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About the MathProfessional Development

LESSON AT A GLANCE

Professional Development Videos

Progressto Algebra

405A Chapter 7

Interactive Student Edition

Personal Math Trainer

Math on the Spot Video

Animated Math Models

iTools: Base-Ten Blocks

HMH Mega Math

Progress to AlgebraTeaching for DepthIn the previous lesson, children learned to compare numbers and identify the symbol for is greater than. In this lesson, they learn to compare numbers and identify the symbol for is less than.

> is greater than < is less than

It is important that children distinguish the symbols, but they also need to understand that either symbol can be used to express the same inequality. For example, 26 > 15 and 15 < 26 mean the same. Switching the symbols and the position of the number that is greater and the number that is less provides the same information in different ways. In either form, the inequality symbol always points to the number that is less.

Hands On: Algebra • Less Than

LESSON 7.2

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

Language ObjectiveChildren list in their Math Journals comparison words that show which number is less.

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.)MP3 Construct viable arguments and critique the reasoning of others. 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

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ENGAGE1Daily Routines

Common Core

1 23 4 Pages 40–41 in Strategies and Practice for Skills and Facts Fluency provide additional fluency support for this lesson.

Lesson 7.2 405B

How can you compare two numbers to f ind which is less?

Name That Number

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

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

with the Interactive Student Edition

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

Making ConnectionsInvite children to tell you what they know about comparing.

• How do you compare two cube trains to tell which has fewer cubes? Possible answer: Lay the cube trains next to each other.

• How do you know which cube train has fewer cubes? Possible answer: The cube train that is shorter has fewer cubes.

Learning ActivityInvite children to tell how many flowers are in the flower bed. 45 flowers How many flowers are in the flowerpot? a number less than 45 Have children draw quick pictures to model the number.

• How would using a model help you compare the numbers? Answers will vary.

• How many tens are in 45? 4 How many ones are in 45? 5

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 less than.

• Invite children to list the things Avery tells them about the flowers in the flower bed and the flowerpot.

1 23 4 Fluency BuilderAdd Within 10Materials connecting cubes

Show a 3-cube train of one color and a 4-cube train of another color.

• What addition fact do these cube trains show? 3 + 4 = 7 or 4 + 3 = 7

Write the addition fact on the board. Then model other addition facts within 10. Have volunteers write the facts on their MathBoards.

Problem of the Day 7.2Basic Facts Write a number sentence to go with the picture.

9 − 4 = 5 —— 3 + 5 = 8 ——

or 5 + 3 = 8

Vocabulary is less than <

Interactive Student EditionMultimedia Glossary e

Common Core Fluency Standard 1.OA.C.6

Listen and DrawListen and Draw

MATHEMATICAL PRACTICES 3MathTalk

Name HANDS ON

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Chapter 7 four hundred fi ve 405

Use to solve. Draw quick pictures to show your work.

Lesson 7.2Algebra • Less ThanEssential Question How can you compare two numbers to find which is less?

Tens Ones

Compare How does your drawing show which number is less? Explain.FOR THE TEACHER • Read the problem. Which

number is less, 22 or 28? Have children use base-ten blocks to solve.

HandsOn

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

MATHEMATICAL PRACTICESMP3, MP5, MP7

Math Talk: Possible answer: 22 and 28 have the same number of tens, but 22 has fewer ones than 28. So 22 is less than 28.

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EXPLORE21.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 <.

Name 

74

44

37

31

65

43

23

26

Algebra • Less Than

You can compare numbers to find which is less.

23 — is less than 26 —.

23 — < 26 —

43 — is less than 65 —.

43 — < 65 —

Draw lines to match. Write the numbers to compare.

1.

31 — is less than 37 —.

31 — < 37 —

2.

44 — is less than 74 —.

44 — < 74 —

Lesson 7.2Reteach

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7-7 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

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Name

24 — < 49 — 22 — < 33 —

44 — < 46 —

70 — < 90 — 77 — < 81 —

51 — < 66 —

Which Is Less?Read the sentence. Circle true or false. Then write the numbers to make the comparison true.

1. Eric said 66 is less than 51.

true

false

2. Dan said 44 is less than 46.

true

false

3. Anna said 81 is less than 77.

true

false

4. Shanta said 90 is less than 70.

true

false

5. Lars said 22 is less than 33.

true

false

6. Kerry said 49 is less than 24.

true

false

Writing and Reasoning Write four numbers that are less than 61.Possible answer: 59, 45, 37, 22.

Lesson 7.2Enrich

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7-8 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

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DifferentiatedInstruction1

2

3

Progressto Algebra

405 Chapter 7

Listen and DrawMaterials base-ten blocks, connecting cubes

Have children recall what they know about the terms fewer and less. Help them understand that fewer is used with things that are countable, and less is used to compare numbers, or something that is not countable.• Ron has 19 crackers. Minnie has 13 crackers.

