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Math on the Spot Video Tutor Online Assessment

System

Soar to Success Math Online Intervention

iTools Virtual Manipulatives

Digital ManagementCenter organizes program resources by TEKS!

Interactive Student Edition provides students

with an interactive learning environment!

Resources

e

Texas Essential Knowledge and Skills

Number and Operations—3.4.GUse strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties Also 3.4.E, 3.4.K

MATHEMATICAL PROCESSES3.1.A Apply mathematics to problems3.1.B Use a problem-solving model3.1.E Create and use representations

Are You Ready?Access Prior KnowledgeUse the Are You Ready? 9.1 in the Assessment Guide to assess students’ understanding of the prerequisite skills for this lesson.

Vocabulary

Go to Multimedia eGlossary at thinkcentral.com

9.1 PROBLEM SOLVING • Use the Distributive Property

How can you use the strategy draw a diagram to multiply with multiples of 10?

Essential Question?

How can you use the strategy draw a diagram to multiply with multiples

of 10?

Lesson OpenerMaking ConnectionsInvite students to tell you what they know about multiples of 10.

What is a multiple of 10? (A number that has 10 as a factor.) What pattern do you see in multiples of 10? (Possible answer: They end in 0.) What digit does 30 end in? (0)

Using the Digital LessonYou may want to discuss how multiples of ten can be represented by tens bars, tens cubes, or tens lines.

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

• How many boxes are there? (3 boxes)

• How many golf balls are in each box? (30 golf balls)

• What operations could you use to find the total number of golf balls? (multiplication, addition)

• What equations could you use to find the total number of golf balls? (3 × 30, 30 + 30 + 30)

Literacy and MathematicsChoose one or more of the following activities.

• Ask students to clarify the story and the problem by asking them to pick out the important information from the lesson opener.

• Have students think of reasons a golfer might hit so many golf balls. Why did he want to practice?

Lesson 9.1 275A

Essential Question?

3

10

30

1 10

30

Unlock the ProblemUnlock the Problem

Name

9.1

Read SolveWhat do I need to find?

I need to find how many ___

are at the assembly.

Draw a diagram. Finish the shading to

show 3 rows of 20 chairs.

I can use the sum of the products

of the smaller rectangles to find how

many third graders are at the assembly.

3 × 10 = _ 3 × 10 = _

_ + _ = _

3 × 20 = _

So, _ third graders are at

the assembly.

What information am I given?

There are _ chairs in each row.

The third graders fill _ rows of

chairs.

PlanWhat is my plan or strategy?

The Distributive Property tells me

I can ___ the factor 20

to multiply.

3 × 20 = 3 × (10 + _)

The school assembly room has 10 rows of chairs with

20 chairs in each row. If the third-grade classes fill 3 rows

of chairs, how many third graders are at the assembly?

How can you use the strategy draw a diagram to multiply with multiples of 10?

Number and Operations—3.4.G Also 3.4.E, 3.4.K

MATHEMATICAL PROCESSES3.1.A, 3.1.B, 3.1.E

PROBLEM SOLVING • Use the Distributive Property

1. Explain how breaking apart the factor 20 makes finding

the product easier. ___________

third graders

Possible explanation: I can use facts I know to fi nd the product.

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English Language Learners Language SupportELL

10

4 x 30 = 4 x (10 + 10 + 10)

10 1030

4

+ +

ELPS 1.A.2, 1.D, 3.H.3Leveled Activities ELPS

Beginning: Activity 8 2.1.4, 3.G.1, 3.H.3

Intermediate: Activity 40 4.F.6, 4.G.2, 4.G.4

Advanced: Activity 57 2.C.4, 3.D.2, 3.E

Advanced High: Activity 30 1.F, 2.I.3, 3.H.3

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

Strategy: DrawMaterials: Base-Ten Grid Paper (see eTeacher Resources)

• Have students draw to break apart a larger rectangle into smaller ones. Students can use their drawings to help explain how to use the Distributive Property.

• Have students use their models to explain how they arrived at their answers.

VisualSmall Group

Unlock the ProblemAn area model helps students visualize multiplication and how the Distributive Property can be used to multiply with greater numbers.

Make sure students understand that they need to find the number of third graders at the assembly. Discuss with students how the graphic organizer helps to organize their problem solving.

• Why are you using the Distributive Property? Possible answer: if I break apart the factor 20 into smaller numbers, I can multiply using facts I know.

