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About the MathProfessional Development

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LESSON AT A GLANCE

Progressto Algebra

359A Chapter 5

Add to Find Differences

LESSON 5.8

MP6 Attend to precision.A number line can be used to solve subtraction problems. By using this tool, children can see how to add to fi nd the difference between two numbers (or the missing addend). It is important to guide the class through the multistep process when they begin.

• First show how to start with the subtrahend and fi nd how many ones need to be added to get to the next tens number.

• Then fi nd how many more ones they need to add to get to the minuend.

• Demonstrate how to keep track of the numbers and how they are used in the model by writing an addition sentence. Help children understand that the sum of the numbers they model on the number line and write in the addition sentence is the difference in the subtraction problem.

Learning ObjectiveUse addition to fi nd differences.

Language ObjectiveChildren discuss with a partner what they learned about how you can use addition to solve subtraction problems.

MaterialsMathBoard

F C R Focus:Common Core State Standards

2.NBT.B.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

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. MP3 Construct viable arguments and critique the reasoning of others. MP5 Use appropriate tools strategically. MP6 Attend to precision. MP8 Look for and express regularity in repeated reasoning.

F C R Coherence:Standards Across the GradesBefore1.OA.A.1 1.NBT.C.4

Grade 2.NBT.B.5

After3.NBT.A.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 313J.

FOCUS COHERENCE RIGOR

Interactive Student Edition

Personal Math Trainer

Math on the Spot Video

iTools: Number Lines

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ENGAGE1Daily Routines

Common Core

Lesson 5.8 359B

How can you use addition to solve

subtraction problems?

with the Interactive Student Edition

Essential QuestionHow can you use addition to solve subtraction problems?

Making ConnectionsAsk children to discuss what they already know about how addition and subtraction are related.

What addition facts relate to the subtraction fact 18 − 8 = 10? 8 + 10 = 18; 10 + 8 = 18 How would you explain in your own words the relationship between subtraction facts and addition facts? Sample answer: if you are given an addition fact, you can subtract either addend from the sum and the answer will be the other addend.

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

• In this story, what is the whole? What are the parts? Possible answer: The whole is the total number of eggs. The parts are the number of eggs that hatched and the number of eggs that have not hatched.

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

• Have children write a story that involves finding the difference of two 2-digit numbers. Ask them to underline the number they are to subtract using a blue crayon.

• Have children represent the numbers 12 and 24 using base-ten blocks. Have them group the base-ten blocks to find the sum. Then have them write two related subtraction facts.

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

Children read the book and learn about 2-digit addition and subtraction with regrouping.

Party Plans

1 23 4 Fluency BuilderRelated FactsReview with children that related facts consist of the same parts and whole. Write the number sentence 42 + 14 = 56 on the board. Ask: Which numbers are the parts? Which number is the whole? 42 and 14 are the parts. 56 is the whole.

Ask children to write a related subtraction fact that has the same whole and parts. 56 − 14 = 42, or 56 − 42 = 14 On the board, write all four related facts on the board and have children identify the parts and the whole in each fact.

Problem of the Day 5.8Number of the Day 50

Find the missing addend.

47 + ++ = 50 3

44 + + = 50 6

41 + + = 50 9

VocabularyInteractive Student EditionMultimedia Glossary e

MATHEMATICAL PRACTICES 1MathTalk

Listen and DrawListen and Draw

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Chapter 5 three hundred fi fty-nine 359

Draw pictures to show the problem. Then write a number sentence for your drawing.

Now draw pictures to show the next part of the problem. Write a number sentence for your drawing.

Possible answer:

25 − 3 = 22 ———

Possible answer:

22 + 3 = 25 ———

Add to Find DifferencesEssential Question How can you use addition to solve subtraction problems?

Lesson 5.8

22 — markers

25 — markers

FOR THE TEACHER • Have children draw pictures to represent this problem. Sophie had 25 markers. She gave 3 markers to Josh. How many markers does Sophie have now? Then ask children: How many markers will Sophie have if Josh gives the 3 markers back to her?

