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LESSON AT A GLANCE

Progressto Algebra

423A Chapter 7

Interactive Student Edition

Personal Math Trainer

Math on the Spot Video

iTools: Base-Ten Blocks

MP8 Look for and express regularity in repeated reasoning.After identifying numbers that are 10 less and 10 more, children may notice certain regularities in the numbers. Guide children to focus on similarities and differences, generalize from these examples, and create shortcuts.

• Compare the starting number and the number that is 10 less. How are the numbers alike? different? The number of ones is the same; the number of tens is different.

Have children share their observations. If needed, explain that only the tens place changes when they count 10 less or 10 more. This rule encourages the use of mental math.

Hands On • 10 Less, 10 More

LESSON 7.5

Learning ObjectiveIdentify numbers that are 10 less or 10 more than a given number.

Language ObjectiveChildren write down a secret clue to how they can identify numbers that are 10 less or 10 more than a number.

MaterialsMathBoard, base-ten blocks

F C R Focus:Common Core State Standards

1.NBT.C.5 Given a two-digit number, mentally fi nd 10 more or 10 less than the number, without having to count; explain the reasoning used.

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. MP2 Reason abstractly and quantitatively. MP3 Construct viable arguments and critique the reasoning of others.MP6 Attend to precision.

F C R Coherence:Standards Across the GradesBeforeK.CC.C.6

Grade 11.NBT.C.5

After2.NBT.B.8

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 100–101 in Strategies and Practice for Skills and Facts Fluency provide additional fluency support for this lesson.

Lesson 7.5 423B

How can you identify numbers that are 10 less

or 10 more than a number?

Problem of the Day 7.5Word of the Day sumCircle the number sentence that has a sum of 9.

17 − 8 = 9 9 + 9 = 18 8 + 1 = 9

Have children identify what “9” is in the other two number sentences. In 17 − 8 = 9, 9 is the difference. In 9 + 9 = 18, both 9s are addends.

VocabularyInteractive Student EditionMultimedia Glossary e

1 23 4 Fluency BuilderMaterials MathBoards

Make 10 to AddDisplay number sentences like these on the board. Have children copy and complete them by filling in the missing numbers.

Then have children recite each number sentence with a partner or whole class.

8 + 7 = 10 + 5 = 15

5 + 6 = 10 + 1 = 11

7 + 9 = 10 + 6 = 16

9 + 5 = 10 + 4 = 14

6 + 7 = 10 + 3 = 13

4 + 8 = 10 + 2 = 12

3 + 9 = 10 + 2 = 12

7 + 7 = 10 + 4 = 14

9 + 8 = 10 + 7 = 17

8 + 6 = 10 + 4 = 14

with the Interactive Student Edition

Essential QuestionHow can you identify numbers that are 10 less or 10 more than a number?

Making ConnectionsInvite children to talk about how they know one number is greater or less than another.

How do you know that 35 is greater than 29? Possible answer: I know that 3 tens is more than 2 tens.

What number is 1 more than 25? 26 How do you know? 6 is one more than 5

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

Ask the following questions.

• How do you know when a model shows a number that is 10 less than another number? The model has one fewer ten-block.

• How can you model the number that is 10 more than 25? Possible answer: I can add one more ten-block to my model.

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

• Have children make up a partner game to practice naming numbers that are ten less or ten more than a given number.

• Have children write a how-to paragraph to explain how to find the number that is ten less or ten more than another number.

Common Core Fluency Standard 1.OA.C.6

DifferentiatedInstruction1

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Listen and DrawListen and DrawHands

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MATHEMATICAL PRACTICES 6MathTalk

HANDS ONName

Chapter 7 four hundred twenty-three 423

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

10 Less, 10 MoreEssential Question How can you identify numbers that are 10 less or 10 more than a number?

Pat

12

Tony

22

Jan

32

FOR THE TEACHER • Read the following problem. Tony has 2 boxes of markers and 2 more markers. Pat has 10 fewer markers than Tony. Jan has 10 more markers than Tony. How many markers does each child have?©

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Lesson 7.5

Number and Operations in Base Ten—1.NBT.C.5

MATHEMATICAL PRACTICESMP1, MP2, MP3, MP6

What number has one less 10 than 12? Explain.

Math Talk: Possible answer: 12 has 1 ten and 2 ones. 1 ten minus 1 ten is zero tens. So, the number with one less ten than 12 has 0 tens and 2 ones, or 2.

