EXPLAIN3

Share and ShShare and ShShare and Show MATHBOARDMATHBOARD

Model and DrawModel and Draw

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400 four hundred

Use your MathBoard and to show each number.

To compare 25 and 17, fi rst compare the tens.

If the tens are the same, compare the ones.

2 tens are more than 1 ten.

7 ones are more than 5 ones.

25 — is greater than 17 — .

25 — > 17 —


17 — > 15 —

Circle thegreaternumber.

Did tens orones helpyou decide?

Write the numbers.

1. 62 65 tens ones 65 — is greater than 62 — .

65 — > 62 —


84 — > 48 —


72 — > 70 —

79 > 59

79 is greater than 59.

Advanced Learners

MATHEMATICAL PRACTICES

Advanced Learners

COMMON ERRORS

Quick Check

If

Rt I RRR1

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Then

Lesson 7.1 400

Error Children may always say that the tens help them decide which number is greater.

Example For Exercise 3, children circle tens in the middle column.Springboard to Learning Have children tell how they compared the numbers. Point out that if the tens are the same, it is the ones that help them decide which number is greater.

a child misses the checked exercises

Differentiate Instruction with • Reteach 7.1

• Personal Math Trainer 1.NBT.B.3

• RtI Tier 1 Activity (online)

Model and DrawMP5 Use appropriate tools strategically. Work through the first model with children, and have them trace the dashed numbers.• Why do you first compare the tens? Possible

answer: If the tens are different, then the number with more tens is greater.

Work through the second model with children and have them trace the dashed numbers.• Why do you need to compare the ones?

Possible answer: Both numbers have 1 ten.

Share and Show MATHBOARDMATHBOARDMBMMMBBBMATHABOARDMMMAAATHATHTHHAAAAAAAAATTAAAABOARDBOARDBOARD

Help children use the chart. Point out that the two numbers to model are in the first column.• How do you know whether to circle tens

or ones? Possible answer: If I only need to look at the tens to decide which number is greater, I circle tens. Sometimes the tens will be the same so I have to compare the ones. Then I will circle ones.

• How do you know your answer is correct? Possible answer: I know that the open part of the symbol is nearest the greater number.

Use the checked exercises for Quick Check. Children should use their MathBoards to show the solutions.

Materials Workmat 3 (see eTeacher Resources), base-ten blocks

• Write pairs of two-digit numbers from 50 to 99 on the board for children to compare.

• Partners work together to decide which number is greater.

• Partners write greater than sentences with words and symbols for the numbers they model.

• Which digit did you look at first to compare the numbers? the digit that shows the number of tens

• Encourage children to use.base-ten blocks and Workmat 3 to check their work.

Visual / Kinesthetic Individual / Partners

4 ELABORATE

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

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Chapter 7 • Lesson 1 four hundred one 401

Circle thegreaternumber.

Did tens orones help you decide?

Write the numbers.


75 — > 57 —


98 — > 94 —

MATHEMATICALPRACTICE 5 Use a Concrete Model

Use if you need to.

On Your OwnOn Your Own

Write or draw to solve.

6. SMARTER Pam and Jake play a game for points. Pam’s points are 1 ten 6 ones. Jake’s points are 1 one 6 tens. Who has the greater number of points?

7. DEEPER John has 51 cards.Paul has 32 cards. George has a number of cards greater than either Paul or John. How many cards might George have? cards

Accept any number

greater than 51.

Jake

401 Chapter 7

On Your Own MP5 Use appropriate tools strategically. If children answered Exercises 2 and 3 correctly, assign Exercises 4–7.

SMARTER

Exercise 6 requires children to compare two numbers described as tens and ones.

• How can you tell which of two numbers is greater without modeling them? I can compare the tens digit in each number.

• If the tens are the same, how can you tell which number is greater? I compare the ones digit in each number.

DEEPER

MP1 Make sense of problems and persevere in solving them. To extend thinking, ask these questions about comparing numbers.• What if you could not compare the tens and

ones? How else could you explain why 98 is greater than 94? Possible answer: I know that 98 is closer to 100 than 94, so 98 is the greater number.

• If 91 is greater than 19, what do you also know about 19 and 91? Possible answer: I know that 19 is less than 91.

MP7 Look for and make use of structure. • Sal drew 2 tens and 14 ones. Malik drew

3 tens and 4 ones. Whose model shows the greater number? Their models show the same number because 2 tens and 14 ones is the same as 3 tens and 4 ones.

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

EVALUATE5 Formative Assessment

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIESD

MATHEMATICAL PRACTICES

Math

MATHEMATICAL PRACTICES COMMUNICA C

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402 four hundred two

TAKE HOME ACTIVITY • Write 38, 63, 68, and 83 on slips of paper. Show your child two numbers, and ask which number is greater. Repeat with different pairs of numbers.

8. SMARTER Color the balloons that show numbers greater than 56.

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1 ten 6 ones

50

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1 one 6 tens

65

100

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

37 is greater than 43. ● Yes ● No

41 is greater than 39. ● Yes ● No

48 > 52 ● Yes ● No

86 > 68 ● Yes ● No

Lesson 7.1 402

Children practice comparing numbers in the teens to move along the game path.

Children read the book and compare numbers to complete a hundred chart.

Children complete orange Activity Card 4 by modeling and comparing numbers.

GamesThe Greater Game

LiteratureName That Number

Activities20 Through 50

Essential QuestionReflect Using the Language Objective Have children use comparison words and rephrase to answer the Essential Question.• How can you compare two numbers to

find which is greater? Possible answer: First, I compare the tens. The number with more tens is the greater number. If the tens are the same, then I compare the ones.

