320 Unit 5 Big Numbers, Estimation, and Computation

Teaching the Lesson materials

Key ActivitiesStudents use their knowledge of extended multiplication facts to play Multiplication Wrestling.This game prepares students for the partial-products algorithm, which will be introduced in Lesson 5�5.

Key Concepts and Skills• Write numbers in expanded notation. [Number and Numeration Goal 4]• Add multidigit numbers. [Operations and Computation Goal 2]• Use basic facts to compute extended facts.

[Operations and Computation Goal 3]• Solve multidigit multiplication problems.

[Operations and Computation Goal 4]• Evaluate numeric expressions containing parentheses.

[Patterns, Functions, and Algebra Goal 3]• Use the Distributive Property of Multiplication over Addition.

[Patterns, Functions, and Algebra Goal 4]

Ongoing Assessment: Informing Instruction See page 322.

Ongoing Learning & Practice materialsStudents solve problems based on data about recent U.S. presidents.

Students practice and maintain skills through Math Boxes and Study Link activities.

Ongoing Assessment: Informing Instruction See page 323.

Ongoing Assessment: Recognizing Student Achievement Use journal page 110. [Patterns, Functions, and Algebra Goal 2]

Differentiation Options materials

Students practice the partial-sums additionmethod.

Students use estimation to determine the winner of a Multiplication Wrestlingcompetition.

� Teaching Masters (Math Masters,pp. 141 and 142)

ENRICHMENTREADINESS

3

� Math Journal 1, pp. 109 and 110� Study Link Master (Math Masters,

p. 140)

2

� Student Reference Book, p. 253� Study Link 5 �1� Game Master (Math Masters, p. 488)� Transparency (Math Masters,

p. 488; optional)� per partnership: 4 each of number

cards 0–9 (from the Everything MathDeck, if available) or a 10-sided die

� slate� index cards (optional)

See Advance Preparation

1

Objectives To provide practice with extended multiplication

facts; and to introduce the basic principles of multiplication

with multidigit numbers.

Technology Assessment Management System

Math Boxes, Problem 3See the iTLG.

Additional InformationAdvance Preparation For Part 1, make copies of Math Masters, page 488 (at least 1 per student). Make enough copies so that some are always on hand for playing Multiplication Wrestling.

Links to the Future

� Math Message Follow-UpHave students share their solutions in small groups. There arethree possible combinations of the numbers:

(2 � 4) � (6 � 8) � 84

(2 � 6) � (4 � 8) � 96

(2 � 8) � (4 � 6) � 100

Each of these combinations of numbers can be arranged in manydifferent ways because the order in which two numbers are addedor multiplied does not affect the answer (the turn-around rule).The largest possible answer is 100.

� Playing Multiplication Wrestling(Student Reference Book, p. 253; Math Masters, p. 488)

Tell students that in this lesson they will learn to play a gamethat provides computation practice. Players must calculate fourpartial products and then find the sum of the partial products.

Review the rules of Multiplication Wrestling on Student ReferenceBook, page 253 with the class.

Playing Multiplication Wrestling prepares students for the partial-products algorithm, introduced in Lesson 5-5.

PARTNER

ACTIVITY

SMALL-GROUP

DISCUSSION

1 Teaching the Lesson

Lesson 5�2 321

Getting Started

Study Link 5�1 Follow-Up Students compare answers and review shortcutsfor solving multiplication problems in which one ormore of the factors is a multiple of 10.

Mental Math and Reflexes Pose extended multiplication facts problems. Suggestions:

4 � 50 � 200 20 � 40 � 800 70 � 800 � 56,00030 � 7 � 210 50 � 40 � 2,000 600 � 40 � 24,00070 � 8 � 560 90 � 30 � 2,700 900 � 900 � 810,000

ExampleExample

Games

Player 1: Draws 4, 5, 7, 8Forms 75 and 84

75 * 84Team 1 Team 2

(70 � 5) * (80 � 4)

