Divide by 4 - St. Gregory the Great Catholic Academy · 2018. 12. 23. · One way to divide is to count back on a number line. Find the quotient. 12 4 4 Count back by 4s as many times

389A Chapter 7

About the MathProfessional Development

LESSON AT A GLANCE

Divide by 4

LESSON 7.5

12 ÷ 4 = ■ Think: 4 = 2 × 2

Divide by 2. There are 2 groups of 6.

Divide by 2 again. There are 4 groups of 3.

This process can be abbreviated by dividing the dividend by a factor of the divisor. Then divide that quotient by the other factor of the divisor.

12 ÷ 2 = 6

6 ÷ 2 = 3

So, 12 ÷ 4 = 3.

Professional Development Videos

It is important that students explore different methods for dividing to find the way that works best for them. In this lesson, using factors is introduced as a division strategy.

• Factors of 4 are 2 and 2, so dividing by 2 twice is the same as dividing by 4. It might be easy for some students to think about taking half of the total amount and then half of that amount. This method relates to the doubling method students used for multiplication.

• To divide 12 by 4, first divide 12 by 2. The quotient is 6.

• Then divide 6 by 2. The quotient is 3. So, the answer to 12 divided by 4 is 3.

Learning ObjectiveUse an array, equal groups, factors, or a related multiplication fact to divide by 4.

Language ObjectiveStudents explain to a partner what strategies you can use to divide by 4.

MaterialsMathBoard

F C R Focus:Common Core State Standards3.OA.C.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing

that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Also 3.OA.A.2, 3.OA.A.3, 3.OA.A.4, 3.OA.B.6

MATHEMATICAL PRACTICESMP3 Construct viable arguments and critique the reasoning of others. MP4 Model with mathematics. MP7 Look for and make use of structure. MP8 Look for and express regularity in repeated reasoning.

F C R Coherence:Standards Across the GradesBefore2.NBT.A.2

Grade 33.OA.C.7

After4.NBT.B.5

F C R Rigor:Level 1: Understand Concepts....................Share and Show ( Checked Items)Level 2: Procedural Skills and Fluency.......On Your OwnLevel 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 363J.

FOCUS COHERENCE RIGOR

ENGAGE1

Lesson 7.5 389B

Daily RoutinesCommon Core

Daily RoutinesCommon Core

What strategies can you use to divide by 4?

with the Interactive Student Edition

Essential QuestionWhat strategies can you use to divide by 4?

Making ConnectionsInvite students to tell you what they know about hot air balloons.

How do hot air balloons stay up? The balloon is filled with hot air which rises. How do people ride in hot air balloons? in a basket attached to the bottom of the balloon

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

• What question does the problem ask? How many people are in each balloon?

• How many hot air balloons are there? 4 hot air balloons

• How many people in all are riding in the hot air balloons? 16 people total

• When you know the total, what operation can you use to find how many are in each equal set? division

Literacy and MathematicsChoose one or more of the following activities.

• Ask students to clarify the question by picking out the important information to answer the question.

• Ask students to predict whether Lucia will decide to ride in a hot air balloon and explain why or why not.

Problem of the Day 7.5There were 736 people at a basketball game on Saturday and 829 people at a basketball game on Tuesday. How many more people went to the game on Tuesday than on Saturday? 93

Vocabulary• Interactive Student Edition• Multimedia Glossary e

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

Unlock the ProblemUnlock the Problem

MATHEMATICAL PRACTICES 6MathTalk

Name

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

• Im

age

Cred

its: ©

Todd

Mus

kopf

/Ala

my

Imag

es

Chapter 7 389

Lesson 7.5

Divide by 4Essential Question What strategies can you use to divide by 4?

A tree farmer plants 12 red maple trees in 4 equal rows. How many trees are in each row?

One Way Make an array.

• Look at the array.

• Continue the array by drawing 1 tile in each of the 4 rows until all 12 tiles are drawn.

• Count the number of tiles in each row.

There are _ tiles in each row.

So, there are _ trees in each row.

Write: _ ÷ _ = _ or 4 q w 12

Read: Twelve divided by four equals three.

Other Ways A Make equal groups.

• Draw 1 counter in each group.

• Continue drawing 1 counter at a time until all 12 counters are drawn.

There are _ counters in each group.

• What strategy could you use to solve the problem?

Operations and Algebraic Thinking—3.OA.C.7 Also 3.OA.A.2, 3.OA.A.3, 3.OA.A.4, 3.OA.B.6

MATHEMATICAL PRACTICESMP2, MP4, MP6

Compare How is making an array to solve the problem like making equal groups?

