Partial-Products Multiplication (Part 2) - Everyday Math · PDF fileKey Concepts and Skills ... Partial-Products Multiplication (Part 2) ... Decide which two numbers need to be multiplied

www.everydaymathonline.com

Lesson 5�6 343

Advance PreparationFor Part 1, place copies of Math Masters, page 403 or 431 near the Math Message. For the optional Readiness

activity in Part 3, make transparencies of Math Masters, pages 432 and 433, and tape them together.

Teacher’s Reference Manual, Grades 4–6 pp. 39, 40, 126–132, 260, 261

Key Concepts and Skills• Write numbers in expanded notation.

[Number and Numeration Goal 4]

• Use the partial-products algorithm to

solve multiplication problems with 2-digit

multipliers.

[Operations and Computation Goal 4]

• Estimate whether a product is in the tens,

hundreds, thousands, or more.


• Apply the Distributive Property

of Multiplication over Addition.

[Patterns, Functions, and Algebra Goal 4]

Key ActivitiesStudents learn how to extend the partial-

products algorithm to 2-digit multipliers.

They make rough estimates and then use

the partial-products method.

Ongoing Assessment: Recognizing Student Achievement Use Mental Math and Reflexes. [Operations and Computation Goal 6]

Ongoing Assessment: Informing Instruction See page 345.

MaterialsMath Journal 1, pp. 122 and 123

Study Link 5�5

Math Masters, p. 403 or 431; p. 388 or 389

(optional)

slate

Playing Name That NumberStudent Reference Book, p. 254

Math Masters, p. 489 (optional)

per partnership: deck of number

cards (the Everything Math Deck,

if available)

Students practice representing

numbers in different ways.

Math Boxes 5�6Math Journal 1, p. 121

Students practice and maintain skills

through Math Box problems.

Study Link 5�6Math Masters, p. 154

Students practice and maintain skills

through Study Link activities.

READINESS

Modeling Multiplication with Base-10 Blockstransparencies of Math Masters, pp. 432

and 433 � base-10 blocks � erasable

marker � transparent tape

Students explore the partial-products

algorithm using a concrete model.

ENRICHMENTScoring a Dart GameMath Masters, p. 155

Students solve a multistep number story

involving a dart game.

ENRICHMENTSolving Venn Diagram PuzzlesMath Masters, p. 156

Students apply their understanding of

extended multiplication and division facts.

ENRICHMENTWriting Multiplication Number StoriesStudents write and solve multiplication

number stories.

Teaching the Lesson Ongoing Learning & Practice

132

4

Differentiation Options

Partial-ProductsMultiplication (Part 2)

Objectives To introduce and provide practice with the

partial-products algorithm for 2-digit multipliers.

Op

��

eToolkitePresentations Interactive Teacher’s

Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

343_EMCS_T_TLG1_G4_U05_L06_576817.indd 343343_EMCS_T_TLG1_G4_U05_L06_576817.indd 343 2/28/11 3:44 PM2/28/11 3:44 PM

344 Unit 5 Big Numbers, Estimation, and Computation

122

Multiplication Number StoriesLESSON

5 � 6

Date Time

Follow these steps for each problem.

a. Decide which two numbers need to be multiplied to give the exact answer.

Write the two numbers.

b. Estimate whether the answer will be in the tens, hundreds, thousands, or more.

Write a number model for the estimate. Circle the box to show your estimate.

c. On the grid below, find the exact answer by multiplying the two numbers.

Write the answer.

1. The average person in the United States drinks about 61 cups of soda per month.

About how many cups of soda is that per year?

a. � b. c.

numbers that give number model for your estimate exact answer

the exact answer

2. Eighteen newborn hummingbirds weigh about 1 ounce. About how many of them

does it take to make 1 pound? (1 pound � 16 ounces)

a. � b. c.

numbers that give number model for your estimate exact answer

the exact answer

28820 � 20 � 4001618

73260 � 10 � 6001261

1,000,000s100,000s10,000s100s10s 1,000s

1,000,000s100,000s10,000s100s10s 1,000s

17 18184

Math Journal 1, p. 122

Student Page

Mental Math and Reflexes �Write multiplication problems on the board. Have students write number models to show their estimates. Suggestions:Sample answers are given.

