correctionkey=d lesson 2.6 hands on • subtract to compare · lesson 2.6 99b 12 34 fluency builder...

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Progress to AlgebraComparison situations differ from taking from and taking apart situations in that they involve only two discrete quantities that are not parts of a whole or related in that way. The two quantities are compared to fi nd which is greater or less. In some comparison problems, you may know one quantity and how it compares to an unknown quantity. By subtracting the difference from the known quantity, you fi nd the other quantity.

To help children understand comparing situations, as well as the ideas of more and fewer, fi rst act out comparing problems with cube trains. Then introduce the comparison subtraction bar model. One bar is drawn to represent the greater quantity. A shorter bar is drawn to represent the smaller quantity. The distance from the end of the shorter bar to the end of the longer bar represents the difference in quantities.



LESSON AT A GLANCE

Progressto Algebra

99A Chapter 2

Hands On • Subtract to Compare

LESSON 2.6

8 – 5 = 3

8

5

3Jill has 8 stickers. Jill has 5 more stickers than Derek. How many stickers does Derek have?

Using Comparison Subtraction Bar Models

Learning ObjectiveModel and compare groups to show the meaning of subtraction.

Language ObjectiveChildren tell how to use models to compare and subtract by completing the sentence frame, When I use a model to compare and subtact, I can see — .

MaterialsMathBoard, two-color counters

F C R Focus:Common Core State Standards

1.OA.A.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

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.MP6 Attend to precision.

F C R Coherence:Standards Across the GradesBeforeK.OA.A.1K.OA.A.2

Grade 11.OA.A.1

After2.OA.A.1

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 65J.

FOCUS COHERENCE RIGOR

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ENGAGE1

How can you use models to compare

and subtract ?

Daily RoutinesCommon Core

Lesson 2.6 99B

1 23 4 Fluency BuilderWays to Make 10Tell children that you will say a number. They are to show with their fingers how many more we need to add up to 10.

For example, say,

“I have 5 stamps. I need 10. How many more do I need?”

with the Interactive Student Edition

Essential QuestionHow can you use models to compare and subtract?

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

How can you show that one number is greater than another number? Possible answers: Use the > or < symbol, mark the numbers on a number line, create a model.

Learning ActivityDirect children to think about how to compare the numbers to find the difference.

How many pink flowers do you see? 7

How many blue flowers do you see? 5

Which is greater: the number of blue flowers or the number of pink flowers? pink flowers

How can comparing the numbers help you subtract? Possible answer: You subtract the smaller number from the larger number.

What is another way to model this problem? Possible answers: Draw a picture, use counters.

Literacy and MathematicsHave children work in pairs to write a story problem that compares two groups of animals.

Problem of the Day 2.6Basic Facts

Solve.

21 5

51 2

81 0

01 8

7 7 8 8

VocabularyInteractive Student EditionMultimedia Glossary e

Common Core Fluency Standard 1.OA.C.6

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

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6         -    4         =    2        

  8          -   6          =   2         

2— more rocks

more balloons 2

Subtract to Compare

You can use to show the bar model.

Andy has 8 balloons. Jill has 6 balloons. How many more balloons does Andy have than Jill?

Read the problem. Use the bar model to solve. Write the number sentence. Then write how many.

1. Bo has 6 rocks.Jen has 4 rocks. How many more rocks does Bo have than Jen?

Lesson 2.6Reteach

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ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

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7 - 4 = 3

8 - 5 = 3

5 - 2 = 3

Get Ready for SchoolWrite numbers for the problem. Use the bar model to solve. Write the number sentence.

1. Jay has pencils. Jay has more pencils than Ken. How many pencils does Ken have?

2. Sam has scarves. Sam has more scarves than Jane. How many scarves does Jane have?

3. Lee has books. Lee has more books than Amy. How many books does Amy have?

Writing and Reasoning How do you know which number belongs in the top of the bar model in Exercise 3?