Number and Operations in Base Ten—2.NBT.B.5

MATHEMATICAL PRACTICESMP1, MP5, MP8

Describe what happens when you add back the number that you had subtracted.

Math Talk: Possible answer: The sum matches the number that I started with.

Check children’s drawings.

Check children’s drawings.

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EXPLORE2

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Writing and Reasoning How did you decide which numbers to use in Exercise 1?

Possible answer: I looked for the two numbers

that have a difference of 5.

Riddles with a DifferenceWhich numbers go in each story?Write numbers from the box thatwork for each story. Then write a subtraction sentence.

81 75 73 64 52 47

1. The Lions scored 47 — points in the game. The Bears scored 52 — points in the game. The Bears won by 5 points.

2. A choir has� 81 — singers. 6 singers missed the concert. So only 75 — singers sang in the concert.

3. A parking lot has 73 — spaces in all. Mr. Lee counted 9 empty spaces. So he knew that there were 64 — cars parked in the lot.

Lesson 5.8Enrich

Possible answers are given.

73 2 64 5 9

81 2 75 5 6

52 2 47 5 5

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5-20 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

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+4+3

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+3

Name

7 was added to get to 34.

2. 43 - 38 = 5 —

Add to Find Differences

Count up to solve. 34 – 27 = ?Start at 27. Count up 3 to 30.

To get to 34 from 30, count up 4 more.

So, 34 - 27 = 7 — .

Count up to find the difference.

1. 41 - 37 = 4 —

Lesson 5.8Reteach

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5-19 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

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2.NBT.B.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

1

2

3 DifferentiatedInstruction

Progressto Algebra

Problem Type: Take From • Result Unknown

Problem Type: Add To • Result Unknown

359 Chapter 5

Enrich 5.8Reteach 5.8

LESSON 5.8

Listen and DrawMATHEMATICAL PRACTICES

MP5 Use appropriate tools strategically. Read the following problem aloud.

Sophie had 25 markers. She gave 3 markers to Josh. How many markers does Sophie have now?

Have children draw pictures to represent the problem.• What are you asked to fi nd? The number of

markers Sophie has now.

• How can you draw a picture to show this problem? Possible answer: First, I draw 2 tens and 5 ones for 25. Then I cross out 3 ones to show what I am taking away. There are 2 tens and 2 ones left.

Have children write a number sentence for their drawing.• Did you regroup in this problem? Explain.

No; I can subtract 3 ones from 5 ones without regrouping.

How many markers will Sophie have if Josh gives the 3 markers back to her?

Have children draw pictures and write a number sentence to represent the problem.• Will you add or subtract to solve this

problem? Explain. Add; Possible answer: Josh is giving Sophie 3 markers, so I need to fi nd how many markers she has in all.

MathTalk MP1 Make sense of problems and

persevere in solving them. Use Math Talk to focus on children’s understanding of how subtraction and addition are related.

ELL Strategy: Cooperative Grouping

Have children work in pairs to ensure comprehension of subtraction word problems and to practice language skills.• Read the following problem: Chin has 27

toy cars. He gives 5 cars to Mateo. How many cars does Chin have now?

• Have pairs discuss the problem. Encourage English speakers to model language as needed.

• Then have pairs use a bar model to write a number sentence to show the problem.

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+2 +5

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2 + 5 = 7

Model and DrawModel and Draw

Share and ShShare and ShShare and Show MATHBOARDMATHBOARD

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360 three hundred sixty

1. 36 − 27 = 9 —

2. 56 − 49 = 7 —

3. 64 − 58 = 6 —

Use the number line. Count up to fi nd the difference.

Count up from the number you are subtracting to fi nd the difference.

Start at 38. Count up to 40.

So, 45 − 38 = 7 — .

Then count up 5 more to 45.

45 − 38 = ■

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Check children’s work.