3

3

312 4

3

3

Possible answer: make an array.

Possible explanation: each row is like one of the equal groups. You place 1 tile at a time in rows just as you put 1 counter at a time in the circles.

DO NOT EDIT--Changes must be made through "File info"CorrectionKey=B

3_MNLESE342132_C07L05.indd 389 09/10/14 8:00 PM

EXPLORE2

10 1

1 2 3 4 5678

0 11 2 3 4 5 6 7 8 9 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

10 1

123

0 11 2 3 4 5 6 7 8 9 12

Name

Start at 12.

Start at 32.

Divide by 4

One way to divide is to count back on a number line.

Find the quotient. 12 4 4

Count back by 4s as many times as you can until you reach 0.

Count the number of times you jumped back 4. 3 times

So, 12 4 4 5 3.

Find the quotient. 32 4 4

Count back by 4s as many times as you can until you reach 0.

Count the number of times you jumped back 4. 8 times

So, 32 4 4 5 8.

Find the quotient.

1. 24 4 4 5 2. 5 12 4 3 3. 16 4 4 5 4. 5 8 4 4

5. 4 4 2 5 6. 5 28 4 4 7. 36 4 4 5 8. 20 4 4 5

Find the unknown number.

9. 4 4 4 = ▲ 10. 40 4 10 = t 11. 8 4 2 5 g 12. 21 4 7 5 m

▲ = t = g = m =

Lesson 7.5Reteach

2446

3441

5972

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

7-13 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

3_MNLEAN343009_C07R05.indd 13 17/02/14 8:13 PM

Name

15. Who won the game? Explain.

16. Stretch Your Thinking Drew asks if he can play the game. He wants to use the sign fi (is not equal to). How many points would Drew get for fi? Explain.

1. 2 3 8 24 4 4 2. 36 2 15 3 3 7

3. 16 4 4 8 1 5 4. 2 3 8 24 4 3

5. 36 4 4 1 3 9 6. 28 2 15 30 4 3

7. 17 1 8 6 3 6 8. 3 3 3 18 4 2

9. 28 4 4 16 4 2 10. 11 1 9 4 3 5

11. 0 1 7 32 4 4 12. 2 3 7 12 4 3

13. 20 4 4 15 4 3 14. 27 4 3 54 2 45

Arial Brian Craig

Lesson 7.5Enrich

Count the Signs

Arial, Brian, and Craig are playing a game. Arial gets a point every time the answer to a problem is 5. Brian gets a point every time the answer is ,, and Craig gets a point when it is .. Write ,, ., or 5. Keep track of each player’s points.

|||| | |||| ||||

8 points; Possible explanation: if an answer was , or .,

it would also be fi. So, I added Brian’s and Craig’s scores

together to � nd Drew’s score: 4 1 4 5 8.

Arial; Possible explanation: I counted 6 answers with the 5.

That was more than the , or .. Brian and Craig each had 4 points. So, Arial won with 6 points.

5 5

5

5

5

5

,

,

,

,

.

.

.

.

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

7-14 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

3_MNLEAN343009_C07E05.indd 14 17/02/14 10:55 PM

DifferentiatedInstruction1

2

3

389 Chapter 7

Enrich 7.5Reteach 7.5

3.OA.C.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Unlock the ProblemMATHEMATICAL PRACTICES

MP1 Make sense of problems and persevere in solving them. Be sure students understand that they need to find the number of trees in each of 4 equal rows.

One WayThis method uses an array. There is 1 tile shown in each of 4 rows. Students continue the array by drawing 1 tile in each row until all 12 tiles are drawn.

• What does the number of tiles in each row represent? how many trees are in each row, or the answer

Other WaysThis method uses counters and equal groups.

• Which represents the answer—the number of circles or the number of counters in each circle? the number of counters in each circle

MathTalk Use Math Talk to have students

compare the two division strategies they used to solve the problem.

• Explain how your array or picture of equal groups would change if the problem asked how many trees in 3 equal rows instead of 4. The array would have 4 tiles in each of 3 rows and the picture would show 3 equal groups instead of 4.

MP4 Model with mathematics.• Marco has 28 trading cards that he divides

equally among 4 friends. A student draws an array with 4 rows to model the problem. What does the number of rows in the array represent? the number of friends What does the number of tiles in each row represent? how many trading cards each friend gets

ELL Strategy: Develop Meanings

Have students make two sets of flash cards. One set for vocabulary—quotient, dividend, factor, array— and the other set to define the terms through words, symbols, and drawings.

• Have half the students hold the vocabulary cards and the other half hold the definition cards.

• Students find their match and then say the word and definition aloud.