Lesson 2.6Enrich

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model because Lee has more books than Amy.Amy’s number. I put 7 in the longer box of the bar

Possible answer: I need to compare Lee’s number to

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EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

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DifferentiatedInstruction

Progressto Algebra

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MATHEMATICAL PRACTICES 6MathTalk

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Chapter 2 ninety-nine 99

FOR THE TEACHER • Read the problem. Mindy has 8 puzzle pieces. David has 5 puzzle pieces. How many more puzzle pieces does Mindy have than David?

Use to show the problem. Draw the .Model the problem using the bar model.

Subtract to CompareEssential Question How can you use models to compare and subtract?

HandsOn

Lesson 2.6HANDS ON

Operations and Algebraic Thinking—1.OA.A.1 Also 1.OA.D.8

MATHEMATICAL PRACTICESMP1, MP4, MP6

Explain how counters and a bar model can be used to find how many more puzzle pieces Mindy has than David.

Math Talk: Possible answer: I placed 8 red counters to show Mindy’s puzzle pieces and wrote 8 in the longer box in the bar model. Then I placed 5 yellow counters to show David’s puzzle pieces and wrote 5 in the shorter box in the bar model. I matched each yellow counter to a red counter. There are 3 more red counters than yellow counters. I wrote 3 to show how many more puzzle pieces Mindy has.

R R R R R R R R

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Problem Type: Compare • Difference Unknown

99 Chapter 2

LESSON 2.6

ELL Strategy: Frontload

Take time before the lesson to check children’s understanding of the bar model. Write 5 − 3 = 2.Draw a bar model like the one in the lesson. • Look at the number sentence. What

number does the big bar represent? 5• What number does the short bar

represent? 3Help children talk about how the bar model illustrates subtraction.

Listen and Draw Materials two-color counters

Present this problem for children to solve.Mindy has 8 puzzle pieces. David has 5 puzzle pieces. How many more puzzle pieces does Mindy have than David?

Have children use red counters to represent Mindy’s puzzle pieces and arrange them in a row. Then have children use yellow counters to represent David’s puzzle pieces. Have them arrange the yellow counters under the row of 8 red counters so that there is a one-to-one correspondence.• Who has more puzzle pieces? Mindy So, do

you write 8 or 5 in the longer box of the model? 8

Have children write 8 in the longer bar.• Where do you write the number of David’s

puzzle pieces in the model? in the shorter box

• How can you compare the number of counters in each row? Possible answer: I can match each yellow counter to a red counter.

• Are there red counters that do not match yellow counters? How many? Yes; 3

• So, how many more puzzle pieces does Mindy have than David? 3

Have children write 3 to show the difference in lengths of the bars in the the bar model.

MathTalk

MP6 Attend to precision. Use Math Talk to focus on children’s understanding of using counters and bar models to compare and subtract.

HandsOn

1.OA.A.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. Also 1.0A.8

Enrich 2.6Reteach 2.6


EXPLAIN3

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Quick Check

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Share and ShowShare and ShowShare and ShowShare and ShowShare and ShowShare and ShowShare and ShowShare and Show MATHBOARDMATHBOARDMATHBOARDMATHBOARDMATHMATHMATHMATHBOARDBOARDBOARDBOARD

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100 one hundred

James has 4 stones. Heather has 7 stones. How many fewer stones does James have than Heather?


3 — fewer stones

2 — more stamps

2 —

keys

3 — fewer books

1. Abby has 8 stamps. Ben has 6 stamps. How many more stamps does Abby have than Ben?

2. Daniel has 3 books. Vicky has 6 books. How many fewer books does Daniel have than Vicky?

7 — C 2 4 — C

5 3 —

8 — C 2 6 — C

5 2 —

6 —

C 2 3 —

C 5 3 —

Possible number sentences shown.



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Then

MATHEMATICAL PRACTICES

Advanced Learners

Problem Type: Compare • Difference Unknown

Lesson 2.6 100

Error Children may not understand how to model the problem.

Example In Exercise 2, children write 3 in the top box of the bar model and 6 in the bottom left box.Springboard to Learning Have children represent the numbers with connecting cubes. Build the connection among the greater number, the longer cube train, and the longer part of the bar model.

a child misses the checked exercises

Differentiate Instruction with • Reteach 2.6

• Personal Math Trainer 1.OA.A.1

• RtI Tier 1 Activity (online)

Model and DrawMP4 Model with mathematics. Work with children to fi ll in the bar model.

