lesson 3.11 progress correctionkey=d to algebra …lesson 3.11 reteach check children’s work. do...

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LESSON AT A GLANCE

Progressto Algebra

191A Chapter 3

Interactive Student Edition

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Progress to AlgebraWhy Teach ThisThis second lesson on the Associative Property of Addition now has children making their own choice of which two addends they will add fi rst. Children must analyze the problem by looking for relationships between two of the three addends. Children become active learners when they think about the mathematics involved in choosing a strategy. Encourage children to discuss their reasoning in choosing a strategy and to explain their solution process.

• Children may fi nd the fi rst strategy of choice is looking for two addends with a sum of ten. When two addends make a ten, they can quickly add the third addend.

• Using doubles is another powerful strategy. Doubles facts are easy to recognize because two addends are the same. It is also possible to create a doubles fact when the sum of two addends equals the third addend.

Algebra • Add 3 Numbers

LESSON 3.11

Learning ObjectiveUnderstand and apply the Associative Property or Commutative Property of Addition to add three addends.

Language ObjectiveChildren model how to group numbers to add three addends.

MaterialsMathBoard, crayons, (optional) connecting cubes

F C R Focus:Common Core State Standards

1.OA.B.3 Apply properties of operations as strategies to add and subtract.

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. MP 8 Look for and express regularity in repeated reasoning.

F C R Coherence:Standards Across the GradesBeforeK.OA.A.3

Grade 11.OA.B.3

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

How can you group numbers to add

three addends?

Daily RoutinesCommon Core

1 23 4 Pages 52–53 in Strategies and Practice for Skills and Facts Fluency provide additional fluency support for this lesson.

Lesson 3.11 191B

with the Interactive Student Edition

Essential QuestionHow can you group numbers to add three addends?

Making ConnectionsInvite children to tell you what they know about addition.

Does the order of addends in an addition problem matter? no What happens when you add 10 to a one-digit number? Possible answer: Put a one in the tens place and the one-digit number in the ones place.

Learning ActivityDirect children to think about how to add two numbers. Discuss what children already know about adding two numbers.

How many are in each of the three groups of acorns? 4, 6, and 9

What is the sum of 4 and 9? 13



What does Avery want to know? how many acorns Sam has

Literacy and MathematicsChoose one or more of the following activities.

Have pairs work together to write a story about gathering acorns. Have them describe how many acorns are in each basket.

Have children write about how to add three numbers.

1 23 4 Fluency BuilderMaterials Number Cube labeled 0–5, Number Cube labeled 5–10 (see eTeacher Resources), two-color counters or connecting cubes

Roll and SubtractHave children play a game to practice using mental math to subtract within 10.

Have one child toss the two cubes to generate two numbers. The partner subtracts the lesser number from the greater number, or if two fives are tossed, the child subtracts the number from itself.

Have partners work together to check the answer by modeling the fact with counters or cubes.

Partners switch roles and repeat as time permits.

Problem of the Day 3.11Calendar Math Max starts reading a book on the 5th. Max finishes the book 3 days later. On what day does Max finish the book? the 8th

Have children show how they found the answer.

Vocabulary

101

7

Common Core Fluency Standard 1.OA.C.6

Interactive Student EditionMultimedia Glossary e

Name

What Four?Solve. Draw a picture.

1. Lance sees 3 birds in the nest.Dustin sees 2 birds on a branch.Will sees 4 birds on the ground.Luisa sees 5 birds in the sky.How many birds do they see? 14 — birds

2. Juan eats 3 berries.Shayla eats 7 berries.Joseph eats 6 berries.Sara eats 3 berries.How many berries do they eat? 19 — berries

3. Four friends buy 17 books.Mateo buys 6 books.Lucy buys 4 books.Cara buys 2 books.How many books does Li buy? 5 — books

Writing and Reasoning Explain how you added each number in Exercise 3.

First, I added 6 + 4 to make 10. I knew that the

friends bought 17 books, and I know 10 + 2 = 12,

so I added 5 to 12 to make 17.

Lesson 3.11Enrich

Possible answer:

Check children’s drawings.



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EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

3-26

1_MNLEAN342682_C03E11.indd 26 12/02/14 11:24 AM

Name

B

BB

B10

B B

4 + 4 = 8 is a doubles fact.

8 + 6 =14BB

4 + 6 make a 10.

