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Math on the Spot Video Tutor Online Assessment

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Resources

e

Texas Essential Knowledge and Skills

Number and Operations—3.4.H Determine the number of objects in each group when a set of objects is partitioned into equal shares or a set of objects is shared equally

3.4.K Solve one-step and two-step problems involving division within 100 using pictorial models, including equal groups

Algebraic Reasoning—3.5.B Represent and solve one- and two-step division problems within 100 using equations

MATHEMATICAL PROCESSES3.1.D Communicate mathematical ideas and reasoning3.1.E Create and use representations3.1.F Analyze mathematical relationships

Are You Ready?Access Prior KnowledgeUse the Are You Ready? 10.4 in the Assessment Guide to assess students’ understanding of the prerequisite skills for this lesson.

Vocabulary

Go to Multimedia eGlossary at thinkcentral.com

10.4ALGEBRA

Relate Subtraction and Division How is division related to subtraction?Essential Question?

Lesson OpenerMaking ConnectionsInvite students to tell you what they know about recycling.

Have you even seen a trash can that is for recycling? How can you tell? (Sample answer: It is a blue/yellow bin that has a recycling sign on it.) What kind of things can be recycled? (Paper, plastics) What happens to trash that is not recycled? (Sample answer: It goes to a landfill.)

Using the Digital LessonYou may want to use small items, such as beans or buttons, to model the problem. Recycling trash cans can be one color and regular trash cans can be a different color.

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

• How many trash cans are there total? (21 trash cans)

• There are two types of trash cans. What are they? (Regular and recycling)

• How many of each kind? (2 for recycling and 1 regular)

• How many trash cans in all go to each house? (3 trash cans)

Literacy and MathematicsChoose one or more of the following activities.

• Ask students to come up with a set of questions they would ask the people from the trash company.

• Have students infer why the trash company is delivering the new trash cans.

How is division related to subtraction?

Lesson 10.4 325A

Unlock the ProblemUnlock the Problem

ERROR AlertBe sure to keep subtracting 2 until you are unable to subtract 2 anymore.

Essential Question?

Name

How is division related to subtraction?

10.4 Relate Subtraction and Division

Number and Operations—3.4.H, 3.4.KAlgebraic Reasoning—

3.5.BMATHEMATICAL PROCESSES3.1.D, 3.1.E, 3.1.F ALGEBRA

• How many newspapers were brought in altogether?

• How many newspapers did the two girls bring in altogether each day?

Serena and Mandy brought a total of

12 newspapers to school for the recycling

program. Each girl brought in one

newspaper each day. For how many

days did the girls bring in newspapers?

One Way Use repeated subtraction.

12 − 2

_

10

10 − 2

_

8

8 −2

_

6 −2

_

4 −2

_

2 −2

_

Number of times you subtract 2: 1 2 3 4 5 6

• Start with 12.

• Subtract 2 until

you reach 0.

• Count the number

of times you

subtract 2.

Since you subtract 2 six times,

there are _ groups of 2 in 12.

So, Serena and Mandy brought in

newspapers for _ days.

Write: 12 ÷ 2 = 6 or 6 2 ) ‾ 12

Read: Twelve divided by two equals six.

12 newspapers

2 newspapers

6

6

6 4 02

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English Language Learners Language SupportELL

ELPS 2.I.3, 4.F.2, 4.G.4Leveled Activities ELPS

Beginning: Activity 2 2.I.4, 3.C.4, 3.G.2

Intermediate: Activity 3 2.D.2, 2.E.3, 3.F.2

Advanced: Activity 47 2.D.2, 2.I.5, 3.D.1

Advanced High: Activity 60 2.I.3, 4.F.7, 4.G.3

Go to thinkcentral.com for the ELL Activity Guide containing these leveled activities.

Strategy: DrawMaterials: color pencils

• Students can draw to show conceptual understanding.• Write the division situation on the board. Miguel brought in 8 cans of

food. He brought an equal number of cans each day for 2 days.• Have students draw a picture to represent the situation.• Ask questions about the drawings,

such as: How many cans did Miguel bring each day? 4 cans How many cans did he bring in all? 8 cans

Auditory / VisualSmall Group

Unlock the ProblemDo students at your school bring in items to recycle? Read the problem to find out what Serena and Mandy brought to school for recycling.