• What do you need to fi nd? how many fewer stones James has than Heather

• Where do you write 7 in the bar model? in the longer box because it is the greater number

• Where do you write 4 in the model? I write 4 in the shorter box.

• How do you fi nd the difference? Subtract. I start with the number in the longer box and subtract the number in the smaller box.

Share and Show MATHBOARDMATHBOARDMBOARDMMMMBOARDBOARDBOARDBOARDMATHATHABOARDMMMMAAAATHATHATHTHTHATHATHATHAATHAAAATHAAATHATHTHTHATHATHAAATHATHATHAAATHABOARDBOARDBOARDBOARD

Have children complete Exercises 1 and 2. • Look at Exercises 1 and 2. How are they

the same? How are they different? Both are about comparing. One asks how many more and the other asks how many fewer.

• How do you know your answer is correct? Possible answer: I hear the word more in question 1 and I see more as part of the answer. I hear the word fewer in question 2 and fewer is part of the answer.

Use the checked exercises for Quick Check.

Visual / AuditoryPartners

Materials two sets of Numeral Cards 1–9 (see eTeacher Resources), drawing paper

• Shuffl e two sets of Numeral Cards 1–9, and place them facedown in two piles.

• Have children work in pairs. Each partner chooses a card from one pile. Partners compare the two numbers by subtracting the lesser number from the greater number. Partners draw and use a bar model to fi nd how many fewer. Then partners write the subtraction sentence that shows their answer.

• Partners repeat the activity, choosing two cards and making bar models to compare the quantities. Partners should fi nd how many more.


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Chapter 2 • Lesson 6 one hundred one 101

MATHEMATICALPRACTICE 4 Use Models Read the problem.

Use the bar model to solve. Write the number sentence. Then write how many.

6 — fewer marbles

3 — more feathers

2 —

keys

3. SMARTER Pam has 4 marbles. Rick has 10 marbles. How manyfewer marbles does Pam have than Rick?

4. Sally has 5 feathers. James has 2 feathers. How many more feathers does Sally have than James?

7 — C 2 4 — C

5 3 —

10 — C 2 4 — C

5 6 —

5 —

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On Your OwnOn Your Own

5. DEEPER Kyle has 6 keys. Kyle has 4 more keys than Lee. How many keys does Lee have?

TAKE HOME ACTIVITY • Have your child explain how he or she solved exercise 3 using the bar model.

Possible number sentences shown.


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EVALUATE5 Formative Assessment

PROBLEM TYPE SITUATIONS

101 Chapter 2

On Your OwnMP4 Model with mathematics. If children answered Exercises 1 and 2 correctly, assign Exercises 3–5.

SMARTER

Exercise 3 requires children to use higher order thinking skills as they solve a problem in which the whole and one part is known and the difference needs to be found.

Essential QuestionRefl ect Using the Language Objective Have children complete the sentence frame, When I use a model to compare and subtract, I can see _____ , to answer the Essential Question. How can you use models to compare and subtract? Possible answer: I can use a bar model to compare the numbers. Then I can subtract to fi nd the difference.

Math Journal Math

Write a subtract to compare problem and draw a bar model to solve it.

DEEPER

MP1 Make sense of problems and persevere in solving them. Give children this comparison subtraction problem: Lee has 5 marbles. Sarah has 8 marbles. What is the difference in the number of marbles each child has? Guide children to see that it is a comparison problem even though it does not ask How many more? or How many fewer? Discuss other questions that could be asked for this problem, such as How many fewer marbles does Lee have? Children will see that the number that represents the difference is the same, but knowing what the number relates to in each problem is important.

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

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

Addition and Subtraction

Compare • Difference Unknown Exercises: 1, 2, 3, 4

Compare • Smaller Unknown Exercise: 5


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102 one hundred two

Concepts and SkillsConcepts and Skills

Circle the part you are taking from the group. Then cross it out. Write how many there are now. (1.OA.A.1)

1.