COMMON ERRORS

EXPLAIN3

Lesson 5.8 360

Error Children may miscount the spaces on the number line when counting up.

Example In Exercise 2, children write the difference as 6.Springboard to Learning Have children draw an X below each space on the number line that is contained within the jumps that they draw. Then have children count each X to check their answers.

Quick Check

If

Rt I RR1

2

3

a child misses the checked exercises

Differentiate Instruction with • Reteach 5.8

• Personal Math trainer 2.NBT.B.5

• RtI Tier 1 Activity (online)

Share and Show MATHBOARDMATHBOARDMBMMMBBBMATHABOARDMMMAAATHATHTHHAAAAAAAAATTAAAABOARDBOARDBOARD

Connect Exercises 1–3 to the learning model. Remind children to first count up to the next tens number.• In Exercise 1, how can you count up to find

the difference? Possible answer: I count up 3 from 27 to get to 30. Next, I count up 6 more to get to 36. Then I add 3 and 6 to find the difference for the problem: 9.

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

Then

Model and Draw MATHEMATICAL PRACTICES

MP8 Look for and express regularity in repeated reasoning. Work through the model with children. • How many spaces do you need to count up

from 38 to get to 40? 2 spaces

• How many more spaces do you need to count up from 40 to get to 45? 5 spaces

• How many spaces did you count up in all? 7 spaces

Discuss with children that this strategy works well when the number being subtracted has a 7, 8, or 9 in the ones place because the number is close to the next tens number.

Advanced Learners

• Write the subtraction sentence 43 − 18 = ___ on the board.

• Have children work with a partner to draw a number line that they can use to help them solve the subtraction problem. Have children find ways to use the strategy of counting up from the subtrahend to find the difference. 25

• Have children repeat this activity with the subtraction sentences 37 − 11 = ___, 48 − 17 = ___, and 31 − 19 = ___. 26; 31; 12

• Have partners share their number lines with others and describe how they found the differences for the problems.

InterpersonalPartners

z

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Chapter 5 • Lesson 8 three hundred sixty-one 361

Use the number line. Count up to fi nd the difference.

4. 33 − 28 = 5 —

6. 58 − 49 = 9 —

5. 45 − 37 = 8 —

7. SMARTER There were 55 books on the table. Sandra picked up some of the books. Now there are 49 books on the table. How many books did Sandra pick up?

On Your OwnOn Your Own

6 — books

Check children’s work.

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4 ELABORATE

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

PROBLEM TYPE SITUATIONS

On Your OwnIf a child answers the checked exercises correctly, assign Exercises 4–7.Have children fi rst count up to the next tens number and label each jump they draw on the number line

DEEPER

MP3 Construct viable arguments and critique the reasoning of others. To extend thinking, challenge children to choose one of the exercises on this page and show a different way to use addition to fi nd the difference. Children may choose a way that does not use the number line or does not include getting to the next tens number. For example, in Exercise 6, children might fi rst add 5 to 49 to get to 54 and then add 4 more to get to 58. Have children describe their strategies.

SMARTER

Exercise 7 assesses children’s ability to use number lines to fi nd a missing number in a subtraction problem. Ask children to explain the process they use to fi nd how many books Sandra picked up.

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

361 Chapter 5

Addition and Subtraction

Take From • Result Unknown Exercises: 8, 9

Take From • Change Unknown Exercise: 7

Additional ExamplePut Together/Take Apart • Both Addends Unknown• Nick fi nds 43 shells at the beach. Together,

Sophia and Bella fi nd the same number of shells as Nick. How many shells could each girl have found? Answers will vary. The two addends must have a sum of 43.

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Math

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Math

MATHEMATICAL PRACTICES COMMUNICA C

362 three hundred sixty-two

8 — game pieces

Solve. You may wish to use the number line to help.

8. There are 46 game pieces in a box. Adam takes 38 game pieces out of the box. How many game pieces are still in the box?