10 + 4 =14

13


What strategies help you add 3 numbers?

4

4 + 6

_

14

4

4 + 6

_

14

Choose a strategy. Circle two addends to add first. Write the sum. Then find the total sum.

1. 7

3 + 3

_

2. 2

2 + 8

_

12

3. 4

3 + 3

_

10

4. 5

5 + 4

_

14

Lesson 3.11Reteach

Check children’s work.

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3-25 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

1_MNLEAN342682_C03R11.indd 25 12/02/14 11:28 AM

DifferentiatedInstruction1

2

3

EXPLORE2Progressto Algebra

Listen and DrawListen and Draw

MATHEMATICAL PRACTICES 3MathTalk

Name

Chapter 3 one hundred ninety-one 191

Lesson 3.11Algebra • Add 3 NumbersEssential Question How can you group numbers to add three addends?

Listen to the problem. Show two ways to group and add the numbers.

3 6 3

Apply Describe the two ways you grouped the numbers to add.

FOR THE TEACHER • Read the following problem. There are 3 children at one table. There are 6 children at another table. There are 3 children in line. How many children are there?©

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Operations and Algebraic Thinking—1.OA.B.3 Also 1.OA.C.6

MATHEMATICAL PRACTICESMP3, MP6, MP8

Math Talk: Possible answer: I used doubles. I used count on 3.

Possible answer: 3 + 3 + 6 = 6 + 6 = 12 and 3 + 6 + 3 = 9 + 3 = 12

DO NOT EDIT--Changes must be made through “File info”CorrectionKey=A

1_MNLESE341845_C03L11.indd 191 26/02/14 8:57 AM

Problem Type: Put Together/Take Apart • Total Unknown

191 Chapter 3

LESSON 3.11

Enrich 3.11Reteach 3.11

Listen and DrawMaterials crayons in 3 colors, (optional) connecting cubes Read the following story aloud. Have children solve the problem by grouping the numbers in two different ways.

There are 3 children at one table. There are 6 children at another table. There are 3 children in line. How many children are there? 12

• What are you asked to fi nd? how many children there are

• What three numbers do you need to add? 3, 6, and 3

After deciding which two numbers to add fi rst, have children draw and/or write to fi nd the solution to the problem. Encourage them to use a different color for each addend.• How did you decide which two numbers to

add fi rst? Explain. Possible answer: I added 3 and 3 because they are doubles.

After grouping the numbers in a different way, have children record their work on the right side of the page. Discuss the different strategies they used.

MathTalk

MP3 Construct viable arguments and critique the reasoning of others. Use Math Talk to focus on children’s ability to apply their understanding of the Associative Property and point out that numbers can be added in any order.

ELL Strategy: Scaffold Language

Children demonstrate their understanding of adding three numbers.List the addition strategies: count on, doubles, doubles plus 1 and doubles minus 1, and make a ten.Write the problem 2 + 6 + 8 = _______. Have children describe the strategy they would use to solve it. Encourage discussion about their choices.Repeat with different addition problems involving three addends.

1.OA.B.3 Apply properties of operations as strategies to add and subtract.Also 1.OA.6


Model and DrawModel and Draw

Share and ShowShare and ShowShare and ShowShare and ShowShare and ShowShare and ShowShare and ShowShare and ShowMATHBOARDMATHBOARDMATHBOARDMATHBOARDMATHMATHMATHMATHBOARDBOARDBOARDBOARD

You can group the addends in any order and in different ways to fi nd the sum.

THINKUse count on,

doubles, doubles plus one, doubles

minus one, or make a ten to add.

3

4 + 4

_

11

3

4 + 4

_

11

2

5 + 0

_

7

2

5 + 0

_

7

B

B B B B

192 one hundred ninety-two

6

4 + 2

_

12

6

4 + 2

_

12

3.

B B B

Choose a strategy. Circle two addends to add fi rst. Write the sum. Then fi nd the total sum. Then use a different strategy and add again.

1.

2.

4. 5

4 + 5

_

14

5

4 + 5

_

14

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Add 8 and 2 to use the strategy make a ten.

Then add 10 and 6.

B 8

6 + 2

_

16

10

Add 6 and 2 to use the strategy count on.

Then add doubles 8 and 8.

B 8

6 + 2

_

16

8

10

5

8

10

6

7 9

7

Circled addends may vary.