2. There are 4 cans. 1 can is red. The rest are yellow. How many cans are yellow?

Use to solve. Draw to show your work. Write the number sentence and how many. (1.OA.A.1)

7 birds 3 birds fl y away. 4 — birds now

3 — yellow cans 4 —

C − 1 —

C = 3 —

9 − 3 5 6 —

3. SMARTER Jennifer has 3 crayons. Brad has 9 crayons. How many fewer crayons does Jennifer have than Brad? (1.OA.A.1)

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Mid-Chapter Checkpoint 102

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

Exercise 3 assesses understanding of the bar model to find a missing number in subtraction. Children who do not write the correct answer may not understand the meaning of each number in the story. Model the story with counters for children who need extra help.

LESSONS 2.1 TO 2.6

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 ErrorPersonal

Math TrainerIntervene with

1 2.1 1.OA.A.1 May cross out the wrong number of birds 1.OA.A.1 R—2.1

2 2.3 1.OA.A.1 May draw the wrong number of red and yellow counters 1.OA.A.1 R—2.3

3 2.6 1.OA.A.1 May choose the number of crayons Jennifer has instead of the difference 1.OA.A.1 R—2.6

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1. Ben has 7 flowers. Tim has 5 flowers. How many fewer flowers does Tim have than Ben?

2 —

fewer fl owers 7 — − 5 — = 2 —

7 — − 1 — = 6 —

6 — more pens

Subtract to Compare


Complete the number sentence to solve.

2. Maya has 7 pens. Sam has 1pen. How many more pensdoes Maya have than Sam?

COMMON CORE STANDARD—1.OA.A.1 Represent and solve problems involving addition and subtraction.

Lesson 2.6Practice and Homework

3. Math Write a subtract to compare problem and draw a bar model to solve it.

Check children’s drawings.

Check children’s work.

103 Chapter 2

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.

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FOR MORE PRACTICE GO TO THE

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1. Use the bar model to solve.Write the number sentence.Jesse has 2 stickers. Sara has 8stickers. How many fewer stickersdoes Jesse have than Sara?

8 —

− 2 — = 6 —

6 —

fewer stickers

Spiral Review (1.OA.A.1)

2. Solve. There are 6 sheep. 5 sheep walk away. How many sheep are there now?

1 —

sheep 6 — − 5 — = 1 —

3. Complete the bar model and the number sentence. 5 cows stand in a field. 2 more cows join them. How many cows are in the field now?

5 + 2 = 7 —

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Lesson Check (1.OA.A.1)

Monitoring Common Core Success

Maintaining Focus on the Major WorkThe major work in Grade 1 includes representing and solving problems involving subtraction (1.OA.A). In Lessons 2.1–2.6, children are introduced to a variety of concepts that will tie into the conceptual understanding of the meaning of subtraction. Children represent problems by modeling how a group of objects can be moved to be separate from the whole group in Lessons 2.1 and 2.2. This builds the foundation for understanding subtraction by taking apart found in Lesson 2.3. Pictures and models can also be used when comparing groups to subtract in Lessons 2.5 and 2.6.

Connecting Content Across Domains and ClustersIn Lessons 2.1–2.6, children work within two different clusters of the Domain of Operations and Algebraic Thinking. Children first work on learning how to represent and solve problems involving subtraction conceptually in Cluster 1.OA.A. Their work with subtraction is connected to comparing groups to determine the unknown. When working in Cluster 1.OA.D, children are introduced to the idea that equations can be used to represent subtraction problems.

Building FluencyIn Lessons 2.1–2.6, children work within 1.OA.A.1, using

subtraction to solve word problems and to build subtraction skills by taking apart groups of items. Through these lessons, children become fluent in mastering subtraction situations, and representing these situations with models and equations. The contextual nature of the problems presented in these lessons benefits children by helping them visualize subtraction and supports children in building fluency in 1.OA.C.6.

The Teacher Resource Book offers blackline masters that will aid in fluency building. Use Teacher Resource Book: Facts Practice, pp.TR88–TR89 to strengthen children’s mastery of addition and subtraction within 10.

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Lesson 2.6 104

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.

correctionkey=d lesson 2.6 hands on • subtract to compare · lesson 2.6 99b 12 34 fluency builder...

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