Who has fewer crackers? Minnie Which number is less, 13 or 19? 13

• Name another number less than 19. Possible answers: Any number from 0 to 18 is correct.

Read the following problem aloud. Then have children use base-ten blocks to model.

Which number is less, 22 or 28?

Children then represent their models by drawing quick pictures of 22 in the upper portion of the place-value chart and 28 in the lower portion of the chart.• How do you use your models or pictures to

fi nd which number is less? Possible answer: Both numbers have 2 tens, so I compare the ones. 22 has fewer ones than 28, so 22 is less than 28.

• How is this like the process you used to fi nd the number that is greater? Possible answer: In both cases, you compare the tens fi rst. If the tens are the same, you compare the ones.

MathTalk MP3 Construct viable

arguments and critique the reasoning of others. Use Math Talk to focus on children’s understanding of how the drawing helps them compare the numbers.

ELL Strategy: Scaffold Language

Use scaffolding language to help children understand the concept of less than.Use base-ten blocks to show the numbers 27 and 23. Have children describe the models and identify the numbers they represent.Provide the steps to compare two two-digit numbers.• Compare the tens to fi nd out which number

is less. If the tens are equal, compare the ones.

Have the children use the steps to compare 27 and 23.Repeat the activity with other two-digit numbers.

LESSON 7.2

HandsOn

Enrich 7.2Reteach 7.2

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Model and DrawModel and Draw

Share and ShShare and ShShare and Show MATHBOARDMATHBOARD

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Use your MathBoard and to show each number.

Compare numbers to fi nd which is less. How do you know which

number is less?

Circle thenumber that is less.

Did tens orones help you decide?

Write the numbers.

1 . 39 36 tens ones 36 — is less than 39 — .

36 — < 39 —

2. 80 94 tens ones 80 — is less than 94 — .

80 — < 94 —

3. 57 54 tens ones 54 — is less than 57 — .

54 — < 57 —

43 — is less than 49 — .

43 — < 49 —

EXPLAIN3

MATHEMATICAL PRACTICES

Advanced Learners

Quick Check

If

Rt I RRR1

2

3

COMMON ERRORS

Then

Lesson 7.2 406

Error Children may write the numbers in the sentence using the order in which they were given.

Example For Exercise 3, children write 57 is less than 54.Springboard to Learning Have children look at the number they circled as being less and write that number first in the comparison.

a child misses the checked exercises

Differentiate Instruction with • Reteach 7.2

• Personal Math Trainer 1.NBT.B.3

• RtI Tier 1 Activity (online)

57 < 82

82 > 5757 82

Materials Workmat 3, Numeral Cards 50–100 (see eTeacher Resources), base-ten blocks

• Have partners mix up the Numeral Cards for 50–100 and place them facedown in a pile.

• Each child picks a card and turns it faceup. Partners work together to write two different number sentences using > and < symbols to compare the numbers.

• Children use base-ten models to check that their number sentences are correct.

VisualIndividual / Partners

Model and DrawMP5 Use appropriate tools strategically. Work through the model with children. Have them trace the dashed numbers. Point out that when the tens are the same, they then compare the ones.Have children read aloud the comparison statement “43 is less than 49.”• How is the is less than symbol different

from the is greater than symbol? Possible answer: It points left, which is the opposite direction of the is greater than symbol that points right.

Share and Show MATHBOARDMATHBOARDMBMMMBBBMATHABOARDMMMAAATHATHTHHAAAAAAAAATTAAAABOARDBOARDBOARD

Help children use the chart. Point out that the two numbers to model are in the first column.• Which do you compare first, the ones or

the tens? Explain. I compare the tens; if one of the numbers has fewer tens, then I know it is less without having to compare the ones.

• How can you check that your answers are correct? Possible answer: I can compare the models .

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

4 ELABORATEName

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Chapter 7 • Lesson 2 four hundred seven 407

Circle thenumber that is less.

Did tens orones help you decide?

Write the numbers.

4. 47 48 tens ones 47 — is less than 48 — .

47 — < 48 —

5. 82 28 tens ones 28 — is less than 82 — .

28 — < 82 —

6. 96 90 tens ones 90 — is less than 96 — .

90 — < 96 —

7. 23 32 tens ones 23 — is less than 32 — .

23 — < 32 —

MATHEMATICALPRACTICE 5 Use a Concrete Model

DEEPER Use if you need to.

On Your OwnOn Your Own

Write a number to solve.

8. SMARTER Ella has 22 beads. Lauren has fewer beads than Ella. How many beads might Lauren have? beads

Accept any number less than 22.

On Your Own MP5 Use appropriate tools strategically. If children answered Exercises 2 and 3 correctly, assign Exercises 4–8.• For Exercises 4–7, how can you tell which of

two numbers is less just by looking at them? Possible answer: I can look at the tens digit of each number. The number with a smaller tens digit is less than the other number. If the tens are the same, I look at the ones digit. The number with a smaller ones digit is less than the other number.