Ongoing Assessment: Mental Math

and Reflexes �Recognizing Student Achievement

Use Mental Math and Reflexes to assess students’ ability to estimate

reasonable solutions to whole-number multiplication problems. Students are

making adequate progress if they can write appropriate number models for the

and problems. Some students may be able to estimate products for

the problems.


1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASSDISCUSSION

Go over the answers. Ask:

● How would you solve 4 ∗ 29 in your head? Sample answer: Multiply 4 ∗ 30 and then subtract 4 from the product.

● How would you solve 803 ∗ 6 in your head? Sample answer: Multiply 800 ∗ 6 and 3 ∗ 6 and then add the two products.

� Estimating Products PARTNER ACTIVITY

(Math Journal 1, pp. 122 and 123)

Tell students that in this lesson they will apply the partial-products algorithm to multiply a 2-digit number by a 2-digit number.

Getting Started

Math MessageSolve the following problems on a computation grid:

4 ∗ 29 = 116 803 ∗ 6 = 4,818

3 ∗ 260 = 780 418 ∗ 7 = 2,926

Study Link 5�5 Follow-Up Have students compare answers and share how they decided whether an average person blinks more than or fewer than 100,000 times per day.

3 ∗ 52 3 ∗ 50 = 150

4 ∗ 26 4 ∗ 30 = 120

9 ∗ 74 10 ∗ 74 = 740

8 ∗ 632 8 ∗ 600 = 4,800

6 ∗ 569 6 ∗ 600 = 3,600

3 ∗ 248 3 ∗ 250 = 750

2 ∗ 7,414 2 ∗ 7,500 = 15,000

5 ∗ 8,299 5 ∗ 8,000 = 40,000

7 ∗ 6,172 7 ∗ 6,000 = 42,000

NOTE For additional practice

using a standard procedure for

rounding whole numbers to the

nearest ten and hundred, see

www.everydaymathonline.com.

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Multiplication Number Stories continuedLESSON

5�6

Date Time

3. A test found that a lightbulb lasts an average of 63 days after being turned on.

About how many hours is that?

a. 63 ∗ 24 b. 60 ∗ 20 = 1,200 c. 1,512 numbers that give number model for your estimate exact answer

the exact answer

4. A full-grown oak tree loses about 78 gallons of water through its leaves per day.

About how many gallons of water is that per year?

a. 78 ∗ 365 b. 80 ∗ 400 = 32,000 c. 28,470 numbers that give number model for your estimate exact answer

the exact answer

1,000,000s100,000s10,000s100s10s 1,000s

1,000,000s100,000s10,000s100s10s 1,000s

EM3MJ1_G4_U05_106-136.indd 123 1/14/11 9:08 AM


Student Page

Lesson 5�6 345

100s

∗

6

1

+

7

10s

6

1

0

1

2

3

1s

1

2

0

0

0

2

2

Ò 10 [60s] or 10 ∗ 60

Ò 10 [1s] or 10 ∗ 1

Ò 2 [60s] or 2 ∗ 60

Ò 2 [1s] or 2 ∗ 1

Problem 1: 12 ∗ 61 = ?

Adjusting the Activity

60 1

10 600 10

2 120 2

For each problem on pages 122 and 123, students first decide which two numbers need to be multiplied to give the exact answer (Step a). In Step b, they make a rough estimate of that product and write a number model that shows how they made that estimate. They should not do Step c at this time. Do Problem 1 as a class:

Step a An average person drinks about 61 cups of soda in 1 month. In 1 year, a person will drink 12 times that amount. To find the amount of soda a person drinks in one year, you would multiply 12 ∗ 61. Write 12 ∗ 61, but do not calculate the exact answer at this time.

Step b To estimate the answer, round 12 to 10 and write a number model for the rough estimate: 10 ∗ 61 = 610. Or round 61 to 60 and write a number model for the rough estimate: 12 ∗ 60 = 720. Looking at the number models, you can tell that the answer will be in the hundreds, so circle “100s.”

Have students work with a partner to complete Steps a and b for the rest of the problems.