Discuss with students that drawing a model on grid paper is like making an array. It shows rows and columns but there is no space between the rows and columns. This model is called an area model.

• How does the diagram show the Distributive Property? Possible answer: it shows 3 rows of 10 added to another 3 rows of 10.

Help students work through the steps of finding and adding the products of the smaller rectangles to solve.

• Why do you add the products of the smaller rectangles to find the total product? Possible answer: the products of the two smaller rectangles combined equal the total number of third graders at the assembly.

• Why is it helpful to break apart 20 into 10 + 10? Possible answer: It is easy to multiply with 10.

• Could you break apart the factors in a different way? Explain. Yes; possible explanation: I could break apart the 3 into a 1 and a 2. Multiply 2 × 20 = 40 and 1 × 20 = 20. Add 40 + 20 = 60.

275 Module 9

Try Another ProblemTry Another Problem

Mathematical ProcessesMath Talk

404040

10

4

1 10 1 10

2. Explain how you can use the Distributive Property to

help you find a product.

Megan is watching a marching band practice.

The band marches by with 4 rows of people playing

instruments. She counts 30 people in each row. How

many people are marching in the band?

Read SolveWhat do I need to find? Record the steps you used to solve

the problem.

What information am I given?

PlanWhat is my plan or strategy?

Explain how you can check to see if your answer is

reasonable.

Possible explanation: I can break apart the greater factor to use facts I know. Then I can

add the products to fi nd the total product.

I will draw a diagram and break apart the factor 30 into 10 + 10 + 10 to use facts I know.

First, I shade 4 rows of 30, or 10 + 10 + 10.Next, I fi nd the products of the three smaller rectangles. 4 × 10 = 40 4 × 10 = 40 4 × 10 = 40 Then, I fi nd the sum of the three products. 40 + 40 + 40 = 120 4 × 30 = 120

So, 120 people are marching in the band.

The band has 4 rows of people playing instruments. There are 30 people in each row.

I need to fi nd how many people are marching in the band.

Possible explanation: there are 4 rows with 30 people in each row; 30 + 30 + 30 + 30 = 120. So, my answer of 120 people is reasonable.

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

Enrich

10

4 x 60 = 4 x (10 + 10 + 10 + 10 + 10 + 10)

4+ 10 + 10 + 10 + 10 + 10

40 40 40 40 40 40

Materials: Base-Ten Grid Paper (see eTeacher Resources)

• Have students find all the possible ways to break apart a factor into multiples of 10 for 4 × 60 = ■. Students should break apart 60 into addends that are multiples of 10. Let students know that they may use any number of addends.

• Have students show each example on grid paper with an equation that shows the Distributive Property. One possible way is shown.

• Have students write an explanation for how they found all the ways to break apart the factor.

Visual / KinestheticIndividual / Partners

Try Another ProblemFor this problem, make sure students understand that they need to find the number of people marching in the band. Have students answer the questions in the graphic organizer and solve the problem. Invite students to share their diagrams by sketching them on the board. Ask them to communicate the steps they used.

• What strategy and steps did you use to solve the problem? Possible answer: I broke apart the factor 30 into 10 + 10 + 10. I shaded 4 rows of 10 three times. I used the diagram to find the products of the smaller rectangles. Then I added the products.

• Why do you add the products of the smaller rectangles to find the total product? Possible answer: each smaller product is part of the total product. I add the parts together to find the whole product.

• How could you break apart the factor 30 into three addends? Possible answer: I could break apart 30 into 10 + 10 + 10.

• What is another way you can break apart the factor 30? Possible answer: 10 + 20

Math Talk Use Math Talk to help students understand the reasonableness of their answer.

Mathematical Processes

COMMON ERRORSError Students may use addition instead of multiplication when using an area model to solve a problem.

Example Students write:

4 + 10 = 14 4 + 10 = 14 4 + 10 = 14

14 + 14 + 14 = 42

4 × 30 = 42

Springboard to Learning Remind students that an area model shows equal groups. Help students recognize that these groups are shown by rows, which each have the same number of squares. Point out that the number of rows and the number of squares in each row represent factors.

CE

Lesson 9.1 276

Problem SolvingProblem Solving

Share and ShowShare and Show

Unlock the ProblemUnlock the ProblemUnlock the ProblemTips

60

10

6

1

60

1

60

1

60

10 10 10

Name

3. Multi-Step Tova sewed 60 pieces of blue ribbon

together to make a costume. Each piece of ribbon was 2 meters long.