Be sure students understand that they need to first find the total number of newspapers both girls brought in each day and then divide to find how many days the girls brought in newspapers.

One WayThis method uses repeated subtraction to divide.

• Explain in your own words how to subtract to divide. Start with the dividend. Keep subtracting the divisor until you get to zero. To find the quotient, count the number of times you subtracted.

• Why is it important to keep subtracting until you get 0? so you are sure you have all the groups

• What is an advantage of using division to solve the problem? Possible answer: it takes less time to write 12 ÷ 2 = 6 than it does to write 12 – 2 – 2 – 2 – 2 – 2 – 2 = 0.

HandsOn

325 Module 10

Share and ShowShare and Show

2 3 4 5 6 7 8 9 10 121110

1236 5 4

1 2 3 4 5 6 7 80

2 3 4 5 6 7 8 9 10 121110

123

Mathematical ProcessesMath Talk

Mathematical ProcessesMath Talk

HandsOn

1. Draw the rest of the jumps on the number line to

complete the division equation.

12 ÷ 4 = _

Write a division equation.

2. 10 − 5

_

5

5 − 5

_

0

3.

• What do your jumps of 2 represent?

Another Way Count back on a number line.

• Start at 12.

• Count back by 2s as

many times as you

can. Draw the rest

of the jumps on the

number line.

• Count the number

of times you

jumped back 2.

You jumped back by 2 six times.

There are _ jumps of 2 in 12.

12 ÷ 2 = _

Explain in your own words how you found

the answer.

Explain how counting back on a number line is like using repeated

subtraction.

3

8 ÷ 2 = 4

Possible explanation: each time you count back the same number on the number line, it is like subtracting the number.

10 ÷ 5 = 2

Each jump represents a day the girls brought in

2 newspapers.

Check students’ drawings. There should be 6 jumps of 2 on the number line.

6

6

Possible explanation: I continued to draw jumps from 8 to 6, 6 to 4, 4 to 2, and 2 to 0. There were 6 jumps of 2 in all, so 12 ÷ 2 = 6.

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Go to Go to thinkcentral.com for additional enrichmentactivities in the Enrich Activity Guide.

Enrich

1 2 3 4 5

12345

6 7 8 9 10 110 12

• Write the following riddle on the board.

• Have students solve the problem and then write the division equation it represents. 18 ÷ 3 = 6

• Then have students write their own division riddles.

Logical / MathematicalIndividual

1

2

3

a student misses the checked exercises

Quick Check

IF

THENDifferentiate Instruction withRtI Tier 1 Lesson 48

Math Talk Use Math Talk to help students recognize the similarities between counting back on a number line and using repeated subtraction.

Mathematical Processes

Another WayThis method uses a number line to count back by 2s to divide.

After students complete the page, ask:

• Why did you start at 12 and count back by 2? because you want to find how many groups of 2 are in 12

• What does the number of jumps represent? the answer: how many groups of 2 are in 12, which is 6

HandsOn

Share and ShowThe first problem connects to the learning model. Have students use the MathBoard to explain their thinking.

Use the checked exercises for Quick Check.

COMMON ERRORSError Students may not continue the jumps all the way to zero when counting back on a number line to divide.

Example

Springboard to Learning Remind students that when they skip counted to multiply, they started at 0. Have students observe that when counting back on a number line to divide, they need to go to 0.

CE

Subtract 3 from me 6 times and you will reach 0.

What number am I? 18

Lesson 10.4 326

Problem SolvingProblem Solving

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Matt PaigeStudent

0

5

10

15

20

25

30

Dwayne Alma

Box Top Collections

Write MathWrite Math Show Your Work

Name

Use the graph for 4–6.

4. Matt puts his box tops in 2 equal piles.

How many box tops are in each pile?

5. Multi-Step Paige

brought an equal number of

box tops to school each day for

5 days. Alma also brought an

equal number of box tops each

day for 5 days. How many box

tops did the two students bring

in altogether each day? Explain.

6. Write MathWrite Math What’s the Question?

Dwayne puts all his box tops into bins. He

puts an equal number in each bin. The

answer is 5. What’s the question?

