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About the MathProfessional Development

Professional Development Videos

LESSON AT A GLANCE

Progressto Algebra

161A Chapter 3

Interactive Student Edition

Personal Math Trainer

Math on the Spot Video

Animated Math Models

iTools: Number Charts

HMH Mega Math

Practice the Strategies

LESSON 3.6

If Children Ask• In this lesson, children analyze addition facts to select

appropriate solution strategies. Some children may fi nd memorization easy and resist explaining their strategies. “I just know it!” is a common response. These children may ask why they need to explain their reasoning even though they get the correct answer.

• Selecting a solution strategy requires that children analyze the relationship between the addends, categorize problems by the features of the addends, and use that information to make a choice.

• Challenge children who easily memorize facts to describe to another child who may be struggling a strategy they could use to fi nd the sum.

Learning ObjectiveUse the strategies count on, doubles, doubles plus 1, and doubles minus 1 to practice addition facts within 20.

Language ObjectiveChildren work in teams to brainstorm and share the strategies you can use to solve addition fact problems.

MaterialsMathBoard, red, blue, and yellow crayons , (optional) connecting cubes or two-color counters

F C R Focus:Common Core State Standards

1.OA.C.6 Add and subtract within 20, demonstrating fl uency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 − 4 = 13 − 3 − 1 = 10 − 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 − 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

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. MP7 Look for and make use of structure.

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

Grade 11.OA.C.6

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 127J.

FOCUS COHERENCE RIGOR

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ENGAGE1

What strategies can you use to solve

addition fact problems?

Daily RoutinesCommon Core

1 23 4 Pages 56–57 in Strategies and Practice for Skills and Facts Fluency provide additional fluency support for this lesson.

Lesson 3.6 161B

with the Interactive Student Edition

Essential QuestionWhat strategies can you use to solve addition fact problems?

Making ConnectionsReview with children the strategies count on, doubles, doubles plus 1, and doubles minus 1.

What is the count on strategy? It is when you count on 1, 2, or 3 from a number to find a sum of a number plus 1, 2, or 3. What are doubles facts? addition facts with the same addends What is the doubles plus 1 strategy? It is when you add 1 to a doubles fact. What is the doubles minus 1 strategy? It is when you subtract 1 from a doubles fact.

Learning ActivityAsk the following question.

How can you model this problem with counters? Possible answer: I can use 2 red counters for the soccer balls and 4 yellow counters for the footballs.

Literacy and MathematicsChoose one or more of the following activities.

Make a class chart showing addition fact strategies. Work with children to include drawings that represent each strategy.

Have children write a number sentence showing each strategy.

1 23 4 Fluency BuilderOne Up , One DownMaterials connecting cubes, writing paper, Basic Facts (See eTeacher Resources)

Have children work in pairs. Give one partner 20 red connecting cubes and give the other partner 20 blue connecting cubes.

Tell children to make a cube train. Tell children their cube trains can have 1 to 10 cubes. Have partners exchange cube trains.

Tell children to use their partner’s cube train to make a doubles fact. Have children write their doubles fact. Then have them use the cube trains to write doubles plus one and doubles minus one. Tell children to write the number sentence for each doubles plus one and doubles minus one they show with their cube trains.

Have children read their number sentences aloud to their partners.

Repeat the activity by having children take back their cube trains and making a new cube train.

Problem of the Day 3.6Word of the Day fewerSam and Derrick collect dinosaur models. Sam has 9 models. Derrick has 12 models. Who has fewer models? Sam

Ask children to explain how they solved the problem.

Vocabulary

Common Core Fluency Standard 1.OA.C.6

Interactive Student EditionMultimedia Glossary e

EXPLORE2

Listen and DrawListen and Draw

MATHEMATICAL PRACTICES 7MathTalk

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Chapter 3 one hundred sixty-one 161

FOR THE TEACHER • Encourage children to use different strategies to show two ways they can solve 4 + 3. Have children share answers and discuss all strategies.

Think of different addition strategies. Write ordraw two ways you can solve 4 + 3.

Practice the StrategiesEssential Question What strategies can you use to solve addition fact problems?

Lesson 3.6

Way 2Way 1

Look for Structure Why is the sum the same when you use different strategies?

Operations and Algebraic Thinking—1.OA.C.6 Also 1.OA.D.8

MATHEMATICAL PRACTICESMP3, MP7

4 + 3 = 7 —

Possible answers or drawings show strategies such as: count on, doubles plus one, or doubles minus one.

Math Talk: The addends are the same in both strategies, so the sum will be the same.

