Teaching the Lesson materials

Key ActivitiesStudents use name-collection boxes to practice representing whole numbers in different ways.

Key Concepts and Skills• Give equivalent mathematical expressions for whole numbers. [Number and Numeration Goal 4]• Use conventional notation to write expressions using the four basic arithmetic operations.

[Patterns, Functions, and Algebra Goal 2]• Insert grouping symbols to make number sentences true. [Patterns, Functions, and Algebra Goal 3]

Key Vocabulary equivalent name • name-collection box

Ongoing Assessment: Recognizing Student Achievement Use journal page 30. [Number and Numeration Goal 4]

Ongoing Learning & Practice materials

Students play Name That Number to practice representing numbers in different ways.

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

Differentiation Options materials

Students sortdominoes intocollections accordingto the sums of thedominoes’ dots.

Students investigatea pan-balanceapproach to findequivalent names for numbers.

Students complete name-collectionboxes.

Students solveproblems involvingRoman numerals.

� Teaching Masters (Math Masters,pp. 43 and 44)

� Teaching Aid Masters (MathMasters, pp. 394–397)

� number cards 0–18 (1 of each)� 5-Minute Math, pp. 4–6

EXTRA PRACTICEEXTRA PRACTICEENRICHMENTREADINESS

3

� Math Journal 1, p. 31� Student Reference Book, p. 254� Study Link Master (Math Masters,

p. 42)� Game Master (Math Masters,

p. 489)� deck of number cards; index

cards (optional); calculator(optional)

2

� Math Journal 1, p. 30� Study Link 2�1� Teaching Aid Master (Math

Masters, p. 389)� calculator (optional)� index cards (optional)� slate

See Advance Preparation

1

Objective To review equivalent names for whole numbers and

name-collection boxes.

Technology Assessment Management System

Journal page 30, Problem 6See the iTLG.

Additional InformationAdvance Preparation For Part 1, set aside space for a Numbers and Their Uses Museum.(See the Study Link 2-1 Follow-Up.)

Lesson 2�2 89

90 Unit 2 Using Numbers and Organizing Data

� Math Message Follow-UpStudents share names for the number 10 as you record them onthe board. For example: 3 � 7, 48 � 38, 2 � 5, 2 � 2 � 2 � 4,and 20 � 2 are all names for the number 10. Have students indicate “thumbs-up” if they agree with each answer.

Introduce the term equivalent names. Names for the samenumber are called equivalent names. In this lesson students will use numbers and operations to generate equivalent names for whole numbers.

NOTE Equivalent names may be defined broadly to include all kinds of names,including names that do not use numbers and operations. For example, thewords dozen and doce, the Roman numeral XII, 12 tally marks, and a 4-by-3array of dots are all names for the number 12. Encourage students to look forother names that consist of numbers and operations. In mathematics, suchnames are called mathematical expressions.

� Reviewing the Idea that Numbers Have Many Names(Math Journal 1, p. 30)

Draw a name-collection box for the number 12 on the board.(See margin.) Have students suggest operations (�, �, �, �) andnumbers (whole numbers, fractions, decimals, negative numbers)they might use when completing a name-collection box. Recordtheir suggestions on the board.

Ask the class to make up names for 12 as you record them in thename-collection box. Encourage students to come up with unusualnames. For example, some students might offer mathematicalexpressions that include multiple operations, parentheses, or exponents.

PARTNER

ACTIVITY

WHOLE-CLASS

ACTIVITY

1 Teaching the Lesson

Getting Started

Study Link 2�1Follow-UpHave students share examples of numbers they found. Ask them to record a fewinteresting numbers on index cards. Add thecards to your Numbers and Their UsesMuseum. Encourage students to continue tocollect and record additional interesting numberfacts for the display.

Mental Math and ReflexesPose extended subtraction-fact problems. Suggestions:

7 � 1 � 6 14 � 7 � 7 170 � 80 � 9070 � 10 � 60 140 � 70 � 70 1,700 � 800 � 900700 � 100 � 600 1,400 � 700 � 700 17,000 � 8,000 � 9,000

Math MessageOn an Exit Slip, write as many names as you can for the number 10.

24

36 � 1248 / 2

2 � 2 � 2 � 3(10 � 10) � 76

3 � 8

30

1.

Name-Collection BoxesLESSON

2�2

Date Time

Write five names in each box below. Use as many different kinds of numbers (such ascounting numbers, fractions, decimals, negative numbers) and different operations (�, �, �, �) as you can. Draw a star next to the name you find most interesting.

149

2.

3. 4.