7. Pose a Problem Write a word

problem about collecting box tops that can

be solved by using the division equation

28 ÷ 7 = 4. Then solve the problem.

5 box tops

9 box tops; Possible explanation: Paige

brought 25 ÷ 5 = 5 box tops each day;

Alma brought 20 ÷ 5 = 4 box tops each day;

5 + 4 = 9 box tops altogether each day.

Possible question: How many box tops did

Dwayne put in each of 3 bins?

Possible problem: Bella collected 7 box tops each

day. She collected 28 box tops in all. For how

many days did Bella collect box tops? 4 days

Module 10 • Lesson 4 327

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Problem SolvingProblem

Problem 5 requires students to interpret information in a bar graph to solve a multi-step problem. The problem also requires students to explain their solution.

Go DeeperTo extend students' thinking for Problem 6, have them write a division equation to represent the problem. 5 = 15 ÷ 3

Then you might restate the problem as: What If Dwayne puts an equal number of box tops into bins, and the answer is 3, what is the question? How many box tops did Dwayne put in each of 5 bins? Have students write the corresponding equation. 3 = 15 ÷ 5

ProblemFor Problem 7, students must write a word problem that can be solved using a given division equation. Give students the opportunity to share their problems and solutions with the class.

Math on the Spot Video Tutor

Through the Math on the Spot Video Tutor, students will be guided through an interactive solving of this type of H.O.T. problem. Use this video to also help students solve the H.O.T. problem in the Interactive Student Edition. With these videos and the H.O.T. problems, students will build skills needed in the TEXAS assessment.

MV

Math on the Spot videos are in theInteractive Student Edition and atthinkcentral.com.

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3.4.H, 3.4.K, 3.5.B

Name

Find 18 ÷ 6.

Use base-ten blocks. Use repeated subtraction.

Step 1 Start with the number you are dividing, 18.

Step 2 Subtract the number you are dividing by, 6.

Step 3 There are more than 6 left. Subtract 6 again.

Step 4 There are 6 left. Subtract 6 again.

Step 5 Count the number of times you subtract 6.

You subtract 6 three times, so there are 3 groups of 6 in 18.

Write: 18 ÷ 6 = 3 or 6 ⟌ _

18

Write a division equation.

1.

2.

Algebra • Relate Subtraction and DivisionOBJECTIVE Use base-ten blocks, repeated subtraction, and a number line to relate subtraction to division.

LESSON 48

18 -  6

_

12

18 -  6

_

12

27 -  9

_

18

16 -  4

_

12

12 -  4

_

8

8 - 4

_

4

4 - 4

_

0

18 -  9

_

9

9 - 9

_

0

18 -  6

_

12

12 -  6

_

6

12 -  6

_

6

6 - 6

_

0

3

27 ÷ 9 = 3 16 ÷ 4 = 4

Number and Operations 95

Name

Enrich© Houghton Mifflin Harcourt Publishing Company

E48

Enrich 48

Fish Tank Math

Jed works in a pet store that sells fish. He needs to move fish from the old tanks and put them in the new tanks. He can move the fish in small groups only.

Use repeated subtraction to solve each problem. Circle groups

of fish each time you subtract. Then write how many equal

groups Jed can make and how many fish are left over.

1. 19 4 6

_ groups and _ left over

2. 23 4 5

_ groups and _ left over

3. 17 4 3

_ groups and _ left over

4. 15 4 4

_ groups and _ left over

5. Stretch Your Thinking Choose one of the problems. Change the number of fish in each group so there will not be any fish left over. Explain why you chose that tank.

3 1 4 3

5 2 3 3

Students

should circle

3 groups of

6 fish.

Students

should circle

4 groups of

5 fish.

Students

should circle

5 groups of

3 fish.

Students

should circle

3 groups of

4 fish.

Change the number of fish in each group from 4 to 5 in Exercise 4.

Possible explanation: 15 fish can be divided into 3 equal groups or

5 equal groups. None of the fish in the other tanks can be divided

into equal groups.

1

2

3

RtI Tier 1 Lesson 48 Enrich 48

327 Module 10

Daily Assessment TaskDaily Assessment Task

3 6 9 1812 150

Mathematical Processes

TEXAS Test Prep11. Renee has 18 photos. She wants to put the same number

of photos on each of 6 pages in her photo album. How

many photos will be on each page?

