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About the MathProfessional Development

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LESSON AT A GLANCE

Progressto Algebra

411A Chapter 7

Progress to AlgebraIf Children AskSome children may ask how they can remember which way the greater than or less than symbol goes. There are several ways that can help children remember the correct direction. Not all children will fi nd the same way useful. Some children may come up with their own ways.

• Think of the open part of the symbol as the mouth of a hungry fi sh, alligator, or other animal. The animal wants a lot of food, so it eats the greater number.

• Look at the way the symbol gets wider (greater) or narrower (less) as the comparison is “read” from left to right.

• Use fl ash cards or other devices to help memorize each symbol. Practice aloud, reading just the symbol.

Hands On: Algebra • Use Symbols to Compare

LESSON 7.3

Learning ObjectiveUse symbols for is less than “<”, is greater than “>”, and is equal to “=” to compare numbers.

Language ObjectiveChild pairs create a chart to display how to use symbols to show how numbers compare.

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.)MP1 Make sense of problems and persevere in solving them. MP4 Model with mathematics.MP8 Look for and express regularity in repeated reasoning.

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

Interactive Student Edition

Personal Math Trainer

Math on the Spot Video

Animated Math Models

iTools: Counters

HMH Mega Math

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ENGAGE1Daily Routines

Common Core

1 23 4 Pages 88–89 in Strategies and Practice for Skills and Facts Fluency provide additional fluency support for this lesson.

Lesson 7.3 411B

How can you use symbols to show how numbers compare?

with the Interactive Student Edition

Essential QuestionHow can you use symbols to show how numbers compare?

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

Finn is 7 and Fiona is 5, who is older? Finn How do you know? Answers will vary.Amy has 6 counters and Tim has 2 counters. Who has more counters? Amy How do you know? Answers will vary. How can you find out how the amounts are different? Possible answers; draw pictures, use counters.

Learning ActivityUse cubes or another manipulative and have children build models to show the number of points the blue team scored.

• How many points did the blue team score? 24 points

• What is Avery trying to find? which team won the game

• How do you know if a number is less than 24? Encourage discussion. Answers will vary.

Literacy and MathematicsChoose one or both of the following activities.

• Ask children to draw two groups of objects that show the same amount. Have them label the objects.

• Help the children to create a story that includes amounts that are different and how they compare.

1 23 4 Fluency BuilderFind the Unknown AddendPose basic fact questions with missing numbers. Have children use their fingers to show the number that completes the fact.

5 = 5 take away what? 0

7 = 10 take away what? 3

8 = 8 take away what? 0

9 = 14 take away what? 5

3 = 12 take away what? 9

4 = 9 take away what? 5

5 = 12 take away what? 7

6 = 8 take away what? 2

7 = 9 take away what? 2

9 = 18 take away what? 9

Problem of the Day 7.3Calendar Math Write the number that tells how many days are in the month. Draw a quick picture to show how to model that number with base-ten blocks. Answer depends on current month.

Check children’s quick pictures. Then, ask volunteers to draw quick pictures for other numbers

you name from the calendar. Share their pictures with the class.

VocabularyInteractive Student EditionMultimedia Glossary e

Common Core Fluency Standard 1.OA.C.6

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 <.Also 1.OA.D.7

Name 

<

>=< 23 C       18 18 C 

      18 15 C       18

Thissymbolmeans

is greater than.

Thissymbolmeans

is less than.

Thissymbolmeans

is equal to.

Algebra • Use Symbols to Compare

Youcanusesymbolstocomparenumbers.

Write >, <, or =. Complete the sentence.

1.

51 C       57

51is less than ———57.

2.

29 C =    29

29 29.

3.

35 C >    33

35 33.

4.

48 C <    55

48 55.

Lesson 7.3Reteach

is greater than is less than

is equal to

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7-9 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

1_MNLEAN342736_C07R03.indd 9 2/19/14 6:13 PM

Name

<

<

65 — C 56 — 11 — C 11 —

81 — C 82 — 49 — C 49 —

77 — C 58 — 60 — C 64 —

I Spy SymbolsLook at the glasses. Write the numbers and <, >, or =.