1_MNLESE341845_C03L11.indd 192 26/02/14 8:57 AM

MATHEMATICAL PRACTICES

Advanced LearnersAdvanced Learners

EXPLAIN3

COMMON ERRORS

COMMON ERRORS

Quick Check

If

Rt I RR1

2

3

Then

Problem Type: Put Together/Take Apart • Total Unknown

Lesson 3.11 192

Error Children may not add the third addend.

Example In Exercise 2, children find 4 + 4 first and write 8 as the sum of the first two addends and for the entire problem.Springboard to Learning Have children record the addition for each step to make sure they have added all three numbers. For example, 4 + 4 = 8 and 8 + 3 = 11.

a child misses the checked exercises

Differentiate Instruction with • Reteach 3.11

• Personal Math Trainer 1.OA.B.3

• RtI Tier 1 Activity (online)

Model and DrawMP6 Attend to precision. Work through the addition on the left. • Which two numbers are added fi rst? Why

is this a good strategy? Possible answer: 8 and 2 are added fi rst. They make 10.

Have children trace the dashed circles and lines for 8 and 2 and the 10 in the box.• What numbers do you add next to fi nd the

sum? Add 10 and 6 to get 16.

Repeat with the addition on the right, emphasizing the strategies used to add.

Share and Show MATHBOARDMATHBOARDMBOARDMMMMBOARDBOARDBOARDBOARDMATHATHABOARDMMMMAAAATHATHATHTHTHATHATHATHAATHAAAATHAAATHATHTHTHATHATHAAATHATHATHAAATHABOARDBOARDBOARDBOARD

Children solve each problem two ways.• Compare the two strategies you used in

Exercise 1. Which did you fi nd easier? Explain. Answers will vary.

• How do you know your answer is correct? Possible answer: My answers match both times I add the numbers.

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

• Have children work in pairs. Each partner takes a turn completing an addition sentence.

• Have partners compare their sums and discuss their strategies for adding.

• Have partners identify the patterns across and down and write to continue the pattern as far as they can.

0 + 1 + 2 = ___1 + 2 + 3 = ___2 + 3 + 4 = ______ + ___ + ___ = ____

3

3 4 5 12

6

9

Logical / MathematicalPartners


Name

3

4 + 4

_

11

8

2 + 2

_

12

3

4 + 6

_

13

9. 11. 7

7 + 2

_

16

5

4 + 4

_

13

13. SMARTER Susan has 7 shells. Kai has 3 shells. Zach has 5 shells. How many shells do they have?

7 — + 3 — + 5 — = 15 — shells

14. 15.

8 7

Chapter 3 • Lesson 11 one hundred ninety-three 193

6

0 +

8

_

14

6. 2

3 + 7

_

12

8.

1

9 + 1

_

11

10. 5

5 + 5

_

15

12.

B

B + 3

__

11

B

3

+ B

__

10

MATHEMATICALPRACTICE 8 Use Repeated Reasoning

Choose a strategy. Circle two addends to add fi rst. Write the sum.

On Your OwnOn Your Own

5. 7.

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SMARTER Write the missing addends. Add.Possible answers: 0, 7; 1, 6; 2, 5; 3, 4; 4, 3; 5, 2; 6, 1; 7, 0

Possible answers: 0, 8; 1, 7; 2, 6; 3, 5; 4, 4; 5, 3 ; 6, 2; 7, 1; 8, 0



1_MNLESE341845_C03L11.indd 193 3/5/14 7:31 PM

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.

PROBLEM TYPE SITUATIONS

Addition and Subtraction

Put Together/Take Apart • Total Unknown Exercises: 13, 16, 17

Put Together/Take Apart • Both Addends Unknown Exercises: 14, 18

193 Chapter 3

On Your OwnMP8 Look for and express regularity in repeated reasoning. If children answered Exercises 3 and 4 correctly, assign Exercises 5–15. Remind children that they may use different strategies to help them add. List the strategies on the board so children may refer to them: count on, doubles, doubles plus 1, doubles minus 1, and make a ten.

SMARTER

Exercise 13 requires children to use higher order thinking skills as they apply what they have learned about adding three numbers to solve this word problem.

SMARTER

Exercises 14 and 15 are non-routine problems that require children to use higher order thinking skills. Encourage children to apply what they know about the Associative Property as they work backward to fi nd the missing addends.Tell children that more than one correct answer is possible.