She also sewed 40 pieces of red ribbon together that were each 3

meters long. Did Tova use more blue ribbon or red ribbon? Explain.

1. The front section of a theater has 6 rows

with 40 seats in each row. In the front section,

24 seats are reserved. How many seats in the front

section of the theater are not reserved?

Step 1, Write the problem you need to solve. __

Draw and label a diagram to break apart the problem.

Find the products of the smaller rectangles.

6 × 10 = _ _ × _ = _

_ × _ = _ _ × _ = _

Find the sum of the products. _ + _ + _ + _ = __

There are __ seats in the front section of the theater.

Step 2, Find the difference. 240 − _ = __

So, there are __ seats in the front section that are not reserved.

2. What if seats are added to the front section of the theater so

that there are 6 rows with 50 seats in each row? How many seats

are in the front section?

√ Use the Problem Solving MathBoard.

√ Underline important facts.

√ Choose a strategy you know.

60

60

606060

24

60 240

216

240

216

300 seats

She used the same amount. 60 × 2 = 120; 40 × 3 = 120

10

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Module 9 • Lesson 1 277

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

Problem 2 requires students to reinterpret Problem 1 given different information.

Go DeeperHave students compare their models in Problems 1 and 2 and discuss different ways to break apart the factors.

Use the checked exercises for Quick Check. Students should show their answers for the Quick Check on the MathBoard.

Problem SolvingProblem

In Problem 3, students need to multiply to find the lengths of the blue ribbons and the red ribbons and then compare the two products.

1

2

3

a student misses the checked exercises

Quick Check

IF

THENDifferentiate Instruction withRtI Tier 1 Lesson 41

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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Name

There are 6 rows of singers in a performance. There are 20 singers in each row. How many singers are in the performance?

Read Solve

What do I need to find? Record the steps you used to solve the problem.

First, I draw and label a diagram to

show rows of singers.

Next, I break apart 20 into 10 + 10 and find the products of the two smaller rectangles.

6 × 10 = 6 × 10 =

Then, I find the sum of the two products.

+ =

6 × 20 =

So, there are singers.

What information am I given?

There are rows of singers.

Each row has singers.

Plan

What is my plan or strategy?

I can draw a diagram and use the Distributive Property to break apart the factor 20 into 10 + 10 to use facts I know.

1. Eight teams play in a Little League series. Each team has 20 players. How many players are in the series?

2. The assembly room has 6 rows with 30 chairs in each row. If third graders fill 3 rows, how many third graders are in the room?

Problem Solving • Use the Distributive PropertyOBJECTIVE Solve multiplication problems by using the strategy draw a diagram.

LESSON 41

6

6 20

I need to find how many singers

are in the performance

20

60

60 60

60

120

120

120

10 +

6

10

60 60

160 players 90 third graders

Number and Operations 81

1

2

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RtI Tier 1 Lesson 41Name

Enrich© Houghton Mifflin Harcourt Publishing Company

E42

Enrich 42

Apply the Distributive Property

Use the Distributive Property to help solve each problem.

Use this problem for 1–3.

An artist sells 4 paintings for $20 each, 4 sculptures for $60 each, and 4 photographs for $10 each at her art show.

1. How much money does the artist make on these sales in all?

Use this problem for 4–6.

Lee has 6 sheets of stickers with 30 stickers on each sheet. She has 8 sheets with 20 stickers each and 9 sheets with 10 stickers each.

4. How many stickers does Lee have in all?

2. The artist sells 2 more paintings and 4 more sculptures at the same prices. What is the total amount of money the artist has made so far?

5. Lee gives 4 sheets with 20 stickers and 3 sheets with 10 stickers to her sister. How many stickers does Lee have left?

3. How many more paintings, sculptures, and photographs would the artist need to sell to make another $500?

6. Now Lee gives some stickers to her friend Myla. What sheets does Lee give to Myla if she has 200 stickers left?

7. How did the Distributive Property help you solve the problems?

$360

$640

430 stickers

Possible answer: 2 sheets with

30 stickers and 3 sheets with

20 stickers

320 stickers

Possible answer: 5 paintings,

5 sculptures, 10 photographs

Possible answer: I used the Distributive Property to break apart

greater numbers into lesser numbers that are easier to work with.