LESSON 7.5

Meeting Individual Needs

DifferentiatedInstruction


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

390

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

2. _ = 21 ÷ 3

6. 20 ÷ 4 = a

a = _

3. 8 ÷ 4 = _

7. 12 ÷ 2 = p

p = _

4. _ = 40 ÷ 5

8. 27 ÷ 3 = ▲

▲ = _

5. 24 ÷ 4 = _

9. 12 ÷ 4 = t

t = _

1. Use the array to find 28 ÷ 4. _

Find the quotient.


B Use factors to find 12 ÷ 4. C Use a related multiplication fact.

The factors of 4 are 2 and 2.

2 × 2 = 4 12 ÷ 4 = n

↑ ↑ ↑ 4 × n = 12 factors product 4 × 3 = 12

To divide by 4, use the factors.

12 ÷ 4 = n

Divide by 2. 12 ÷ 2 = 6

Then divide by 2 again. 6 ÷ 2 = 3

12 ÷ 4 = _

Think: What number completes the multiplication fact?

A letter or symbol, like n, can stand for an unknown number.

The factors of 4 are 2 and 2. 16 ÷ 4 = ■

Divide by 2. 16 ÷ 2 = _

Then divide by 2 again. 8 ÷ 2 = _

So, 16 ÷ 4 = _.

12 ÷ 4 = _ or 4 q w 12

Think: Dividing by the factors of the divisor is the same as dividing by the divisor.

Try This! Use factors of 4 to find 16 ÷ 4.

↑

↑

MathTalk MATHEMATICAL PRACTICES 4

Use Models How does using an array help you to find a quotient?

3

33

8

4

4

Possible explanation: I counted the number of tiles in each row. There are 7 tiles in each row, so 28 ÷ 4 = 7.

7

3

7 2 8 6

965



3_MNLESE342132_C07L05.indd 390 27/02/14 6:26 PM

COMMON ERRORS

COMMON ERRORS

EXPLAIN3

Quick Check

If

Rt I 1

2

3

Quick Check

If

Rt I 1

2

3

Then

a student misses the checked excercises

Differentiate Instruction with • Reteach7.5

• PersonalMathTrainer3.OA.C.7

• RtITier1Activity(online)Advanced LearnersAdvanced Learners Verbal / LinguisticIndividual / Partners

•Have students write a word problem that has a multiple of 4 (4, 8, 12, 16, 20, 24, 28, 32, 36, or 40) as the dividend.

•The word problem should require division and have 4 as the divisor.

•Provide students with an example:

Kyla buys 28 markers. The markers come in packages of 4 markers each. How many packages does Kyla buy? 7packages

•Have students exchange papers and solve the problems.

Lesson 7.5 390

Error Studentsmaynotrecallarelatedmultiplicationfactcorrectly.

Example Students might write 2 ∙ 8 ∙ 16 for a related fact in Exercise 3.SpringboardtoLearning Remindstudentsthatrelatedfactsusethesamethreenumbers.Therelatedfactsfor8÷4=2shouldallusethenumbers2,4,and8.

In Example B, students divide by 2 twice, which is the same as dividing by 4, since 2 ∙ 2 ∙ 4. Model this method on the board.

• Draw an array with 2 rows of 6 counters. To model dividing 12 by 2, draw a horizontal line to form 2 groups of 6. Then draw a vertical line dividing the 2 groups into 2 equal groups, resulting in 4 groups of 3.

• Why wouldn’t this method be helpful when dividing by 3? becausethetwofactorsfor3are1and3

In Example C, students use a related multiplication fact: 4 × n = 12.

TryThis!Guide students through another example of dividing by 2 twice to divide by 4.

ShareandShow MATHBOARDMATHBOARD

The first problem connects to the learning model. Have students use the MathBoard to explain their thinking.Use the checked excercises for Quick Check.

DifferentiatedInstruction


3

4 9 12 15 18

3 4 5 6 4

4 20 24 28 32

5 6 7 8

On Your OwnOn Your Own

Name

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Practice: Copy and Solve Draw tiles to make an array. Find the quotient.

Chapter 7 • Lesson 5 391

24. 14 ÷ _ = 7 25. 30 ÷ _ = 6 26. 8 ÷ _ = 2 27. 24 ÷ _ = 8

10. 30 ÷ 10

14. 12 ÷ 3 = _

18. 45 ÷ 5 = b

b = _

11. 15 ÷ 5

15. 20 ÷ 4 = _

19. 20 ÷ 10 = e

e = _

12. 40 ÷ 4

16. 4 q w 16

20. 8 ÷ 2 = ■

■ = _

13. 16 ÷ 2

17. 5 q w 25

21. 24 ÷ 3 = h

h = _

22. 23.