Math Journal Math

Write a number that is greater than 29. Draw quick pictures to explain.

Have children complete Exercise 8.

SMARTER

MP7 Look for and make use of structure. In Exercise 8, for three of the balloons, children need to identify the number of tens in each balloon and compare it to the number of tens in 56. You may wish to have children circle the number of tens in these three balloons.

SMARTER

Exercise 9 assesses whether children can compare two numbers to find which is greater. Some children may make errors in the definition of greater than or in recognizing the symbol >. Other incorrect answers may be the result of using only the ones to compare numbers. Have children explain how they compared the numbers and made each choice.

Problem Solving • Applications

Mathematical Practices in Your Classroom PROFESSIONALDEVELOPMENT

Problem SolvingProblem Solving

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Chapter 7 four hundred three 403

Circle the greater number.

Did tens or ones help you decide?

Write the numbers.

1.

22 42

tens ones 42 is greater than 22 .

42 — > 22 —

2.

46 64

tens ones 64 — is greater than 46 — .

64 — > 46 —

3.

88 86

tens ones 88 — is greater than 86 — .

88 — > 86 —

4. Color the blocks that show numbers greater than 47.

Algebra • Greater Than

Use if you need to.

Lesson 7.1Practice and Homework

COMMON CORE STANDARDS—1.NBT.B.3 Understand place value.

5. Math Write a number that is greater than 29. Draw quick pictures to explain.

Check children’s work.

403 Chapter 7

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.

CCSS.Math.Practice.MP6 Attend to precision. As children use the terms greater than and less than to compare numbers, they begin to develop an appreciation for communicating ideas precisely.

In everyday language, the word greater has different meanings, but in mathematics, its meaning is specific. Children often misuse greater and more. The terms greater and greater than are used to describe and compare the magnitude of numbers. The terms more and more than are used to tell “how much” or “how many,” as in the example “Jess has 1 more book than Mike.”

Help children differentiate when to use greater and greater than from more and more than. Provide a general example such as, “One is greater than 2. I have more red counters than blue counters.”

• How can you use the words greater than to compare 17 and 3? Possible answer: 17 is greater than 3.

• How can you use the words more than to describe the number of tens and ones in 52 and 24? Possible answers: 52 has more tens than 24. 24 has more ones than 52.

• When do you use the words greater or greater than? Possible answer: when I compare two numbers

• When do you use the words more or more than? Possible answer: when I compare amounts of things

Personal Math Trainer

FOR MORE PRACTICE GO TO THE

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Lesson Check (1.NBT.B.3)

404 four hundred four

1. Circle the number that is greater than 65.Write the numbers.

37 49 56 66


66 — > 65 —

2. Circle the number that is greater than 29.Write the numbers.

19 20 28 92


92 — > 29 —

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

3. What is 5 + 7? Write the sum.

5 + 7 = 12 —

4. Count forward. Write the number that is missing.

110, 111, , 113, 114112

Connecting Math and Science

SizeBig and small are words that tell about size.

ShapeStar and heart are words that tell about shape.

Active ReadingActive ReadingFind the sentence that tells the meaning of property. Draw a line under the sentence.

What’s It Like?

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A property of matter is one part of what something is like. Some properties are size, shape, color, and texture. Texture is what an object feels like.

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In Chapter 7, children extend their understanding of comparing numbers by understanding inequality symbols and modeling a number comparison situation. These same topics are used often in the development of various science concepts and process skills.

Help children make the connection between math and science through the S.T.E.M. activities and activity worksheets found at www.thinkcentral.com. In Chapter 7, children connect math and science with the S.T.E.M. Activity What’s It Like? and the accompanying worksheets (pages 103 and 104).

Through this S.T.E.M. Activity, children will connect the GO Math! Chapter 7 concepts and skills with various object characteristics including solving word problems involving number comparison. It is recommended that this S.T.E.M. Activity be used after Lesson 7.4.

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S.T.E.M. Activity

S.T.E.M. Activity one hundred three 103

Chapter 7What’s It Like?Develop Vocabulary1. Write the definition using your own words.

property:

texture:

weight:

temperature:

Develop Concepts2. What are some of the properties of matter? What are some

words that describe an object’s size? What are some ways to describe an object’s shape?

3. Which would be heavier––a jar filled with pennies or a jar filled with one-dollar bills?

4. How do you know if a food is hot? Explain.

Use with ScienceFusion pages 92–95.

Possible answer: It feels warm to touch. It might have steam coming

off of it.

A property helps tell what something is.

Texture is how something feels.

Weight is how heavy something is.

Temperature tells how hot or cold something is.

size, shape, color, texture; big and small; round, square, star-shaped, and

heart-shaped

A jar filled with pennies would be heavier.

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104 one hundred four

Do the Math!5. There are 56 small cars and 85 large cars. Compare the

numbers. Use quick pictures to show each number. Write <, >, or =.

6. The texture of the toys on the table is soft. 34 soft toys are on the table. There are 10 more soft toys in the toy box. How many toys are soft?

Summarize7. List some properties we use to classify and describe matter.

Think of an object and describe it using these properties.

— —

soft toys

Size, shape, color, weight, texture, and temperature are properties used to

describe matter. Something small, round, yellowish-green, light, fuzzy, and

warm could be a tennis ball that was sitting in the sun in the summer.

Check children’s work.

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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 7.1 404

correctionkey=d lesson 7.1 hands on: algebra • …...lesson 7.1 reteach do not edit--changes must...

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