Enrich 42

277 Module 9

Mathematical Processes

Daily Assessment TaskDaily Assessment Task

Fill in the bubble for the correct answer choice.

4. Apply A zoo gives 8 tubs of food to the male gorillas. Each

tub has 40 pounds of food. How much food do the male

gorillas eat each day?

A 270 pounds

B 180 pounds

C 320 pounds

D 90 pounds

5. Marcus will make 20 omelets. Each omelet takes 3 eggs.

How many eggs will Marcus use?

A 23 C 60

B 17 D 50

6. Multi-Step Shania makes a scrapbook about her trip to

the state capitol. She makes 2 sections about the history and

4 sections about what she saw. Each history section has

30 pages and each section about what she saw has 20 pages.

How many pages does Shania’s scrapbook have?

A 140 C 80

B 300 D 60

TEXAS Test Prep7. Stefan orders theater tickets for each of the 5 members

in his family. If each ticket costs $20, what is the total

cost for the tickets?

A $70

B $30

C $25

D $100

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Games

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Daily Assessment Task 1

2

3

Differentiated Centers Kit

GamesMultiplication BingoStudents practice multiplication facts through 10.

LiteratureParty Plans by the Numbers!Students read the book and use multiplication facts and strategies to plan a party.

ActivitiesMultiplication DashStudents complete orange Activity Card 17 by using models to apply multiplication facts through 12 by 12.

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 may have added 5 to the tens place.

B They may have broken $20 into $10 + $10 and added $5 to each $10.

C They added $5 to $20.

Essential Question? WriteMathWriteMath

How can you use the strategy draw a diagram to multiply with multiples of 10? Possible answer: I can draw and shade a rectangle on grid paper to show the problem. Then I can break apart a factor to make smaller rectangles for facts I know.

• Enrich 42

• Homework and Practice Lesson 9.1

• Soar to Success MathWarm-Up 12.51

Can students use the strategy draw a diagram to multiply with multiples of 10?

Lesson 9.1 278

Lesson CheckLesson Check TEXAS Test Prep

4. Ari has a rock collection. He puts

20 rocks into each of 8 boxes. How

many rocks does Ari have in his

collection?

A 160

B 28

C 16

D 140

5. At the town picnic, there are 7 stacks

of paper cups on a shelf. Each stack

holds 60 cups. How many cups are

on the shelf?

A 490

B 420

C 670

D 67

6. Mr. Franz buys 4 bags of forks. There

are 30 forks in each bag. Which

number sentence shows how many

forks are there in all?

A 4 + 30 = 34

B 4 × 30 = 120

C 4 + 30 = 120

D 40 + 30 = 70

7. Valerie buys 5 sticker books. Each

book has 80 stickers. Which number

sentence shows how many stickers

Valerie buys?

A 5 × 80 = 40

B 8 + 50 = 58

C 5 × 80 = 400

D 5 × 80 = 450

8. Multi-Step A farm stand has

4 bushels of apples. Each bushel

has 40 red apples. There are also

7 bushels of 30 green apples. How

many apples are there in all?

A 490

B 370

C 280

D 160

9. Multi-Step Marcel buys 3 large

boxes of cherries. Each box holds

40 cherries. He also buys 8 small

boxes. Each small box holds

20 cherries. How many cherries

does Marcel buy?

A 280

B 120

C 480

D 160

Fill in the bubble completely to show your answer.

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Problem SolvingProblem Solving

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PROBLEM SOLVING • Use the Distributive Property9.1

Number and Operations—3.4.GAlso 3.4.E, 3.4.KMATHEMATICAL PROCESSES 3.1.A, 3.1.B, 3.1.E

1. The Morgan family buys 7 booklets of tickets at the carnival.

Each booklet has 30 tickets. Of all the tickets bought, 21 tickets

are for rides. How many tickets are not for rides?

Step 1 + +

× = × =

× =

Find the sum of the products.

+ + =

× =

They have __ tickets.

Step 2 Find the difference. 210 − =

So, there are __ tickets that are not for rides.

2. The roller coaster ride costs 8 tickets.

If 30 people ride the roller coaster,

how many tickets are collected?

× =

3. The giant swing ride costs 6 tickets.

If 50 people ride the giant swing ride,

how many tickets are collected?

× =

Draw and label the diagram to solve.

Find the products of the smaller rectangles.

10

7

70

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7

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10

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21

8 6

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Module 9 • Lesson 1 279

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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.

279-280 Module 9