1. 60 64 2. 77 58

3. 49 49 4. 81 82

5. 11 5 + 6 6. 65 56

Write numbers to make each sentence true.

7. 88 < 99 — 8. 55 — = 55

9. 76 — > 75 10. 56 — > 41

Writing and Reasoning Write your own problem.

Possible answer: 26 > 25

Lesson 7.3Enrich

>=

=

>

2526

Also accept 11 5 5 1 6.

Possible answers given for Exercises 7, 9, and 10.

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7-10 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

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DifferentiatedInstruction1

2

3

Progressto Algebra

Listen and DrawListen and Draw

MATHEMATICAL PRACTICES 4MathTalk

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HANDS ON

Chapter 7 four hundred eleven 411

Use . Draw quick pictures to show your work. Write the numbers to compare.

Algebra • Use Symbols to CompareEssential Question How can you use symbols to show how numbers compare?

Lesson 7.3

– < 36 36 – = 36 – > 36

HandsOn

FOR THE TEACHER • Have children use base-ten blocks to show a number less than 36, a number equal to 36, and a number greater than 36.

Represent Compare 47 and 32 in two ways. What two symbols do you use?

Number and Operations in Base Ten—1.NBT.B.3 Also 1.OA.D.7

MATHEMATICAL PRACTICESMP1, MP4, MP8

Math Talk: Possible answer: 47 is greater than 32, so I can write 47 > 32. 32 is less than 47, so I can write 32 < 47.

Accept any number that is less than 36. Check children’s quick picture.

Quick picture should show the number 36.

Accept any number that is greater than 36. Check children’s quick picture.

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1_MNLESE341913_C07L03.indd 411 07/03/14 2:57 AM

411 Chapter 7

Listen and Draw Materials base-ten blocks, connecting cubes

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

Show a number less than 36, a number equal to 36, and a number greater than 36.

Have children use quick pictures to represent the three numbers. Tell children to check that the numbers they write make the comparison true.

• How did you fi nd a number less than 36? Possible answer: I modeled 36 and then took away 2 ones to show 34.

• How did you fi nd a number greater than 36? Possible answer: I modeled 36 and added 1 ten to show 46.

• Could you have used other numbers to correctly complete each comparison? Explain. I could have used other numbers less than 36 and greater than 36, but only 36 is equal to 36.

MathTalk MP4 Model with mathematics.

Use Math Talk to focus on children’s understanding of what the blocks and quick pictures show and which symbol to write when comparing two numbers.• How does the symbol help you decide

which is the greater number? Possible answer: The symbol is wider on the side by the greater number.

ELL Strategy: Develop Meanings

Children defi ne words by using them in context and by matching symbols to the words.Write the <, =, and > symbols on the board. Have children point to the correct symbol as you name it: is equal to, is greater than, is less than.Ask children to defi ne each symbol in their own words. Repeat until children show understanding.Then write 2 two-digit numbers on the board. Have children point to and identify the symbol that belongs between them.Repeat with other examples so children have practice with each symbol.

LESSON 7.3

HandsOn

Enrich 7.3Reteach 7.3

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EXPLAIN3Model and DrawModel and Draw

Share and ShShare and ShShare and Show MATHBOARDMATHBOARD

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412 four hundred twelve

Use . Draw to show each number.Write <, >, or =. Complete the sentence.

21 <C 24

21 is less than 24.24 =C24

24 is equal to 24.30 >C 24

30 is greater than 24.

1.

28 C< 35

28 is less than —— 35.

2.

16 C= 16

16 is equal to —— 16.

3.

46 C> 31

46 is greater than —— 31.

4.

51 C< 52

51 is less than —— 52.

Check children’s drawings.

Advanced Learners

51 > 68

False True

51 < 68

MATHEMATICAL PRACTICES

Quick Check

If

Rt I RRR1

2

3

COMMON ERRORS

Then

Lesson 7.3 412

Error Children write the correct words, but they may write the wrong symbol.