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EXPLORE2

12 22 32

24 34 44

25 35 45

Name 

10 Less, 10 More

24 is 10 less 44 is 10 more than 34. than 34.

Write the numbers that are 10 less and 10 more.

1.

2.

Lesson 7.5Reteach

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7-13 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

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Name

What Is My Number?Read the riddle. Write the number.

1. 47 is 10 less than my number.67 is 10 more than my number.What is my number? 57

2. 75 is 10 more than my number.55 is 10 less than my number.What is my number? 65

3. 71 is 10 less than my number.What is my number? 81

4. 100 is 10 more than my number.What is my number? 90

5. My number is 10 more than 88. What is my number? 98

6. My number is 10 less than 10. What is my number? 0

Writing and Reasoning Write your own riddle.

Check children’s work. Answers will vary.

Lesson 7.5Enrich

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7-14 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

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DifferentiatedInstruction1

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Progressto Algebra

Problem Type: Compare • Smaller Unknown

Problem Type: Compare • Bigger Unknown

423 Chapter 7

Reteach 7.5 Enrich 7.5

Listen and Draw Materials base-ten blocks

Point out the box of markers at the top of the workspace. Make sure children know that there are 10 markers in the box. Then read the following problem aloud.

Tony has 2 boxes of markers and 2 more markers. Pat has 10 fewer markers than Tony. Jan has 10 more markers than Tony. How many markers does each child have?

• How can you use a model to fi nd the number of markers Pat has? Possible answer: Pat has 10 fewer markers than Tony, so I start by showing Tony’s markers. He has 2 tens and 2 ones, or 22 markers. I take away 1 ten to show Pat’s markers. That leaves 1 ten and 2 ones, or 12 markers for Pat.

• How many markers does Jan have? Explain. 32; Possible answer: Jan has one more ten than Tony. 2 tens + 1 ten is 3 tens. Jan has 3 tens 2 ones, or 32.

Explain to children that they can use mental math to fi nd 10 less and 10 more. Point out that mental math is a quicker way of solving a problem than writing or modeling it.• When you fi nd 10 less or 10 more than a

number, what happens to the number of ones? It stays the same.

Explain that because the tens digit only changes by 1, children can fi nd 10 less or 10 more mentally by subtracting or adding 1 to the number of tens.

MathTalk

MP6 Attend to precision. Use Math Talk to focus on children’s ability to explain their understanding of comparing tens.

ELL Strategy: Model Concepts

Children use models to develop and talk about their understanding of ten less and ten more.Display a model for 27. Have children make the same model. As you model taking away 1 ten, say, I can take away ten. Have children copy you.• What number is 10 less than 27? 17 is 10 less

than 27.

Have children restore their models to 27.• I can add ten. What number is 10 more than

27? 37 is 10 more than 27.

LESSON 7.5

HandsOn

1.NBT.C.5 Given a two-digit number, mentally fi nd 10 more or 10 less than the number, without having to count; explain the reasoning used.

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EXPLAIN3

31 41 5160 70 80

Model and DrawModel and Draw

Share and ShShare and ShShare and Show MATHBOARDMATHBOARD

23 33

Think

43

Think

1. 2.

424 four hundred twenty-four

Use mental math. Write the numbers that are 10 less and 10 more.

3. 4.

23 is 10 less than 33. 43 is 10 more than 33.

5. 6.

7. 8.

14 24 34 76 86 96

27 37 47 5 15 25

56 66 7648 58 68

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MATHEMATICAL PRACTICES

Advanced Learners

Quick Check

If

Rt I RR1

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COMMON ERRORS

Then

Error Children may change the value of the ones digit instead of the tens digit.

Example For Exercise 3, children write 57 and 59.Springboard to Learning Remind children that for 10 less and 10 more, the number of ones stays the same.

Lesson 7.5 424

a child misses the checked exercises

Differentiate Instruction with • Reteach 7.5

• Personal Math Trainer 1.NBT.C.5

• RtI Tier 1 Activity (online)

Model and DrawMP6 Attend to precision. Have children use the model to determine the numbers that are 10 less and 10 more than 33. Have children use mental math. Tell them to think about adding blocks for 10 more and taking away blocks for 10 less.• What number do the blocks on the left

show? 2 tens 3 ones, or 23 How does it compare to the model for 33? It has one fewer ten.

• How do the numbers show that 43 is 10 more than 33? Possible answer: The tens digit changes from 3 to 4. That means there is one more ten in 43 than there is in 33.