Products: 70 * 80 � 5,60070 * 4 � 2805 * 80 � 400

5 * 4 � 20

Total 5,000(add 4 products) 1,200

� 100

6,300

75 * 84 � 6,300

Player 2: Draws 1, 9, 6, 4Forms 64 and 91

64 * 91Team 1 Team 2

(60 � 4) * (90 � 1)

Products: 60 * 90 � 5,40060 * 1 � 604 * 90 � 3604 * 1 � 4

Total 5,000(add 4 products) 700

120� 4

5,824

64 * 91 � 5,824

4

4

5

5

7

7

8

8

1

1

4

4

6

6

9

9

Multiplication Wrestling

Materials � 1 Multiplication Wrestling Worksheet for each player(Math Masters, p. 488)

� number cards 0–9 (4 of each) or 1 ten-sided diePlayers 2Skill Partial-products algorithmObject of the game To get the larger product of two 2-digit numbers. Directions1. Shuffle the deck of cards and place it number-side down on the table.

2. Each player draws 4 cards and forms two 2-digit numbers. Playersshould form their 2 numbers so that their product is as large as possible.

3. Players create 2 “wrestling teams” by writing each of their numbers as a sum of 10s and 1s.

4. Each player’s 2 teams wrestle. Each member of the first team (forexample, 70 and 5) is multiplied by each member of the second team(for example, 80 and 4). Then the 4 products are added.

5. Scoring: The player with the larger product wins the round andreceives 1 point.

6. To begin a new round, each player draws 4 new cards to form 2 newnumbers. A game consists of 3 rounds.

Student Reference Book, p. 253

Student Page

Math Message Use each of the numbers 2, 4, 6, and 8 to fill in theblanks on the left side of the � sign so you get the largest possible answer.

( � ) � ( � ) � ?

322 Unit 5 Big Numbers, Estimation, and Computation

Name Date Time

Multiplication Wrestling Record Sheet 132

4

253Round 1 Cards:

Numbers formed: º

Teams: ( � ) º ( � )

Products: º �

º �

º �

º �

Total (add 4 products):

Round 2 Cards:

Numbers formed: º

Teams: ( � ) º ( � )

Products: º �

º �

º �

º �

Total (add 4 products):

Round 3 Cards:

Numbers formed: º

Teams: ( � ) º ( � )

Products: º �

º �

º �

º �

Total (add 4 products):

�

Math Masters, p. 488

Adjusting the Activity

Game Master

109

Presidential InformationLESSON

5� 2

Date Time

The following table shows the dates on which the most recent presidents of the United States were sworn in and their ages at the time they were sworn in.

1. What is the median age (the middle age) of the presidents at the time they were sworn in? years

2. What is the range of their ages (the difference between the ages of the oldest and the youngest)? years

3. Who was president for the longest time?

4. Who was president for the shortest time?

5. Presidents are elected to serve for 1 term. A term lasts 4 years.Which presidents served only 1 term or less than 1 term?

6. Which president was sworn in about 28 years after Roosevelt?

7. Roosevelt was born on January 30, 1882. If he were alive today, about how old would he be? years old125

KennedyKennedy, Ford, Carter, G. H. Bush

FordF. D. Roosevelt

26

55�12�

73

President Date Sworn In Age

F. D. Roosevelt March 4, 1933 51Truman April 12, 1945 60Eisenhower January 20, 1953 62Kennedy January 20, 1961 43Johnson November 22, 1963 55Nixon January 20, 1969 56Ford August 9, 1974 61Carter January 20, 1977 52Reagan January 20, 1981 69G. H. Bush January 20, 1989 64Clinton January 20, 1993 46G. W. Bush January 20, 2001 54

As of January 30, 2007:

Math Journal 1, p. 109

Student Page

ELL

Acting out “tag team” wrestling may help students better understand therules of Multiplication Wrestling.Using the example 75 � 84, have students write each number as the sum of thevalues of the digits: 70 � 5 and 80 � 4. Record 70 and 5 on separate indexcards of one color and 80 and 4 on separate index cards of another color.Explain that 70 and 5 are one team, and 80 and 4 are a different team.Select four students to hold the cards. Remind students that in a tag-teamwrestling match, a person never wrestles someone from the same team. So, 70and 5 cannot wrestle each other, nor can 80 and 4. Therefore, 70 wrestles 80and then 4. Next, 5 wrestles 80 and then 4. Have students stand next to eachother as they “wrestle,” and record the product after each “wrestling match.”