Example For Exercise 3, children write: 46 < 31

46 is greater than 31.Springboard to Learning Review the < and > symbols, and remind children that each symbol always “points to” the number that is less.

a child misses the checked exercises

Differentiate Instruction with • Reteach 7.3

• Personal Math Trainer 1.NBT.B.3

• RtI Tier 1 Activity (online)

Model and DrawMP4 Model with mathematics. Work through the model with children. Have them trace the quick pictures that represent each number. Then have children read each comparison, tracing the symbol.

• What number is in all three comparisons? 24

• In the middle section, how do you know that the two models both show 24? Possible answer: Both 2 tens 4 ones and 1 ten 14 ones are the same as 24 ones.

Share and Show MATHBOARDMATHBOARDMBMMMBBBMATHABOARDMMMAAATHATHTHHAAAAAAAAATTAAAABOARDBOARDBOARD

Remind children to use quick pictures to draw each representation.• How do you know which symbol to use?

Possible answer: I use the is less than symbol if the first number is less, the is greater than symbol if the first number is greater, and the is equal to symbol if both numbers are the same.

• How do you know your answer is correct? Possible answer: I see that the symbol points to the smaller number.

Use the checked exercises for Quick Check.

Materials index cards

• Prepare index cards with several correct and incorrect comparisons, such as 75 > 76, 48 > 42, 89 > 91, 59 < 67, and 34 = 33.

• Give partners a set of index cards. Have children look at the cards one by one.

• Partners decide if the comparison is true or false. If it is false, they write to make it correct.

• Children continue until all the cards are used.

Logical / MathematicalIndividual / Partners

4 ELABORATE

EVALUATE5 Formative Assessment

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Chapter 7 • Lesson 3 four hundred thirteen 413

REMEMBER < is less than

> is greater than= is equal to

MATHEMATICALPRACTICE 4 Use Symbols

DEEPER Write <, >, or =.Draw a quick picture if you need to. 5.

45 >C 42

6.

38 C< 50

7.90 C< 93

8.87 C= 87

9.64 C> 59

11. 96 = 96

12. 53 >

13. 83 <

14. 40 <

15. 71 >

16. 29 = 29

TAKE HOME ACTIVITY • Have your child show you how to write <, >, and = to compare two numbers. Ask him or her to use words to explain each comparison.

10. SMARTER Gill and Rob win tokens in a game. Gill has 86 tokens. Rob has 61 tokens. 70 tokens are needed for a prize. Who has enough tokens for a prize? Write the number. 86 —

On Your OwnOn Your Own

SMARTER Write numbers to solve.Answers will vary for Exercises 12–15. Check children’s work.

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

413 Chapter 7

Essential QuestionReflect Using the Language Objective Have children pair up to create a chart to answer the Essential Question.How can you use symbols to show how numbers compare? Possible answer: I can write >, <, or = between two numbers to show that the first number is greater than, is less than, or is equal to the second number.

Math Journal Math

Choose some numbers to compare to 55. Use <, >, and =.

On Your Own

DEEPER

MP4 Model with mathematics. If children answered Exercises 3 and 4 correctly, assign Exercises 5–16. Suggest that children use their MathBoards to help them complete the exercises.

SMARTER

Exercise 10 requires children to compare three numbers to determine who has “enough.” Make sure students understand that in this case enough means greater than 70. Children should determine that Gill has enough tokens for a prize because he has 86 tokens.

Exercises 11–16 require children to use higher order thinking skills as they write numbers that make each comparison true.

DEEPER

To extend thinking, have children write sentences to show paired comparisons. For example, 64 > 51, so 51 < 64.MP8 Look for and express regularity in repeated reasoning. • Could you use < or > to compare three

numbers? Explain. Show an example. Possible answer: Yes. 13 < 24 < 30

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

Mid

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Mid-Chapter Checkpoint Personal Math TrainerOnline Assessment and Intervention

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Circle the greater number. Write the numbers. (1.NBT.B.3)

1. 38 83 83 _ is greater than 38 _ .

83 _ > 38 _

Circle the number that is less. Write the numbers. (1.NBT.B.3)

2. 61 29 29 _ is less than 61 _ .