Algebra Complete the table.

Find the quotient.


MATHEMATICALPRACTICE 2 Use Reasoning Algebra Find the unknown number.

28. 36 ÷ _ = 9 29. 40 ÷ _ = 4 30. 3 ÷ _ = 1 31. 35 ÷ _ = 7

32. Mr. Benz arranges 24 music stands in class. He puts the stands in 4 equal rows. How many music stands are in each row?

33. DEEPER Monty has 16 toy cars in 4 equal groups and 24 toy boats in 3 equal groups. How many more toy boats are in each group than toy cars?

34. DEEPER Mia puts 15 animal stickers in 3 equal rows in her sticker book. She puts 28 flower stickers in 4 equal rows. How many more flower stickers than animal stickers are in each row?

3

4

9 2 4 8

5

3 10 8

Check students’ drawings.

2 5 4 3

4 5

4 10 3 5

6 stands 4 more

2 more

391 Chapter 7

On Your OwnIf students complete the checked excercises correctly, they may continue with the On Your Own section. When students finish Exercises 10–23, ask:

• Can you use the make an array or make equal groups strategies to find the quotients for all of Exercises 10–23? yes

• Can you use the use a related multiplication fact strategy to find the quotients for all of Exercises 10–23? yes

• Can you use the use factors strategy to find the quotients for all of Exercises 10–23? Explain. No. The use factors strategy can only be used when the divisor is 4 or another number that has two factors other than 1 and itself.

MP2 Reason abstractly and quantitatively. Exercises 24–31 require students to apply a related fact to find an unknown divisor.MP1 Make sense of problems and persevere in solving them. Have students write the related unknown factor problem for each of the unknown divisor problems. For example, in Exercise 24 students would write 7 × ■ = 14.

ELABORATE4

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIES

Games

EVALUATE5 Formative Assessment

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIES

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

24

Type Number Planted

Trees Planted

Dogwood

Oak

Birch 16

28

MATHEMATICAL PRACTICES ANALYZE • LOOK FOR STRUCTURE • PRECISION

WRITE Math Show Your Work

Personal Math Trainer

392

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

• Im

age

Cred

its: ©

Jam

es R

andk

lev/

Getty

Imag

es

Problem Solving • ApplicationsProblem Solving • Applications

Use the table for 35–36.

35. DEEPER Douglas planted the birch trees in 4 equal rows. Then he added 2 maple trees to each row. How many trees did he plant in each row?

36. SMARTER Mrs. Banks planted the oak trees in 4 equal rows. Mr. Webb planted the dogwood trees in 3 equal rows. Who planted more trees in each row? How many more? Explain how you know.

37. MATHEMATICALPRACTICE 6 Use Math Vocabulary Bryan earns $40

mowing lawns each week. He earns the same amount of money for each lawn. If he mows 4 lawns, how much does Bryan earn for each lawn? Explain how you found your answer.

38. SMARTER For numbers 38a–38d, select True or False for each equation.

38a. 0 ÷ 4 = 4 True False

38b. 4 ÷ 4 = 1 True False

38c. 20 ÷ 4 = 6 True False

38d. 24 ÷ 4 = 8 True False

6 trees

Mr. Webb; 1 more tree; possible explanation:

28 ÷ 4 = 7 and 24 ÷ 3 = 8; 8 − 7 = 1, so Mr. Webb

planted 1 more tree in each row.

$10; Possible explanation: I used the related

multiplication fact. Since 4 × $10 = $40,

$40 ÷ 4 = $10.

DO NOT EDIT--Changes must be made through "File info"CorrectionKey=B

3_MNLESE342132_C07L05.indd 392 09/10/14 8:04 PM

Lesson 7.5 392

Essential QuestionUsing the Language ObjectiveReflect Have students explain to a partner the answer to the Essential Question. What strategies can you use to divide by 4? Possible answers: make an array, make equal groups, use factors of 4: 2 and 2, and use a related multiplication fact.

Math Journal WRITE Math

Write and solve a word problem that involves dividing by 4.

MATHEMATICAL PRACTICES

DEEPER

Have students read Exercise 35 and discuss what they need to find.

SMARTER

Exercise 36 requires students to analyze a multistep problem involving dividing, comparing, and explaining their answers.

LiteratureThe Garden Fence

GamesDivision Cover-Up

Students practice division facts to place counters on the gameboard.

Students read the book and use division facts to find how much wood they need to build a fence.

ActivitiesDivision Matho!

Students complete purple Activity Card 9 by matching a quotient to a given fact.