TAKE HOME ACTIVITY • Have your child describe how he or she used a number line to solve one problem in this lesson. ©

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9. SMARTER Rachel had 27 craft sticks. Then she gave 19 craft sticks to Theo. How many craft sticks does Rachel have now?

Circle the number from the box to make the sentence true.

Rachel has 6

7

8

craft sticks now.

Explain how you can use addition to solve the problem.

Possible answer: I count up 1 to 20 and then 7 more to 27.

EVALUATE5 Formative Assessment

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIESD

Lesson 5.8 362

Children make and solve 2-digit subtraction problems to win counters.

GamesSubtraction Action

Children read the book and learn about 2-digit addition and subtraction with regrouping.

LiteratureParty Plans

Children complete purple Activity Card 13 by solving addition and subtraction problems about coin collections.

ActivitiesWe’re in the Money

Essential QuestionReflect Using the Language Objective Have children discuss with a partner what they learned to answer the Essential Question.How can you use addition to solve subtraction problems? Possible answer: I count up to the next tens number. Then I count up more ones to get to the number that was being subtracted from. I add the two numbers together to find the difference for the problem.

Math Journal Math

Explain how a number line can be used to find the difference for 34 − 28.

MATHEMATICAL PRACTICES

MP6 Attend to precision. Have children read Exercise 8. Ask them to describe how they will solve the problem.

SMARTER

This item assesses children’s abilities to solve word problems involving 2-digit subtraction. Children will need to understand that they will be completing the sentence using the answer to the subtraction problem.

Problem Solving • Applications

COMMON CORECOMCOMCOMMONMONMON CO CO CORERERE

PROFESSIONALDEVELOPMENT Math Talk in Action

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Problem SolvingProblem Solving

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Check children’s work.

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Add to Find Differences

Use the number line. Count up to fi nd the difference.

1. 36 − 29 = 7 —

2. 43 − 38 = 5 —

Chapter 5 three hundred sixty-three 363

Solve. You may wish to use the number line.

3. Jill has 63 index cards. She uses 57 of them for a project. How many index cards does Jill have now?

6 — index cards

4. Math Explain how a number line can be used to find the difference for 34 – 28.

COMMON CORE STANDARD—2.NBT.B.5 Use place value understanding and properties of operations to add and subtract.

Lesson 5.8Practice and Homework

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.

363 Chapter 5

In this discussion, the teacher and children are talking about Exercise 2.

Teacher: How did you use the number line to count up to find the difference?

Ian: I started at 38, and I saw that the next tens number is 2 spaces away. Then I jumped to 40 and saw that 43 is 3 spaces away.

Teacher: How did you find the difference?

Ian: I added my two jumps of 2 and 3 to get the difference: 5.

Destiny: I used the number line in a different way.

Teacher: How did you use the number line?

Destiny: I started at 38 and counted the spaces on the number line by ones to get to 43. I got a difference of 5, too.

Owen: I also started at 38, but I counted the spaces on the number line by twos, then by one. I also got

the difference of 5.

Teacher: What do you notice about these three different ways to solve?

Ian: The way we used the number line is different.

Destiny: But we all counted up to find the difference.

Personal Math Trainer

FOR MORE PRACTICE GO TO THE

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Lesson Check (2.NBT.B.5)

364 three hundred sixty-four

1. 82 − 75 = 7 — 2. 90 − 82 = 8 —

Spiral Review (2.OA.A.1, 2.OA.C.4, 2.NBT.B.5)

3. Jordan has 41 toy cars at home. He brings 24 cars to school. How many cars are at home?

17 — cars

4. Pam has 15 fish. 9 are goldfish and the rest are guppies. How many fish are guppies?

6 — guppies

5. What is the sum? 6. Each table has 5 pencils. There are 3 tables. How many pencils are there altogether?

15 — pencils

3 5 1 1 9

_

Use the number line. Count up to find the difference.

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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 5.8 364