DEEPER

MP8 Look for and express regularity in repeated reasoning. To extend thinking, have children rewrite the comparisons in Exercises 4–7 using the is greater than (>) symbol.Children should make the connection that the greater than and less than comparison statements are opposite. An activity like this one helps to develop children’s critical thinking skills.• If you know that 24 is less than 34, what else

do you know? 34 is greater than 24.

• If you know that 87 is greater than 49, what else do you know? 49 is less than 87.

• How could you use what you know about comparing numbers to compare 120 and 112? Possible answer: I first look at the hundreds. They are the same so I look at the tens. 2 tens is more than 1 ten so I know that 120 is more than 112.

SMARTER

Exercise 8 requires children to demonstrate their understanding of less than in the context of a word problem.

407 Chapter 7

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIES

EVALUATE5 Formative Assessment

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIESD

MATHEMATICAL PRACTICES

Math

MATHEMATICAL PRACTICES

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TAKE HOME ACTIVITY • Write 47, 54, 57, and 74 on slips of paper. Show your child two numbers, and ask which number is less. Repeat with different pairs of numbers.

Write a number to solve.

9. SMARTER Nan makes the number 46. Marty makes a number that is less than 46. What could be a number Marty makes?

10. SMARTER Jack makes the number 92. Kit makes a number that has fewer ones than 92. What could be a number Kit makes?

—

—

———————

———————

11. SMARTER Write a number that is less than 67.

How do you know your number is less than 67?

Accept any number less than 46.

Accept any number that has a 0 or 1 in the ones place.

Possible answer: My number has fewer tens.

Accept any number that is less than 67.Math on the Spot videos are in the Interactive Student Edition and at www.thinkcentral.com.

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.

GamesRainy Day Fun

LiteratureName That Number

Activities20 Through 50

Essential QuestionReflect Using the Language Objective Have children make a list of comparison words in their Math Journals to answer the Essential Question.• How can you compare two numbers to find

which is less? Possible answer: I compare the tens first. The number with fewer tens is less. If the tens are the same, I compare the ones in the same way.

Math Journal Math

Write a number that is less than 41. Draw quick pictures to explain.

MP7 Look for and make use of structure. For Exercises 9 and 10, make sure children understand there is more than one correct answer.

SMARTER

In Exercises 9 and 10, children use higher order thinking skills to decide which digit of each number will guide them in determining a correct answer.

SMARTER

For Exercise 11, most children are likely to correctly identify a number less than 67 but may have difficulty explaining their reasoning. Use question prompts such as whether they compared tens or ones, how a counting sequence may have helped, or whether they used a counting chart. Point out that the ones help them decide which number is less only if the tens are the same.

Lesson 7.2 408

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

Problem Solving • Applications

Cross-Curricular

Problem SolvingProblem Solving

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Chapter 7 four hundred nine 409

Lesson 7.2Algebra • Less Than

Use if you need to.

Circle the number that is less.

Did tens or ones help you decide?

Write the numbers.

1.

34 36 tens ones

34 — is less than 36 — .

34 — < 36 —

2.

75 57

tens ones

57 — is less than 75 — .

57 — < 75 —

3.

80 89

tens ones

80 — is less than 89 — .

80 — < 89 —

Write a number to solve.

4. Lori makes the number 74. Gabe makes a number that is less than 74. What could be a number Gabe makes?

Practice and Homework

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

5. Math Write a number that is less than 41. Draw quick pictures to explain.

Accept any number less than 74.

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.

409 Chapter 7

• Take children on a walk to collect fallen leaves or other small items such as rocks or shells.

• Have small groups of children sort their collections by color, shape, or size.

• Then have children count the number of items in each group and use the words is greater than and is less than to compare the groups.

• Discuss fruits and vegetables you might find for sale at a roadside stand or a farmer’s market.

• Pose this problem: Jenny and Cindy went to a farmer’s market. Jenny bought 25 apples. Cindy bought 18 apples. Who bought fewer apples? Explain. Cindy; 18 is less than 25.

• Give children similar problems to solve. Have them explain their solutions, using the words is less than in their explanations.

SOCIAL STUDIES

Personal Math Trainer

FOR MORE PRACTICE GO TO THE

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410 four hundred ten

Lesson Check (1.NBT.B.3)

1. Circle the number that is less than 52. Write the numbers.

25 52 64 88

25 — is less than 52 — .

25 — < 52 —

2. Circle the number that is less than 76. Write the numbers.

100 81 77 59

59 — is less than 76 — .

59 — < 76 —

Spiral Review (1.NBT.A.1, 1.NBT.B.2)

3. What number does the model show? Write the number.

3 — tens 7 — ones = 37 —

4. Count by tens. Write the missing numbers.

8, 18, 28, 38 , 48 , 58

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 7.2 410