MP6 Attend to precision. For Exercise 37, suggest students include an equation in their explanation.

SMARTER

Students who mark d as True instead of False may be confusing dividing 24 by 3 with dividing 24 by 4. If students struggle, show them how related multiplication facts can help them with challenging division facts. For example, 4 × 4 = 16, not 0, so, 0 ÷ 4 = 4, is false.

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

Meeting Individual Needs

Problem Solving • ThinkingProblem Solving • Applications


Extend the Math Activity

Problem SolvingProblem Solving

Name

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

Divide by 4

Draw tiles to make an array. Find the quotient.


Find the quotient.

17. Ms. Higgins has 28 students in her gym class. She puts them in 4 equal groups. How many students are in each group?

______

18. Andy has 36 CDs. He buys a case that holds 4 CDs in each section. How many sections can he fill?

______

Chapter 7 393

1. _= 16 ÷ 4 2. 20 ÷ 4 = _ 3. 12 ÷ 4 = _ 4. 10 ÷ 2 = _

5. 24 ÷ 3 = _ 6. _= 8 ÷ 2 7. 32 ÷ 4 = _ 8. _= 28 ÷ 4

9. 4 q w 36 10. 4 q w 8 11. 4 q w 24 12. 3 q w 30

4

13. 20 ÷ 5 = a

a = _

14. 32 ÷ 4 = p

p = _

15. 40 ÷ 10 = ■

■ = _

16. 18 ÷ 3 = x

x = _

Lesson 7.5Practice and Homework

COMMON CORE STANDARD—3.OA.C.7 Multiply and divide within 100.

19. WRITE Math Write and solve a word problem that involves dividing by 4.

5 3 5

8 4 8 7

9

4

2

8

6

4

10

6

7 students 9 sections

Check students’ drawings.

Check students’ work.

393 Chapter 7

Practice and HomeworkUse the Practice and Homework pages to provide students with more practice of the concepts and skills presented in this lesson. Students 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 student’s understanding of content for this lesson. Encourage students to use their Math Journals to record their answers.

Comparison Problems

Investigate In this activity, students will discuss using either multiplication or division to represent and solve multiplicative comparison problems.

• Write these problems on the board. Discuss how to write an equation using a letter to represent the unknown value to match each problem.

1. Marta is 5 years old. Sam is 4 times as old as Marta. How old is Sam? 4 3 5 5 s

2. DeShaun is 4 times as old as Ava. DeShaun is 12 years old. How old is Ava? 4 3 a 5 12 or 12 4 4 5 a

3. Nina is 2 years old. Pedro is 16 years old. Pedro’s age is how many times Nina’s age? n 3 2 5 16 or 16 4 2 5 n

• Group students into threes. Have each student write one type of multiplicative comparison problem. Then

students exchange problems and write equations to solve the problem. The group discusses whether the equations and answers are correct.

Math Talk Discuss why the letter that represents the unknown value is in different positions in the equations. Ask questions such as:

• How do you know where to write the letter in an equation? The letter represents the unknown value, so I place it in the equation where the unknown value goes.

• Why can you use a multiplication or a division equation to solve Problems 2 and 3? Multiplication and division are inverse operations, so you can use either operation.

Summarize Give students an opportunity to share their problems and solutions with the class. They should be able to match the language in the problem to the corresponding known and unknown numbers.

Personal Math Trainer

FOR MORE PRACTICE GO TO THE

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

394

5. Use the Commutative Property of Multiplication to write a related number sentence.

4 × 5 = 20

6. Jasmine has 18 model horses. She places the model horses equally on 3 shelves. How many model horses are on each shelf?

3. Find the product.

3 × 7

4. Describe a pattern below.

8, 12, 16, 20, 24, 28

Spiral Review (3.OA.A.2, 3.OA.B.5, 3.OA.C.7, 3.OA.D.9)

1. Darion picks 16 grapefruits off a tree in his backyard. He puts 4 grapefruits in each bag. How many bags does he need?

2. Tori has a bag of 32 markers to share equally among 3 friends and herself. How many markers will Tori and each of her friends get?

Lesson Check (3.OA.C.7)

4 bags

21

5 × 4 = 20

Possible answer: Add 4.

6 model horses

8 markers

Lesson 7.5 394

Continue concepts and skills practice with Lesson Check. Use Spiral Review to engage students in previously taught concepts and to promote content retention. Common Core standards are correlated to each section.

Documents

Divide by 4 - St. Gregory the Great Catholic Academy · 2018. 12. 23. · One way to divide is to count back on a number line. Find the quotient. 12 4 4 Count back by 4s as many times