29 _ < 61 _

414 four hundred fourteen

Name

3. Matt scores 34 points and wins the game. Lee scores points and does not win. The number of Lee’s points is less than the number of Matt’s points. Is Lee’s score 49 or 29? (1.NBT.B.3)

Concepts and SkillsConcepts and Skills

29 —

4. SMARTER Circle the symbol that makes the math sentence true. (1.NBT.B.3)

44

>

<

=

43

1

2

3

Data-Driven Decision Making

Mid-Chapter Checkpoint 414

Formative AssessmentUse the Mid-Chapter Checkpoint to assess children’s learning and progress in the first half of the chapter. The formative assessment provides the opportunity to adjust teaching methods for individual or whole class instruction.

SMARTER

Children have compared numbers previously, but in Exercise 4 they choose between comparison symbols to make a math sentence true. Children who answer incorrectly may need more practice using the < and > symbols. Remind children that the symbol always “points to” the number that is less.

LESSONS 7.1 TO 7.3

Based on the results of the Mid-Chapter Checkpoint, use the following resources to strengthen individual or whole class instruction.

Key: R—Reteach (in the Chapter Resources)

Item Lesson Standard Common Error Personal

Math TrainerIntervene with

1 7.1 1.NBT.B.3 May confuse the tens and ones 1.NBT.B.3 R—7.1

2, 3 7.2 1.NBT.B.3 May compare the ones instead of the tens 1.NBT.B.3 R—7.2

4 7.3 1.NBT.B.3 May confuse the symbols 1.NBT.B.3 R—7.3

Problem SolvingProblem Solving

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Chapter 7 four hundred fi fteen 415

Write <, >, or = to solve. Circle your answer.

9. Tracey has 26 shells. Heba has 29 shells. Who has a greater number of shells?

Tracey Heba 29 C 26

Algebra • Use Symbols to Compare

Write <, >, or =.Draw a quick picture if you need to.

1.

38 C 31

2.

26 C 42

3.

88 C 78

4.

77 C 77

5.

91 C 89

6.

80 C 82

7.

33 C 44

8.

51 C 60

Lesson 7.3Practice and Homework

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

10. Math Choose some numbers to compare to 55. Use <, >, and =.

>

> >

>

<

<< <

=

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.

415 Chapter 7

Personal Math Trainer

FOR MORE PRACTICE GO TO THE

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Lesson Check (1.NBT.B.3)

416 four hundred sixteen

1. Compare each pair of numbers. Write <, >, or =.

22 C 28 28 C 28 22 C 22 28 C 22

2. Compare each pair of numbers. Write <, >, or =.

78 C 87 78C 78 87 C 78 87 C 87

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

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

7 — tens 9 — ones = 79 —

4. Use the model. Write the number three different ways.

1 — ten 8 — ones

10 — + 8 —

18 —

< >

=<

=

>=

=

Monitoring Common Core Success

Maintaining Focus on the Major WorkThe major work in Grade 1 includes understanding place value (1.NBT.B). In Lessons 7.1–7.3, children continue to develop their understanding of the concepts greater than, less than and equal to. Lessons 7.1 and 7.2 introduce the symbols for greater than and less than as well as how to compare numbers using place value by comparing the tens place then the ones place (1.NBT.B.3). Lesson 7.3 ties the first two lessons together as children write the comparison symbols, including the equality symbol.

Connecting Content Across Domains and ClustersThroughout Lessons 7.1–7.3, children work within Cluster 1.NBT.B to understand place value. The content ties directly to 1.NBT.C where children use place value to add and subtract. In Lessons 7.1–7.3, children build the conceptual awareness to compare larger numbers to determine which number is greater

or less than another number. Children then use this place value knowledge for addition and subtraction. This carries over to work in 1.OA.D where children work with addition and subtraction equations.

Focus on Mathematical Practices In Lessons 7.1–7.3, children attend to precision, MP6. When they are using place value to compare numbers, children are able to articulate why the tens place digits are compared first, then the ones place, if the tens digits are the same in both numbers. When teaching about word problems that relate to comparison, refer to the Mathematical Practices in your Classroom feature on page 403 to see how children can confuse the terms greater than and more than. Use the suggested questions to guide children toward understanding the difference. A discussion about the reasonableness of solutions can further stress MP6.

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 7.3 416