16

8 � 2

970 � 954

10 � (60 � 10)

4 � 432 � 2

50

100 � 50100 � 225 � 25

5,000 � 1000.5 � 100

100

2 � 5 � 5 � 2487 � 387

4 � 2520 � 5

102

Make up your own name-collection boxes. Use different kinds of numbers and operations.

5. 6.

Sample answers:

�

Math Journal 1, p. 30

Student Page

12

6 � 6

36 � 3

4 � 3

�12� of 24

(2 � 5) � 2

�224�

Adjusting the Activity

Adjusting the Activity

To focus on the goal of representing numbers in equivalent ways, havestudents use a calculator to help them complete the name-collection boxes.

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

Give more examples if needed. Then have students work with apartner to complete Problems 1–5 on journal page 30. Askstudents to complete Problem 6 independently.

Have students share their favorite answers from journal page 30.List some of them on the board, especially the most inventive.

Ongoing Assessment:Recognizing Student Achievement

Use journal page 30, Problem 6 to assess students’ ability to give equivalentnames for whole numbers. Students are making adequate progress if they areable to name the box and generate correct mathematical expressions involvingone or more of the basic four arithmetic operations. Some students may give mathematical expressions involving grouping symbols or exponents.

[Number and Numeration Goal 4]

� Playing Name That Number(Student Reference Book, p. 254; Math Masters, p. 489)

Students play Name That Number to practice representingnumbers in different ways. Consider having them recordrounds of play on Math Masters, page 489.

Suggest that students write the operation symbols (�, �, �, and �) andparentheses symbols on separate index cards. Then they can arrange the numbers, operations cards, and parentheses cards in various ways to help themfind solutions.

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

PARTNER

ACTIVITY

2 Ongoing Learning & Practice

Journal

page 30

Problem 6�

Lesson 2�2 91

Links to the FutureLesson 3-10 of Fourth Grade EverydayMathematics reviews the use of parenthesesin number sentences. Until students are ableto insert parentheses into their recordedsolutions for Name That Number, have themwrite each calculation separately. Withoutparentheses, students may record numbersentences that do not follow the order ofoperations. Describing and applying theorder of operations is a Grade 6 Goal.

ExampleExample Target number: 16 Player 1’s cards:

Some possible solutions:

10 � 8 � 2 � 16 (3 cards used)

7 * 2 � 10 � 8 � 16 (4 cards used)

8 / 2 � 10 � 7 � 5 � 16 (all 5 cards used)

The player sets aside the cards used to make a solution and draws the same number of cards from the top of the deck.

10

10

7

7

5

5

8

8

2

2

Name That Number

Materials � 1 complete deck of number cardsPlayers 2 or 3Skill Naming numbers with expressions

Object of the game To collect the most cards. Directions

1. Shuffle the cards and deal 5 cards to each player. Place theremaining cards number-side down on the table between theplayers. Turn over the top card and place it beside the deck.This is the target number for the round.

2. Players try to match the target number by adding,subtracting, multiplying, or dividing the numbers on as manyof their cards as possible. A card may only be used once.

3. Players write their solutions on a sheet of paper. Whenplayers have written their best solutions:

♦ Each player sets aside the cards they used to match thetarget number.

♦ Each player replaces the cards they set aside by drawingnew cards from the top of the deck.

♦ The old target number is placed on the bottom of the deck.♦ A new target number is turned over, and another round

is played.

4. Play continues until there are not enough cards left toreplace all of the players’ cards. The player who has setaside the most cards wins the game.

Games

Student Reference Book, p. 254

Student Page

92 Unit 2 Using Numbers and Organizing Data

STUDY LINK

2�2 Many Names for Numbers

Name Date Time

1. Write five names for 64. 2. Write five names for 132.

3. Pretend that the 4-key on your calculator is broken. Write six ways to displaythe number 40 on the calculator without using the 4-key. Try to use differentnumbers and operations.

Example: 2 � 2 � 10

4. Now pretend that all the keys on your calculator work except for the 3-key and the 6-key. Write six ways to display the number 36 without using thesekeys.

5. 20 � 60 � 6. � 60 � 90

7. � 80 � 30 8. 110 � 40 � 705015080

(12 � 4) � 12� 7220 � 10 � 4 � 218 � 2 9 � 4

Sample answers:

750 � 710120 � 3 � 8030 � 1080 � 2 20 � 20

Sample answers:

72 � 2

Try This

Practice

Sample answers:

�12�

�12�

149

64

8 � 832 � 2

16 � 16 � (8 � 4)10 � 54

16 � 16 � 16 � 16

64

8 � 832 � 2

16 � 16 � (8 � 4)10 � 54

16 � 16 � 16 � 16

132

2 � 6611 � 12 66 � 66

(50 � 2) � 32

Math Masters, p. 42

Study Link Master

31

Math Boxes LESSON

2�2

Date Time

5. Complete.

a. 4 ft � in.

b. 4 ft � yd in.

c. 2 yd � ft

d. 72 in. � yd ft

e. 6,756 in. � ft 56302

6121

48

97 128

20

4

1. a. Write the largest number you canmake with the digits 5, 2, 3, 0, 6, 0.Use each digit only once.

b. Use the same digits and write thesmallest number you can make. Do not start with 0.