• What number is 10 more than 43? Explain. 53; Possible answer: The tens digit increases by one.

Share and Show MATHBOARDMATHBOARDMBMMMBBBMATHABOARDMMMAAATHATHTHHAAAAAAAAATTAAAABOARDBOARDBOARD

Have children use mental math to complete the exercises and their MathBoards to explain their thinking.• How do you know your answers are

correct? Possible answer: I check the pattern.

Use the checked exercises for Quick Check.

Materials Numeral Cards 10–90 (see eTeacher Resources)

• Shuffle the Numeral Cards and distribute them facedown in equal piles.

• Working with his or her own pile of cards, each child turns over a card, writes the number, and circles it. To the left of the circled number, the child writes the number that is 10 less. To the right of the circled number, the child writes the number that is 10 more.

VisualIndividual / Partners

58 68 78

4 ELABORATE

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

Name

Chapter 7 • Lesson 5 four hundred twenty-fi ve 425

MATHEMATICALPRACTICE 3 Apply Use mental math.

Complete the chart. Explain your method.

10 Less 10 More

9. 29 39 49

10. 65 75 85

11. 54 64 74

12. 80 90 100

13. 33 43 53

14. 11 21 31

15. 6 16 26

On Your OwnOn Your Own

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16. SMARTER Solve.I have 89 rocks. I want to collect 10 more. How many rockswill I have then? 99 rocks

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PROBLEM TYPE SITUATIONS

425 Chapter 7

On Your OwnMP3 Construct viable arguments and critique the reasoning of others. If children answered Exercises 7 and 8 correctly, assign Exercises 9–16.

SMARTER

Exercise 16 requires children to use higher order thinking skills as they apply what they have learned to a word problem. Have partners explain their solution strategies to one another.

DEEPER

MP2 Reason abstractly andquantitatively. To extend thinking, have children write riddles like the following for a classmate to solve.I am 10 less than 50.I am 10 more than 30.What number am I? 40

MP6 Attend to precision.• How can you check that you found the right

number? Possible answer: I can use a hundred chart. Ten less is the box above a number. Ten more is the number below the box.

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

Addition and Subtraction

Put Together/Take Apart • Total Unknown Exercise: 19

Compare • Difference Unknown Exercise: 18

Compare • Smaller Unknown Exercise: 17

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Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIES

EVALUATE5 Formative Assessment

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIESD

MATHEMATICAL PRACTICES

Math

Personal Math Trainer

MATHEMATICAL PRACTICES COMMUNICA C

426 four hundred twenty-six

Choose a way to solve. Draw or write to show your work.

17. The plant has 4 fewer ladybugs on it than the tree. The tree has 7 ladybugs on it. How many ladybugs are on the plant?

3 ladybugs

18. Amy has 7 ribbons. Charlotte has 9 ribbons. How many more ribbons does Charlotte have than Amy?

2 more ribbons

19. DEEPER Margo has 28 stamps. Chet has 10 more stamps than Margo. Luis has 10 more stamps than Chet. How many stamps does Luis have?

48 stamps

TAKE HOME ACTIVITY • Write a two-digit number, such as 25, 40, or 81. Ask your child to identify the numbers that are ten less than and ten more than that number. Repeat with other numbers.

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20. SMARTER Draw a quick picture to show a number that is 10 less than the model.

What is the new number? B33

Lesson 7.5 426

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

Children read the book and use place value to find the number of strawberries.

Children name numbers that are ten more and ten less than a given number.

GamesPuddle Hopping

LiteratureStrawberries

Activities20 Through 50

Essential QuestionReflect Using the Language Objective Have children write down a secret clue to answer the Essential Question.How can you identify numbers that are 10 less or 10 more than a number? Possible answer: I can think about the number as tens and ones. For 10 less, I count back 1 from the number of tens and keep the ones the same. For 10 more, I count on 1 from the number of tens and keep the ones the same.

Math Journal Math

Choose a number from 10 to 90. Draw and write to show the numbers that are 10 less and 10 more than your number.

Have children solve each problem. Exercises 17 and 18 are Compare/Smaller Unknown and Compare/Difference Unknown problem types.

DEEPER Multi-Step

MP7 Look for and make use of structure. In Exercise 19, children find 10 more than a number and then 10 more again.