DEEPER

To extend thinking, have children list all the possible number combinations to solve Exercise 15. Invite volunteers to come to the board one at a time to compile a class list; 0 and 7, 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, 6 and 1, 7 and 0.

MP1 Make sense of problems and persevere in solving them. • How does keeping an organized list of all

the possible answers help you know you have found all the ways? Possible answer: A list helps me see that all possible numbers have been used. If I keep the list in order, then I can see that the addends increase by one on one side of the list and decrease by one on the other side of the list.

4 ELABORATE


MathMath


194 one hundred ninety-four

Draw a picture. Write the number sentence.

16. Maria has 3 cats. Jim has 2 cats. Cheryl has 5 cats. How many cats do they have?

3 — + 2 — + 5 — = 10 — cats

17. Tony sees 5 small turtles. He sees 0 medium turtles. He sees 4 big turtles.How many turtles does he see?

5 — + 0 — + 4 — = 9 — turtles

18. DEEPER Kathy sees 13 fish in the tank. 6 fish are gold.The rest are blue or red. How many of each could she see?

— + — + 6 = 13 fish

TAKE HOME ACTIVITY • Have your child look at Exercise 18. Have your child tell you how he or she decided which numbers to use. Have him or her tell you two new numbers that would work.

19. SMARTER Write two ways to group and add 2 + 3 + 4.

5 — + 4 — = 9 — 2 — + 7 — = 9 —

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Answers will vary. The missing numbers should have a sum of 7.

Possible drawings shown. Order of addends may vary.

EVALUATE5 Formative Assessment


Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIESD

Lesson 3.11 194

Essential QuestionReflect Using the Language Objective Have children model to answer the Essential Question.How can you group numbers to add three addends? I can use strategies to choose which two numbers to add first. Then I add the third addend.

Math Journal Math

Use pictures or words to explain how you would find 6 + 4 + 4.

MP6 Attend to precision. Have children read and describe how they will solve Exercises 16 and 17.

DEEPER

MP3 Construct viable arguments and critique the reasoning of others. Children may find it helpful to model Exercise 18 with connecting cubes or counters. Some children may first subtract 6 from 13 to find the sum of the two missing addends. Others may add any number to the 6 and then count on to 13. Encourage children to share solution methods since multiple answers are possible.

SMARTER

Exercise 19 assesses whether children understand how to add three numbers. Children who choose the wrong answers may forget to add the third addend. Encourage these children to record the addition for each step to make sure they have added all three numbers. For example, 2 + 3 = 5 and 5 + 4 = 9.

Children practice and review sums to 20.

Children read the book and add the number of hats made by Bunny.

Children complete purple Activity Card 16 by determining that there are many ways to make the same sum.

GamesNeighborhood Sums

LiteratureFunny Bunny Hats

ActivitiesThe Sum Is the Same

Problem Solving • Applications

Problem SolvingProblem Solving

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Chapter 3 one hundred ninety-fi ve 195

Draw a picture. Write the number sentence.

5. Don has 4 black dogs.Tim has 3 small dogs.Sue has 3 big dogs.How many dogs do they have?

4 — + 3 — + 3 — = 10 — dogs


Choose a strategy.Circle two addends to add fi rst. Write the sum.

7 3

+ 3

_

13

6 6

+ 3

_

15

1. 2. 3. 4.

2 0

+ 8

_

10

6. Math Use pictures or words to explain how you would find 6 + 4 + 4.

Practice and HomeworkLesson 3.11

COMMON CORE STANDARD—1.OA.B.3 Understand and apply properties of operations and the relationship between addition and subtraction.

2 2

+ 6

_

10


Possible drawings shown. Order of addends may vary.

Check children’s work.

195 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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196 one hundred ninety-six

1. What is the sum of 4 + 4 + 2?

10 —

2. Circle two addends to add first.Find the sum. Explain your strategy.

7 3

+ 2

_

Spiral Review (1.OA.C.6)

3. Write a doubles plus one fact for the sum of 7.

3 — + 4 — = 7 —

4. What addition sentence does this model show?Write the number sentence.

8 — + 3 — = 11 —

Lesson Check (1.OA.B.3)

________

________

Strategies and circled addends will

vary.

12

Lesson 3.11 196

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 3.11 progress correctionkey=d to algebra …lesson 3.11 reteach check children’s work. do...

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