A 4 C 2

B 3 D 5

Fill in the bubble for the correct answer choice.You may use models or strategies to solve.

8. Multi-Step There are 16 dolphins in a pod. Each pod

has the same number of males and females. The female

dolphins are swimming in pairs. How many pairs of

female dolphins are there?

A 8 C 6

B 4 D 2

9. Representations What division equation is shown?

A 18 ÷ 2 = 9 C 2 × 9 = 18

B 18 ÷ 9 = 2 D 18 ÷ 6 = 3

10. Multi-Step Tim has 30 grapes. He keeps 9 grapes for

himself. Then he gives 7 grapes each to some of his

friends. To how many friends does Tim give grapes?

A 3 C 10

B 4 D 7

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THENIF

YES

NO

Daily Assessment Task 1

2

3

Differentiated Centers Kit

LiteratureCorey’s Cookie CaperStudents read about how Corey and Carly divide cookies equally among friends and family.

ActivitiesDividing NickelsStudents complete blue Activity Card 9 by using nickels to divide by five.

TEXAS Test Prep CoachTest Prep Coach helps teachers to identify common errors that students can make.

In the Test Prep exercise, if students selected:

A They subtracted too many 6s.

C They subtracted only two 6s.

D They incorrectly divided by 6.

Essential Question? WriteMathWriteMath

How is division related to subtraction? You can think of division as repeated subtraction of the divisor.

• Enrich 48

• Homework and Practice Lesson 10.4

• Soar to Success MathWarm-Up 13.10

Can students explain how division is related to subtraction?

Lesson 10.4 328

Lesson CheckLesson Check TEXAS Test Prep

2 31 4 5 6 7 8 9 10 11 12 13 14 15 160

2 31 4 5 6 7 8 9 10 11 120

Fill in the bubble completely to show your answer.

7. Wendy draws this number line.

Which division equation does she show?

A 12 ÷ 6 = 2 C 12 ÷ 3 = 4

B 2 × 6 = 12 D 12 ÷ 4 = 3

8. Tomas draws this number line.

Which division equation does he show?

A 16 ÷ 8 = 2 C 4 × 4 = 16

B 16 ÷ 2 = 8 D 16 ÷ 4 = 4

9. Kev bakes 18 mini-pies. There are

6 pies on each tray. How many trays

does Kev use?

A 12

B 6

C 4

D 3

11. Multi-Step Tara has 32 beads. She

takes out 4 red beads, then sorts the

rest into 4 equal groups. How many

beads are in each group?

A 7 C 8

B 4 D 9

10. Keesha has 14 shoes in all. How many

pairs of shoes does Keesha have?

A 7

B 2

C 28

D 14

12. Multi-Step Jeff has a booklet of

30 stickers. He uses one page of

stickers. If there are 6 stickers on each

page, how many pages were left?

A 4 C 5

B 24 D 6

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Problem SolvingProblem Solving

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Beth MalikStudent

0

3

6

9

12

15

18

Kimi

Bottles Collectedfor Recycling

Homeworkand Practice

Name

Relate Subtraction and DivisionWrite a division equation.

1. 2.

Use the graph for 3–6.

3. Beth sorts an equal number of her

bottles into 3 bins. How many bottles

are in each bin?

4. Malik and Kimi combine their bottles,

then sort an equal number of each

into 3 bins. How many bottles are in

each bin?

10.4

Number and Operations—3.4.H, 3.4.KAlgebraic Reasoning—3.5.BMATHEMATICAL PROCESSES 3.1.D, 3.1.F

14 – 7

_

7

7 – 7

_

0

5. Kimi collects another 7 bottles and sorts an equal number

into 4 bins. How many bottles are in each bin?

6. All of the students want to combine their bottles and sort

an equal number into 6 bins. Can they do this? Explain.

14 ÷ 7 = 2 9 ÷ 3 = 3

4 bottles

No; the total number of bottles is 39 and 39 cannot be divided equally by 6.

9 bottles

4 bottles

Module 10 • Lesson 4 329

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Homework and PracticeUse the Homework and Practice pages to provide students with more practice on the concepts and skills of this lesson.

329-330 Module 10