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7 + 7 =14

Writing and Reasoning How did you decide what fact to write in each balloon? Explain.Possible answer: I thought of a strategy and then I

wrote a fact that I would solve using that way to add.

Fact BalloonsWrite an addition fact in each balloon. Color doubles plus one or doubles minus one facts blue.Then color count on facts green.Color doubles facts red.Color other facts yellow.

Lesson 3.6Enrich

red

Answers will vary.

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EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

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6

Name 

8         — 7         —

4.Usedoubles.

6 + 6 = 12         —

5.Usedoublesplus1.

6 + 7 = 13         —

6.Usedoublesminus1.

6 + 5 = 11         —

PracticetheStrategies

You can use different addition strategies to find sums.

Count On

6 + 2 = 8         —

Doubles

3 + 3 = 6         —

Doubles Plus 1

5 + 6 = 11         —

Doubles Minus 1

5 + 4 = 9         —

1.Counton1.

7 + 1 = 8         —

2.Counton2.

7 + 2 = 9         —

3.Counton3.

7 + 3 = 10         —

Lesson 3.6Reteach

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ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

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3 DifferentiatedInstruction

Progressto Algebra

161 Chapter 3

LESSON 3.6

Enrich 3.6Reteach 3.6

Listen and DrawMaterials (optional) two-color counters or connecting cubes

Read the following problem aloud.

Think of different addition strategies. How can you show two ways to solve 4 + 3?

• What are you asked to fi nd? two different ways to fi nd the sum of 4 + 3

Have children choose two methods to solve the problem and record each way in the workspace. Remind children to write the sum at the top. Encourage them to use words or pictures to communicate their ideas. Have volunteers share their strategies. • What strategies did you use to solve 4 + 3?

Possible answers: model with cubes or counters, count on, doubles minus 1, doubles plus 1

• How did you decide which ways to solve the problem? Explain your reasoning. Possible answers: I counted on because the second addend is 3; I used doubles minus 1 because 3 is 1 less than 4, so 4 + 3 is 1 less than 4 + 4.

Encourage children to look for relationships between addends when they choose a strategy to solve addition fact problems.

MathTalk

MP7 Look for and make use of structure. Use Math Talk to focus on children’s understanding that different addition strategies can be used to fi nd the same sum.• Why is it helpful to know different

strategies for solving the same problem? Possible answer: I can use the way that works best for me.

ELL Strategy: Scaffold Language

Children defi ne new terms by matching visuals to defi nitions. List addition facts. Suggest a strategy, such as “count on 2.” Have children explain how they can apply it to a fact to fi nd the sum.Continue the activity with other strategies: doubles, doubles plus 1, doubles minus 1, count on 1, count on 3.

1.OA.C.6 Add and subtract within 20, demonstrating fl uency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 − 4 = 13 − 3 − 1 = 10 − 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 =12, one knows 12 − 8 5 4); and creating equivalent but easier or known sums (e.g., adding 6 1 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

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EXPLAIN3

COMMON ERRORS

Quick Check

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Model and DrawModel and Draw

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162 one hundred sixty-two

These are the ways you have learned to fi nd sums.

9 + 1 = 10 —

9 + 2 = 11 —

9 + 3 = 12 —

5 + 5 = 10 —

5 + 6 = 11 —

5 + 4 = 9 —

You cancount on.

You can use doubles, doubles

plus 1, and doubles minus 1.

1. Count On 1

4 + 1 = 5 —

5 + 1 = 6 —

6 + 1 = 7 —

7 + 1 = 8 —

2. Count On 2

5 + 2 = 7 —

6 + 2 = 8 —

7 + 2 = 9 —

8 + 2 = 10 —

3. Count On 3

6 + 3 = 9 —

7 + 3 = 10 —

8 + 3 = 11 —

9 + 3 = 12 —

4. Doubles

7 + 7 = 14 —

8 + 8 = 16 —

9 + 9 = 18 —

10 + 10 = 20 —

5. Doubles Plus One

5 + 6 = 11 —

6 + 7 = 13 —

Doubles Minus One

8 + 7 = 15 —

9 + 8 = 17 —

Then

Advanced Learners

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Lesson 3.6 162

Error Children may count on by saying the starting number as the first number they count on.

Example For Exercise 3, children count on for 6 + 3 and get a sum of 8 by counting 6, 7, 8.Springboard to Learning Have children write the greater addend in a counting on fact and then model with counters the addend that is counted on. In this example, they would say “6,” and then count on as they touch each counter to say “7, 8, 9.”

a child misses the checked exercises

Differentiate Instruction with • Reteach 3.6

• Personal Math Trainer 1.OA.C.6

• RtI Tier 1 Activity (online)

Model and Draw MATHEMATICAL PRACTICES

MP7 Look for and make use of structure. Have children solve all the addition facts to review the strategies they have learned in the previous lessons.