200,356

653,200

3. Draw a convex polygon. 4. Measure these line segments to thenearest centimeter.

a.

About centimeters

b.

About centimeters 4

6

6. Divide mentally.

a. 9 � 9 �

b. � 12 � 2

c. � 20 � 5

d. 40 � 10 �

e. 14 � 7 � 24

46

1

10 11

2. Add mentally or with a paper-and-pencilalgorithm.

a. b.

129

Sample answer:

37� 142

179

468� 394

862

Math Journal 1, p. 31

Student Page

� Math Boxes 2�2(Math Journal 1, p. 31)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 2-4. The skill in Problem 6previews Unit 3 content.

Writing/Reasoning Have students write a response to thefollowing: Explain how you know that the polygon you drew inProblem 3 is convex and not concave. Sample answer: All of thevertices are “pushed out.”

� Study Link 2�2(Math Masters, p. 42)

Home Connection Students complete name-collectionboxes and solve broken-calculator problems.

� Sorting Dominoes by Sums(Math Masters, pp. 43 and 394–396)

To explore equivalent names for whole numbers using manipulatives,have students sort dominoes according to sums. Ask each group tomake a list of all the addition facts shown by the dominoes.

15–30 Min

SMALL-GROUP

ACTIVITYREADINESS

3 Differentiation Options

INDEPENDENT

ACTIVITY

INDEPENDENT

ACTIVITY

LESSON

2�2

Name Date Time

Domino Sums

Materials � 1 or 2 sets of double-9 dominoes or Math Masters,pages 394–396

� number cards 0–18 (1 each; from the Everything Math Deck, if available)

Directions

1. Lay out the number cards in order from 0 through 18.

2. Place each domino above the number card that shows the sum of thedomino’s dots. In the example below, the sum of 4 and 1 is 5, and the sum of2 and 3 is 5.

2 � 3 and 4 � 1 are equivalent names for the number 5.

Example:

3. In the space below, list the addition facts shown by the dominoes. Before you begin, decide how you will organize the facts.

149

5

Math Masters, p. 43

Teaching Master

� Solving Pan-Balance Problems(Math Masters, p. 44)

To apply students’ understanding of equivalent names for wholenumbers, have them solve pan-balance problems. Ask students todescribe the pan-balance problems and explain their solutionstrategies.

� Completing Name-Collection Boxes(Math Masters, p. 397)

To provide practice representing numbers in different ways, havestudents complete name-collection boxes. Use Math Masters,page 397 to create problems to meet the needs of individualstudents, or have students create and solve their own problems.

� 5-Minute MathTo offer students more experience with Roman numerals, see 5-Minute Math, pages 4–6.

5–15 Min

SMALL-GROUP

ACTIVITYEXTRA PRACTICE

5–15 Min

INDEPENDENT

ACTIVITYEXTRA PRACTICE

15–30 Min

PARTNER

ACTIVITYENRICHMENT

Lesson 2�2 93

LESSON

2�2

Name Date Time

Pan-Balance Problems

In each figure below, the pans hold equivalent names for a number. The pans are in perfect balance. Fill in the missing numbers. Write the name for the pan balance.

Example:

a. �

b. Pan-balance name

1. 2.

a. � a. �

b. Pan-balance name b. Pan-balance name

3. 4.

a. � a. �

b. Pan-balance name b. Pan-balance name 302163

36 � � 3)(60 � 4) � (� 7 63 �

8120157

96 � � 6613 � 27 �

155

5 � 5 � 5 3 � 5

A pan balance is used to weigh objects. When theweight of the objects in one pan is the same as theweight of the objects in the other pan, the pans arein perfect balance.

Math Masters, p. 44

Teaching Master

Name Date Time

Domino Cutouts

Math Masters, pp. 394–396

Teaching Aid Masters

Name-Collection Boxes

Name ____________________________

Date _____________________________

Name ____________________________

Date _____________________________

Name ____________________________

Date _____________________________

Name ____________________________

Date _____________________________

Name Date Time

Math Masters, p. 397

Teaching Aid Master

Math Masters, pages 394–396 are domino cutouts.