Teaching the Lesson materials

Key ActivitiesStudents use pattern blocks and counters to find the ONE for given fractions, and they solve“What is the ONE?” problems.

Key Concepts and Skills• Given a fractional part of a region, name the ONE.

[Number and Numeration Goal 2]• Given a fractional part of a collection, name the ONE.

[Number and Numeration Goal 2]• Identify a hexagon, trapezoid, and rhombus.

[Geometry Goal 2]

Ongoing Learning & Practice materialsStudents play Fraction Top-It to practice comparing fractions.

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

Ongoing Assessment: Recognizing Student AchievementUse Math Masters, page 506. [Number and Numeration Goal 6]

Differentiation Options materials

Students play Getting to One. Students use clues to determine how a candybar was divided.

� Student Reference Book, p. 248� Teaching Master (Math Masters,

p. 232)� calculator

ENRICHMENTENRICHMENT

3

� Math Journal 2, p. 210� Student Reference Book, p. 247� Study Link Master (Math Masters,

p. 231)� Game Master (Math Masters,

p. 506)� Fraction Cards (Math Journal 2,

Activity Sheets 5 and 6)

2

� Math Journal 2, pp. 208 and 209� Study Link 7�9� pattern blocks � beans, pennies, or other counters � slate� Geometry Template� overhead pattern blocks (optional)

1

Lesson 7�10 621

Objective To guide students as they find the whole, or the ONE,

for given fractions.

Technology Assessment Management System

Math Masters, page 506See the iTLG.

622 Unit 7 Fractions and Their Uses; Chance and Probability

� Math Message Follow-UpDiscuss students’ answers. For Problem 2, have volunteersdescribe or show how they solved the problem.

Tell students that in this lesson they will use pattern blocks and counters as tools to help them find the ONE.

� Using Pattern Blocks toFind the ONEPose problems like those below in which a part is given andstudents are to find the whole, or the ONE. Display one or twopattern blocks on the overhead projector, and tell what fraction is represented by this block or pair of blocks. Then direct studentsto use their pattern blocks to show the ONE. Discuss solutions.Suggestions:

● If is �12�, then what is the ONE?

1 wide rhombus or equivalent

● If is �34�, then what is the ONE?

2 wide rhombuses or equivalent

● If is �23�, then what is the ONE?

3 trapezoids or equivalent

● If is �13�, then what is the ONE?

6 squares

● If is �12�, then what is the ONE?

4 wide rhombuses

WHOLE-CLASS

ACTIVITY

WHOLE-CLASS

DISCUSSION

1 Teaching the Lesson

Getting Started

Math MessageSolve Problems 1 and 2 at the top of journal page 208.

Study Link 7�9Follow-UpHave students share how they solved Problems 1 and 2 and compare the remaining answers.

Mental Math and Reflexes Write fractions with denominators of 10 or 100 on the board, and have students write the equivalent decimals on their slates. Then write decimalson the board, and have students write the equivalent fractions or mixed numbers on their slates. Do not insist that the fractions be in simplest form.Suggestions:

�13040� 0.34

�18000� 0.80, or 0.8

0.6 �160�

0.3 �130�

�113020� 1.32

�210060� 2.06

1.99 �119090�, or 1�1

9090�

65.79 �61,50709

�, or 65�17090�

�1500� 0.05

�1900� 0.09

0.03 �1300�

0.065 �1,60500�

NOTE The blocks that make up the ONEcan often be arranged in several ways.Investigating various arrangements is worth-while, but in this lesson, it does not matterhow the blocks in the ONE are arranged.

Adjusting the Activity

208

What Is the ONE?LESSON

7�10

Date Time

Math Message

1. If the triangle below is �13�, then what is the whole—the ONE? Draw it on the grid.

2. If �14� of Mrs. Chin’s class is 8 students, then

how many students does she have altogether? students

Use your Geometry Template to draw the answers for Problems 3–6.

3. If is �12�, then what is the ONE? 4. If is �

14�, then what is the ONE?

5. If is �23�, then what is the ONE? 6. If is �

25�, then what is the ONE?

32

55

Math Journal 2, p. 208

Student Page

Lesson 7�10 623

209

What is the ONE? continuedLESSON

7�10

Date Time

55

Solve. If you wish, draw pictures at the bottom of the page to help you solve the problems.