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

The record sheet on Math Masters, page 488 is designed to helpstudents organize and keep track of their computations. Allstudents should use this page to record their work for the first 3-round game they play.

Use a transparency of Math Masters, page 488 to demonstratehow to fill in the record sheet. When they have learned the game,many students will not need worksheets to record their results.They may simply write their calculations on a blank sheet ofpaper.

Ask students about the patterns they noticed and the strategiesthey used while playing and completing the record sheet. Forexample, some students may note that for each set of four cardsdrawn, there are many ways of forming 2-digit numbers. The goalis to form two pairs that will yield the largest product.

Ongoing Assessment: Informing InstructionWatch for students who correctly determine the partial products but then addincorrectly. Encourage students to write their partial products so that the digits ineach number are aligned according to their value.

70 5 80 4

Team 2Team 1

Math Boxes LESSON

5 � 2

Date Time

1. Fill in the missing numbers on each number line.

a.

b.2.6 2.72.672.61 2.62 2.63 2.64 2.65 2.66 2.68 2.69

0.20 0.300.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29

2. Measure the line segment to the nearestmillimeter. Record the measurement inmillimeters and centimeters.

a. About mm

b. About cm mm

c. About . cm7474

47

4. Insert � or � to make a true numbersentence.

a. 4,500,999 879,662

b. 23,468,000 23,467,000

c. 568,009,352 568,010,320

d. 400,632 399,800 �

�

�

�

5. Divide mentally.

a. 45 / 9 �

b. 450 / 90 �

c. 1,000 / 200 �

d. � 2,000 / 40

e. � 6,300 / 700950

55

5

3. Tell whether each number sentence istrue or false. Write T for true or F for false.

a. 7.89 � 3.36 � 4.53

b. 12.6 � 4.8 � 3.9 � 3.9

c. (4.6 � 2.9) � 3.1 � 3.7

d. 0.20 � 0.68 � (0.42 � 0.11) TFT

T

128 129

6

34–37148

21

�

110

Math Journal 1, p. 110

Student Page

STUDY LINK

5�2 Extended Multiplication Facts

17

Name Date Time

1. 6 º 7 � 2. 9 º 3 �

6 º 70 � 9 º 30 �

60 º 7 � 90 º 3 �

60 º 70 � 90 º 30 �

600 º 7 � 900 º 3 �

60 º 700 � 90 º 300 �

3. 4 º 8 � 4. 5 º � 15

4 º 80 � 30 º � 150

40 º 8 � 30 º � 1,500

40 º 80 � º 50 � 150

400 º 8 � º 500 � 1,500

40 º 800 � 30 º � 15,000

5. º 9 � 54 6. 8 º � 40

º 90 � 540 8 º � 4,000

º 90 � 5,400 80 º � 4,000

60 º � 540 º 50 � 400

6 º � 5,400 º 5 � 400

6 º � 54,000 º 500 � 400,000

80900

5060

56

33,200

332

50032,000

7. � 6.3 � 8.7 8. 7.36 � 2.14 �

9. � 9.74 � 5.48 10. � 4.6 � 2.81.84.269.515

Practice

Solve mentally.

42 27420 270420 2704,200 2,7004,200 2,70042,000 27,000

320 5320 503,200 3

6 500

9 8

9,000 800

Math Masters, p. 140

Study Link Master

Lesson 5�2 323

� Interpreting a Data Table(Math Journal 1, p. 109)

Social Studies Link Students solve problems based on dataabout the 12 most recent presidents of the United States.

Ongoing Assessment: Informing InstructionIn Problem 4, watch for students who look only at the years of Ford’s andKennedy’s terms and therefore conclude that Kennedy was president for theshortest time. Actually, Kennedy was president for a little more than 2 years and 10 months, while Ford was president for less than 2 years and 6 months.