� Extending the Partial-Products WHOLE-CLASS ACTIVITY

Algorithm to 2-Digit Multipliers(Math Journal 1, pp. 122 and 123)

Demonstrate how to use the partial-products algorithm to find the exact answer and check the estimate for Problem 1 on journal page 122. (See margin.) Work from left to right. Point out that each part of one factor is multiplied by each part of the other factor.

Ongoing Assessment: Informing Instruction

As students say each step, watch for those who say, for example “1 times 6”

instead of “10 sixties” or “10 times 60.” Remind students to consider the value of

each digit.

Do several more problems with the class. Suggestions:

● 18 ∗ 52 = 936 ● 29 ∗ 73 = 2,117

● 26 ∗ 34 = 884 ● 28 ∗ 434 = 12,152

Organize the multiplication problems as follows:12 ∗ 61 = (10 + 2) ∗ (60 + 1)

Students then add the partial products in the table to find the total:

600 + 10 + 120 + 2 = 732.

A U D I T O R Y � K I N E S T H E T I C � T A C T I L E � V I S U A L



Adjusting the Activity

121

Math Boxes LESSON

5 � 6

Date Time

1. a. Measure the line segment to the nearest �1

4� inch.

About inches

b. Draw a line segment that is half as long as the one above.

c. How long is the line segment you drew? About inches2�

12

�

5

2. Estimate the product. Write a number

model to show how you estimated.

a. 48 � 21

Number model:

b. 98 � 72

Number model:

100 � 70 � 7,000

50 � 20 � 1,000

4. Write each number using digits.

a. three hundred forty-two thousandths

b. six and twenty-five hundredths

6.25

0.342

5. If you remove 7 gallons per day from a

65-gallon water tank, how many days will

it take to empty the tank?

About 10 days

3. Multiply. Use the partial-products method.

� 52 � 432,236

128

184 18

27 28 175

Sample answers:

32 626

25

8 0

025 01

º

�

00

4 3


Student Page

Links to the FutureDo not expect all students to master the

partial-products algorithm for two 2-digit

multipliers at this time. This algorithm will

be practiced and reinforced throughout

Fourth Grade Everyday Mathematics.

Fluently multiplying whole numbers using

the standard algorithm is expected in

Grade 5.

Lesson 9-8 introduces multiplication of

decimals. This is a Grade 5 Goal.

� Using the Partial-Products PARTNER ACTIVITY

Algorithm(Math Journal 1, pp. 122 and 123)

Students complete the remaining problems on journal pages 122 and 123 in the same way. They check their estimates and complete Step c by finding the exact answer using the partial-products algorithm.

Ask students to respond to the following question in a Math Log

or on an Exit Slip (Math Masters, page 388 or 389): Explain how the

partial-products algorithm is similar to finding a team’s score in a game of

Multiplication Wrestling.

Look for students to note that every part of one factor is multiplied by every part

of the other factor.

A U D I T O R Y � K I N E S T H E T I C � T A C T I L E � V I S U A L

2 Ongoing Learning & Practice

� Playing Name That Number PARTNER ACTIVITY

(Student Reference Book, p. 254; Math Masters, p. 489)

Students play Name That Number to practice representing numbers in different ways. See Lesson 2-2 for additional information.

� Math Boxes 5�6 INDEPENDENTACTIVITY

(Math Journal 1, p. 121)

Mixed Practice Math Boxes in this lesson are linked with Math Boxes in Lessons 5-8 and 5-10. The skill in Problem 5 previews Unit 6 content.

Writing/Reasoning Have students write a response to the following: Devon wrote 342,000 for Problem 4a. Explain the error he might have made. Sample answer: He wrote 342 thousands, not 342 thousandths.

� Study Link 5�6 INDEPENDENTACTIVITY

(Math Masters, p. 154)

Home Connection Students practice using the partial-products algorithm with 2-digit multipliers.

Algorithm Project The focus of this

lesson is partial products. To teach U.S.

traditional multiplication, see Algorithm

Project 5 on page A21.


STUDY LINK

5�6 More Multiplication

Name Date Time

18

Multiply using the partial-products algorithm. Show your work.