7. If is �13�, then what is the ONE? counters

8. If is �14�, then what is the ONE? counters

9. If 10 counters are �25�, then what is the ONE? counters

10. If 12 counters are �34�, then what is the ONE? counters

11. If �15� of the cookies that Mrs. Jackson baked is 12,

then how many cookies did she bake in all? cookies

12. In Mr. Mendez’s class, �34� of the students take music

lessons. That is, 15 students take music lessons.How many students are in Mr. Mendez’s class? students

13. Explain how you solved Problem 12.

�1250� is an equivalent fraction to �

34�.

So, the whole is 4 � 5, which is 20 students. that each fractional part is equal to 5 students.Sample answer: I divided 15 by 3, which told me

20

60

162516

15

Math Journal 2, p. 209

Student Page

Adjusting the Activity

� Using Counters to Find the ONEPose more problems in which part of a collection of objects is givenand students are to find the ONE. Display beans, pennies, or othercounters on the overhead projector. Tell and write what fraction isrepresented. Ask students to use their slates to write the numberof counters in the ONE. Suggestions:

● If is �12�, then what is the ONE? 6 counters

● If is �13�, then what is the ONE? 9 counters

● If is �25�, then what is the ONE? 10 counters

● If is �23�, then what is the ONE? 6 counters

● If is �14�, then what is the ONE? 8 counters

ELL

Draw boxes around counters to create a visual representation of the problems.

Example 1:

If 3 counters is �12�, then what is the ONE?

Example 2:

If 4 counters is �25�, then what is the ONE?

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

� Solving “What Is the ONE?”Problems(Math Journal 2, pp. 208 and 209)

Students solve problems in which a fractional part is given, andstudents identify the ONE.

ELL

Have students use pattern blocks and counters to model the problems.

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

15

15

ONE

12

ONE

WHOLE-CLASS

ACTIVITY

Adjusting the Activity

210

Math Boxes LESSON

7�10

Date Time

1. Name the shaded area as a fraction and a decimal.

a. fraction:

b. decimal:

0.27

�12070�

31518 19

3. Write 6 fractions equivalent to �1146�.

27 61

4. Divide. Use a paper-and-pencil algorithm.

�71243

� � 51 R9, or 51�194�

53 54

6. Compare.

a. 1 day is times as long as 2 hours.

b. 6 years is times as long as 4 months.

c. 3 gallons is times as much as 8 cups.

d. 8 cm is times as long as 2 mm.

e. 1 meter is times as long as 2 cm.

5040

6

1812

5. Multiply. Use a paper-and-pencil algorithm.

� 68 � 1248,432

22 2317949–51

Sample answers

�78� �

2382�

�2214� �

7800�

�3450� �

116982�

2. Which number sentence is true? Fill in thecircle next to the best answer.

A �56� �

16�

B �140� �

45�

C �17� �1

100�

D �122� � �

36�

Math Journal 2, p. 210

Student Page

624 Unit 7 Fractions and Their Uses; Chance and Probability

� Playing Fraction Top-It(Student Reference Book, p. 247; Math Masters, p. 506)

Students play Fraction Top-It to practice comparing fractions.

ELL

Have students play with the shaded side of the cards up. Or have students play in groups of four and order the fractions. Players score 4 points forthe largest fraction and 2 points for the smallest fraction. The player with themost points at the end of the game is the winner.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

Ongoing Assessment:Recognizing Student Achievement

Use Math Masters, page 506 to assess students’ ability to compare fractions.Students are making adequate progress if they are able to determine which fraction is larger, with or without referring to the shaded sides of the cards, andwrite a number model to illustrate the comparison. Some students may be ableto compare fractions using only the numerical representations.

[Number and Numeration Goal 6]

� Math Boxes 7�10(Math Journal 2, p. 210)

Mixed Practice Math Boxes in this lesson are pairedwith Math Boxes in Lesson 7-12. The skill in Problem 6previews Unit 8 content.

Writing/Reasoning Have students write a response to the following: Describe two different ways to check your answer forProblem 5. Sample answer: I could divide to check the multiplication. 8,432 / 68 � 124 and 8,432 / 124 � 68. I could alsomake a ballpark estimate. 70 � 120 � (70 � 100) � (70 � 20) �7,000 � 1,400 � 8,400. The ballpark estimate 8,400 is close tothe product 8,432.