• Which facts did you solve with counting on? Explain. 9 + 1, 9 + 2, 9 + 3; I count on when adding 1, 2, or 3 to another addend.

• Explain how you know when to use doubles plus 1 or doubles minus 1. I can use doubles plus 1 or doubles minus 1 when one addend is 1 more than the other.

Share and Show MATHBOARDMATHBOARDMBMMMBBBMATHABOARDMMMAAATHATHTHHAAAAAAAAATTAAAABOARDBOARDBOARD

In Exercises 1–5, children complete the table by following the rule at the top. Have them use MathBoards to show how they solved each addition fact.• How do you know your answers are

correct? Possible answer: I followed the rule at the top and used that strategy to find each answer.

Use the checked exercises for Quick Check.

• Have children collect and record information about the class by asking a question such as, How many pencils do you have at your desk? Children should record each name and the information.

• Have children take turns creating addition problems with the information they recorded.

• The child who makes up the problem should point out when it can be solved using count on, doubles, doubles plus one, or doubles minus one. Children solve the problem.

Auditory / Visual Individual / Partners

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Chapter 3 • Lesson 6 one hundred sixty-three 163

6. 9 + 9 = 18 —

red

7. 7 + 1 = 8 —

blue

8. 5 + 3 = 8 —

blue

9. 2 + 9 = 11 —

blue

10. 7 + 3 = 10 —

blue

11. 7 + 7 = 14 —

red

12. 6 + 5 = 11 —

yellow

13. 2 + 8 = 10 —

blue

14. 8 + 8 = 16 —

red

15. 8 + 9 = 17 —

yellow

16. 9 + 3 = 12 —

blue

17. 7 + 8 = 15 —

yellow

18. 8 — birds were in a tree. 2 — more birds flew there. How many birds are in the tree now?

10 — birds

On Your OwnOn Your Own

TAKE HOME ACTIVITY • Have your child point out a doubles fact, a doubles plus one fact, a doubles minus one fact, and a fact he or she solved by counting on. Have him or her describe how each strategy works.

SMARTER Make a counting on problem. Write the missing numbers.

MATHEMATICALPRACTICE 3 Apply Add. Color doubles facts .

Color count on facts . Color doubles plus one or doubles minus one facts .

Answers will vary, but one addend should be 1, 2, or 3.

EVALUATE5 Formative Assessment

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

163 Chapter 3

On Your OwnMP3 Construct viable arguments and critique the reasoning of others. If children answered Exercises 3 and 5 correctly, assign Exercises 6–17. Guide children to find the sum and then color the fact immediately after they solve the problem. Doing so will help them connect the strategy to the problem.

SMARTER

For Exercise 18, children use higher order thinking skills as they choose relevant numbers to make a counting on problem. Remind children that in a counting on problem, one addend must be 1, 2, or 3.

MP7 Look for and make use of structure.• In the problems that you write what will one

of the missing numbers be? Possible answers: 1, 2, or 3. Why? I am making a story that can be solved using counting on and the numbers I can use for counting on are 1, 2, or 3.

Essential QuestionReflect Using the Language Objective Children work in teams to brainstorm and share addition strategies.What strategies can you use to solve addition fact problems? I can use doubles; doubles plus one; doubles minus one; add in any order; or count on 1, 2, or 3.

Math Journal Math

Use pictures or words to explain a strategy you would use to find 8 + 9.

4 ELABORATE

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

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Mid-Chapter Checkpoint Personal Math TrainerOnline Assessment and Intervention

Personal Math Trainer

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Concepts and SkillsConcepts and Skills

Add. Change the order of the addends. Add again. (1.OA.B.3)

1. 2.

Circle the greater addend. Count on to fi nd the sum. (1.OA.C.5)

3. 1 + 8

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9

4. 3 + 7

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10

5. 9 + 2

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6. 6 + 3

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7. 7 + 1

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8. 2 + 8

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Use doubles to help you add. (1.OA.C.6)

9. 7 + 8 = 15 — 10. 6 + 7 = 13 — 11. 9 + 8 = 17 —

8 + 4

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12

B 4

+ B 8

B 12

7 + 9

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16

B 9

+ B 7

B 16

164 one hundred sixty-four Chapter 3

12. SMARTER Write a count on 1 fact to show a sum of 8. Then write a doubles fact to show a sum of 8.

7 + 1 = 8; 4 + 4 = 8

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Data-Driven Decision Making

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Mid-Chapter Checkpoint 164

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.