Personal Math Trainer SMARTER

Be sure to assign Exercise 20 to children in the Personal Math Trainer. It features a video to help them model and answer the problem. The problem assesses whether children can draw and identify a number that is 10 less than a given model. Some children who answer incorrectly may change the value of the ones digit instead of the tens digit. Remind children that for 10 less and 10 more, the number of tens changes but the number of ones stays the same.

Problem Solving • Applications

COMMON CORECOMMCOMMCOMMCOMMON CON CON CON COREOREOREORE

PROFESSIONALDEVELOPMENT Math Talk in Action

Problem SolvingProblem Solving

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Practice and HomeworkLesson 7.5

COMMON CORE STANDARD—1.NBT.C.5 Use place value understanding and properties of operations to add and subtract.

10 Less, 10 More

Use mental math.Complete the chart.

Chapter 7 four hundred twenty-seven 427

10 Less 10 More

1. 38 48 58

2. 73 83 93

3. 8 18 28

4. 27 37 47

5. Jim has 16 books. Doug has 10 fewer books than Jim. How many books does Doug have? 6 books

Name

Choose a way to solve. Draw or write to show your work.

6. Math Choose a number from 10 to 90. Draw and write to show the numbers that are 10 less and 10 more than your number.

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.

427 Chapter 7

After completing Exercises 1–4, discuss ways to find 10 more or 10 less.

Teacher: How did you find your answers for Exercise 2?

Ruthie: I pictured in my head what the blocks would look like if I made 83. Then I imagined taking one ten away to make 73. I thought about add-ing one ten to 83 to make 93.

Teacher: Good. Did anyone use a different way?

Farah: I thought about tens. 83 has 8 tens. 8 tens 2 1 ten is 7 tens. So the number that is 10 less than 83 has 7 tens 3 ones, or 73.

Stephen: And the number that is 10 more than 83 has 8 1 1 tens, or 9 tens. Ten more than 83 is 93.

Teacher: You only added the tens. What about the ones?

Farah: You are finding 10 more and 10 less. The ones always stay the same.

Teacher: That is correct. Is there another way to find 10 more and 10 less than 83?

Caryn: You can add and subtract. 83 minus 10 is 73. 83 plus 10 is 93.

Teacher: You have come up with several different waysto use tens. Great thinking!

18eighteen

Personal Math Trainer

FOR MORE PRACTICE GO TO THE

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1. What number is 10 less than 67?Write the number.

57 —

2. What number is 10 more than 39?Write the number.

49 —

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

3. How many tens and ones make this number?Write how many.

1 —

ten 8 — ones

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

7 — tens = 70 —

Lesson Check (1.NBT.C.5)

428 four hundred twenty-eight

Monitoring Common Core Success

Maintaining Focus on the Major WorkThe major work in Grade 1 includes understanding place value (1.NBT.B). In Lesson 7.4, children use place value skills to compare numbers that are greater than or less than a set of two-digit numbers. Children read the word problem and use place value skills learned in the earlier lessons to identify individual numbers in the set that fit the criteria. In Lesson 7.5, children use models, then use mental math to identify numbers 10 less or 10 more than a number.

Connecting Content Across Domains and ClustersLessons 7.4 and 7.5 focus on Clusters 1.NBT.B and 1.NBT.C. In 1.NBT.B, children compare numbers based on the meaning of the ones and tens digits. They problem solve using models to find a solution that fits a specific set of criteria. They connect this skill to Cluster 1.NBT.C found in Lesson 7.5. In this lesson, children are given a two-digit number and must find a number that is 10 more or 10 less. The work in both of these clusters ties place value to the counting sequence, connecting the lessons to Cluster 1.NBT.A. As children use mental math to identify a number that is 10 more or 10 less, the tens digit is the only digit that changes in the number.

Focus on Mathematical Practices In Lessons 7.4 and 7.5, children must make sense of problems and persevere to solve them, MP1. The problems found in Lesson 7.4 have children persevere through a problem with two steps. First they identify the numbers in the set that are less than or greater the number in the problem. Then they use the same place value comparison skill for the next number in the problem. This is a good chance to emphasize MP1 by helping children know what the problem is asking and how the given information can be used to solve the problem. Lesson 7.5 similarly requires children to make sense of quantitative comparisons like “10 more than” or “10 less than.”

Go Math! author Juli Dixon brings the mathematical practices to life by modeling the integration of Mathematical Practice 1 (making sense and persevering in solving problems) in Mathematical Practices Professional Development Videos, Segment 1.

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 7.5 428