INDEPENDENT

ACTIVITY

Math MastersPage 506

PARTNER

ACTIVITY

2 Ongoing Learning & Practice

Name Date Time

Top-It Record Sheet 132

4

Play a round of Top-It. Record your number sentence and your opponent’s number sentence. Write , , or � to compare the number sentences.

263 264

Round Player 1 >, <, = Player 2

Sample 4+6=10 < 8+3=11

1

2

3

4

5

Math Masters, page 506

STUDY LINK

7�10 What Is the ONE?

44

Name Date Time

For Problems 1 and 2, use your Geometry Template or sketch the shapes.

1. Suppose is �14�. Draw each of the following:

Example: �34� a. 1 b. 1�

12� c. 2

2. Suppose is �23�. Draw each of the following:

a. �13� b. 1 c. �

43� d. 2

Use counters to solve the following problems.

3. If 14 counters are �12

�, then what is the ONE?

counters

4. If 9 counters are �13

�, then what is the ONE?

counters

5. If 12 counters are �25�, then what is the ONE? counters

6. If 16 counters are �49�, then what is the ONE? counters36

3027

28

7. � �14� � �

12� 8. �

13� � �

16� �

�36�, or �

12��

34�

Practice

9. �34� � �

14� � 10. � �

56� � �

13�

�36�, or �

12��

24�, or �

12�

Math Masters, p. 231

Study Link Master

ExampleExample Player 1 chooses the mystery number 65.

Player 2 guesses: 45. Player 1 keys in: 45 65 .Answer: 0.69 Too small.

Player 2 guesses: 73. Player 1 keys in: 73 65 .Answer: 1.12 Too big.

Player 2 guesses: 65. Player 1 keys in: 65 65 .Answer: 1. Just right!

Getting to One

Materials 1 calculatorPlayers 2Skill EstimationObject of the game To guess a mystery number in as fewtries as possible.Directions

1. Player 1 chooses a mystery number that is between 1 and 100.

2. Player 2 guesses the mystery number.

3. Player 1 uses a calculator to divide Player 2’s guess bythe mystery number. Player 1 then reads the answer inthe calculator display. If the answer has more than 2decimal places, only the first 2 decimal places are read.

4. Player 2 continues to guess until the calculator result is 1.Player 2 keeps track of the number of guesses.

5. When Player 2 has guessed the mystery number, playerstrade roles and follow Steps 1–4 again. The player whoguesses his or her mystery number in the fewest number ofguesses wins the round. The first player to win 3 roundswins the game.

Games

Advanced Version Allow mystery numbers up to 1,000.

Student Reference Book, p. 248

Student Page

Lesson 7�10 625

in out

55 0.846... When 55 is divided by the ONE, the result is adecimal close to one. The ONE must be greaterthan 55.

70 1.076... When 70 is divided by the ONE, the result isgreater than 1. The ONE must be less than 70.

65 1 When 65 is divided by the ONE, the result is 1.The ONE must be 65.

� Finding the ONE(Math Masters, p. 232)

To apply students’ understanding of the concept of theONE, have them determine how a candy bar was divided.

15–30 Min

INDEPENDENT

ACTIVITYENRICHMENT

� Study Link 7�10(Math Masters, p. 231)

Home Connection Students solve “What is the ONE?”problems.

� Playing Getting to One(Student Reference Book, p. 248)

To apply students’ proportional reasoning skills and their understanding of the concept of the ONE, have them play Gettingto One. Ask students to use a “What’s My Rule?” table to organizetheir guesses and explain their thinking. For example:

5–15 Min

PARTNER

ACTIVITYENRICHMENT

3 Differentiation Options

INDEPENDENT

ACTIVITY

LESSON

7�10

Name Date Time

16

Sample answer: I shaded �14� of a

bar for Harriet. Then I divided the remaining �

34� into 12 pieces because

6 is �12� of 12. If �

34� � 12, then �

44� � 16.

LESSON

7�10

Name Date Time

A Whole Candy Bar

Two friends cut a large candy bar into equal pieces. Harriet ate �14� of the pieces.

Nisha ate �12� of the remaining pieces. Six pieces were left over.

1. How many pieces was the candy bar originally divided into? pieces

2. Explain how you got your answer. Include a drawing and number models as part of your explanation.

16

Sample answer: I shaded �14� of a

bar for Harriet. Then I divided the remaining �

34� into 12 pieces because

6 is �12� of 12. If �

34� � 12, then �

44� � 16. Harriet Nisha

Sample answer:

Math Masters, page 232