Personal Math Trainer SMARTER

Be sure to assign Exercise 12 to children in the Personal Math Trainer. It features a video to help them model and answer the problem. Children should demonstrate an understanding that a sum of 8 can be shown in more than one way, using more than one strategy. Model the strategies with counters for children who struggle to write a count on 1 fact and a doubles fact with sums of 8.

LESSONS 3.1 TO 3.6

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 Standards Common ErrorPersonal

Math TrainerIntervene with

1–2 3.1 1.OA.B.3 May have difficulty changing the order of the addends 1.OA.B.3 R—3.1

3–8 3.2 1.OA.C.5 May not identify the greater addend or may count on incorrectly 1.OA.C.5 R—3.2

9–11 3.4 1.OA.C.6 May use an incorrect doubles fact 1.OA.C.6 R—3.4

12 3.5 1.OA.C.6 May have difficulty recognizing doubles plus one or doubles minus one facts 1.OA.C.6 R—3.5

Problem SolvingProblem Solving

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Chapter 3 one hundred sixty-fi ve 165

1. 8 + 8 = 16 — 2. 8 + 1 = 9 — 3. 1 + 7 = 8 —

4. 8 + 3 = 11 — 5. 5 + 5 = 10 — 6. 8 + 7 = 15 —

7. 8 + 9 = 17 — 8. 6 + 3 = 9 — 9. 6 + 6 = 12 —

Practice the Strategies

Add. Color doubles facts . Color count on facts . Color doubles plus one or doubles minus one facts .

Make a counting on problem. Write the missing numbers.

10. 7 — apples are in a bag.3 — more apples are put in the bag.

How many apples are in the bag now? 10 — apples

11. Math Use pictures or words to explain a strategy you would use to find 8 + 9.

Practice and Homework

COMMON CORE STANDARD—1.OA.C.6 Add and subtract within 20.

Lesson 3.6

red

red

redyellow

blue

blue blue

blue

yellow

Answers will vary, but one addend should be 1, 2, or 3.

Check children’s work.

165 Chapter 3

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.

Personal Math Trainer

FOR MORE PRACTICE GO TO THE

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166 one hundred sixty-six

Lesson Check (1.OA.C.6)

1. Which strategy would you use to find 2 + 8? Explain how you decided.

———————

———————

2. What is the sum of 9 + 9? Write the number.

18 —

Spiral Review (1.OA.A.1, 1.OA.B.3)

3. What is the sum of 5 + 2 or 2 + 5? Why is the sum the same?

———————

———————

4. How many flowers are there?

Write the number.

3 flowers and 3 more flowers 6 — flowers

Count on. Possible explanation: When I add 2 to 8,

I can count on, 9, 10.

7; Possible explanation: The addends are the same.

Only the order is different.

Lesson 3.6 166

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.

Monitoring Common Core Success

Maintaining Focus on the Major WorkPart of the major work in Grade 1 is addition within 20 (1.OA.C). In Lessons 3.1–3.6, children are introduced to a variety of strategies for addition (1.OA.C.6). In Lesson 3.1, children extend their knowledge of the Commutative Property to sums of 20. Lesson 3.2 focuses on the strategy of counting on from the greater addend. Lessons 3.3–3.5 have children recognize the usefulness of doubles when finding sums. They practice these strategies in Lesson 3.6 when children apply them to addition facts within 20.

Connecting Content Across Domains and ClustersIn Lessons 3.1-3.6, children work in two different clusters within the Domain of Operations and Algebraic Thinking. Children first work in Cluster 1.OA.B where they apply the Commutative Property of Addition for sums within 20. They connect their knowledge of the Commutative Property to 1.OA.C. In 1.OA.C, children use different strategies to solve addition problems. Children will be able to use fluency within 10 and apply the “count on” strategy for sums within 20.

Building FluencyIn Lessons 3.1–3.6, children learn strategies to help them

add within 20. The strategies are presented as ways to bridge gaps between known addition facts and unknown addition facts and to learn new addition facts. In all cases, children recall known addition facts, helping them work towards fluency in addition up to 20.

Build fluency with associated fact fluency activities and strengthen children’s proficiency with various math strategies. Use Strategies and Practices for Skills and Fact Fluency—Primary, GK–3: Level 1, Worksheets 11A–11B to strengthen children’s mastery of addition and subtraction.

1 23 4

Name_________________________________________ Date __________________

BASIC FACTSUsing Doubles to Add

Draw dots to show a double. Complete the number sentence.

1. 2.

4 � _____ � _____ 6 � _____ � _____

3. 4.

5 � _____ � _____ 8 � _____ � _____

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