� Math Boxes 5�2(Math Journal 1, p. 110)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 5-4. The skill in Problem 5previews Unit 6 content.

Ongoing Assessment:Recognizing Student Achievement

Use Math Boxes, Problem 3 to assess students’ ability to determine whether anumber sentence is true or false. Students are making adequate progress if theycan use mental arithmetic, a paper-and-pencil algorithm, or a calculator to determine whether the number sentences are true or false. Some students maybe able to suggest how to change a false number sentence to make it true.

[Patterns, Functions, and Algebra Goal 2]

� Study Link 5�2(Math Masters, p. 140)

Home Connection Students practice extended multiplication facts.

INDEPENDENT

ACTIVITY

Math Boxes

Problem 3 �

INDEPENDENT

ACTIVITY

INDEPENDENT

ACTIVITY

2 Ongoing Learning & Practice

324 Unit 5 Big Numbers, Estimation, and Computation

LESSON

5�2

Name Date Time

A Multiplication Wrestling Competition

1. Twelve players entered a Multiplication Wrestling competition. The numbers they chose are shown in the following table. The score of each player is the product of the two numbers. For example, Aidan’s score is 741, because 13 º 57 � 741. Which of the 12 players do you think has the highest score?

Check your guess with the following procedure. Do not do any arithmetic forSteps 2 and 3.

2. In each pair below, cross out the player with the lower score. Find thatplayer’s name in the table above and cross it out as well.

3. Two players are left in Group A. Cross out the one with the lower score.Two players are left in Group B. Cross out the one with the lower score.Two players are left in Group C. Cross out the one with the lower score.

Which 3 players are still left?

4. Of the 3 players who are left, which player has the lowest score? Cross out that player’s name.

5. There are 2 players left. What are their scores?Sarah’s is 3,763.

6. Who won the competition? Sarah

EmilyEmily, Liza, and Sarah

Answers vary.

Liza’s is 3,723;

Group A Group B Group C

Aidan: 13 º 57 Indira: 15 º 73 Miguel: 17 º 35

Colette: 13 º 75 Jelani: 15 º 37 Rex: 17 º 53

Emily: 31 º 75 Kuniko: 51 º 37 Sarah: 71 º 53

Gunnar: 31 º 57 Liza: 51 º 73 Tanisha: 71 º 35

Aidan; Colette Indira; Jelani Miguel; Rex

Emily; Gunnar Kuniko; Liza Sarah; Tanisha

Math Masters, p. 142

Teaching Master

LESSON

5�2

Name Date Time

Partial-Sums Addition

Example: 2,000 � 280 � 300 � 42 � ?

2,000280300

� 42Add the thousands: 2,000Add the hundreds: 500 (200 � 300)Add the tens: 120 (80 � 40)Add the ones: � 2Find the total: 2,622

Solve each problem.

1. 800 � 120 � 160 � 24 � 2. 700 � 420 � 50 � 30 �

3. � 600 � 180 � 40 � 12 4. � 2,400 � 160 � 420 � 28

5. � 1,500 � 90 � 240 � 24 6. 5,600 � 420 � 400 � 30 � 6,4501,8543,008832

1,2001,104

10

Math Masters, p. 141

Teaching Master

� Reviewing Partial-SumsAddition(Math Masters, p. 141)

To explore partial-sums addition in preparation for adding partialproducts in Multiplication Wrestling, have students find the sum of four multidigit numbers. The problems are presented horizontally to provide practice in correctly aligning the digits in a vertical format.

� Judging a MultiplicationWrestling Competition(Math Masters, p. 142)

To apply students’ understanding of the Distributive Property of Multiplication over Addition, have them useestimation strategies to determine which player in a

Multiplication Wrestling competition has the highest score. On theback of Math Masters, page 142, ask students to explain how theysolved Problem 4 and to show their work for Problem 5.

5–15 Min

INDEPENDENT

ACTIVITYENRICHMENT

5–15 Min

INDEPENDENT

ACTIVITYREADINESS

3 Differentiation Options