1. 582 º 7 � 2. 56 º 30 �

3. 42 º 50 � 4. � 27 º 18

5. � 46 º 71 6. 340 º 50 � 17,0003,2664862,100

1,6804,074

Try This

7. � 241 º 31 8. � 768 º 4937,6327,471

9. � 283 � 5,439 10. 6,473 � 4,278 �

11. 5,583 � 4,667 � 12. � 9,141 � 6,3722,76991610,7515,722

Practice

Math Masters, p. 154

Study Link Master

Lesson 5�6 347

3 Differentiation Options

READINESS SMALL-GROUP ACTIVITY

� Modeling Multiplication 15–30 Min

with Base-10 Blocks(Math Masters, pp. 432 and 433)

To explore the partial-products algorithm using a concrete model, have students use base-10 blocks to model multiplication problems involving two 2-digit numbers.

Place taped transparencies of Math Masters, pages 432 and 433 on a table. To model 17 * 32, use an erasable marker to mark off a portion of the grid that is 17 squares high and 32 squares wide (17 by 32).

Start here.

Array model of 17 ∗ 32

Ask students to cover the array using as few base-10 blocks (flats, longs, and cubes) as possible.

Start here.

Base-10 block model of 17 ∗ 32



LESSON

5�6

Name Date Time

Sorting Numbers

Study the Venn diagrams in Problems 1 and 2. Label each circle and add at least one

number to each section.

1.

Try This

2.

720

2,400

300

180

4,200

4,000 240 2,100

80

5,600

160

p

multiples of 30divisible by 80

Sample answers:

990

1,230

360

120

1,500 420

2,000 3,500 770

1,050

750

1,200

210

840

4,200

6,300

350

7,000

250

4,000

650

560

490

280

30 as a factor

build arrays with

50 rows

multiples of 70

Sample answers:Sample answers:

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Math Masters, p. 156

Teaching Master

LESSON

5�6

Name Date Time

A Dart Game

Vanessa played a game of darts. She threw 9 darts.

Each dart hit the target. She scored 550 points.

Where might each of her 9 darts have hit? Use the

table to show all possible solutions.

200

100

50

25

111

12234

63

741

246

24

200 100 50 25

EM3cuG4MM_U05_139-176.indd 155 12/28/10 1:38 PM

Math Masters, page 155

Now match each part of the 17-by-32 array with a partial product.

� Match the 3 flats with 10 ∗ 30 = 300. These cover 300 squares.

� Match the 2 vertical longs with 10 ∗ 2 = 20. These cover 20 squares.

� There are 7 rows with 3 longs in each row. These cover 7 ∗ 30 = 210 squares.

� There are 7 rows with 2 cubes in each row. These cover 7 ∗ 2 = 14 squares.

� There are 544 (300 + 20 + 210 + 14) cubes in all.

Erase the transparencies. Use the transparencies and base-10 blocks to model and solve other 2-digit-times-2-digit problems.

ENRICHMENT INDEPENDENTACTIVITY

� Scoring a Dart Game 5–15 Min


To apply students’ multidigit multiplication skills, have them use various strategies to solve a multistep number story involving a dart game with more than one possible answer. Ask students to explain how they know they found all the solutions.

ENRICHMENT PARTNER ACTIVITY

� Solving Venn Diagram Puzzles 5–15 Min


To apply students’ understanding of extended multiplication and division facts, have them solve Venn diagram puzzles based on factors.

ENRICHMENT PARTNER ACTIVITY

� Writing Multiplication 5–15 Min

Number StoriesTo apply students’ understanding of multiplication algorithms, have them write and solve multistep multiplication number stories. Then have them record a number model using a letter for the unknown. Some students may be interested in writing and solving problems that involve distances, intervals of time, liquid volumes, masses of objects, or money. Stories may look similar to the following:

� Simon is filling the ketchup bottles at his restaurant. Each bot-tle holds 16 ounces of ketchup. There are 12 tables in each room and 3 rooms in the restaurant. How many ounces of ketchup will he need to fill one bottle for each table? Answer: 576 oz; Number model with unknown: (12 ∗ 3) ∗ 16 = n; Number model with answer: (12 ∗ 3) ∗ 16 = 576

Provide opportunities for students to revise and share their writing. Then have partners solve each other’s problems.


Documents

Partial-Products Multiplication (Part 2) - Everyday Math · PDF fileKey Concepts and Skills ... Partial-Products Multiplication (Part 2) ... Decide which two numbers need to be multiplied