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Lesson 7�10 621

Advance Preparation

Teacher’s Reference Manual, Grades 4–6 pp. 143–147

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]

Key ActivitiesStudents use pattern blocks and counters to

find the ONE for given fractions, and they

solve “What is the ONE?” problems.

MaterialsMath Journal 2, pp. 208 and 209

Study Link 7� 9

pattern blocks � beans, pennies, or other

counters � slate � Geometry Template �

overhead pattern blocks (optional)

Playing Fraction Top-ItStudent Reference Book, p. 247

Math Masters, p. 506

Fraction Cards (Math Journal 2,

Activity Sheets 5 and 6)

Students practice comparing fractions.

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

Plotting Insect DataMath Journal 2, pp. 209A and 209B

Students plot insect lengths on a

line plot.

Math Boxes 7�10Math Journal 2, p. 210

Students practice and maintain skills

through Math Box problems.

Study Link 7�10Math Masters, p. 231

Students practice and maintain skills

through Study Link activities.

ENRICHMENTPlaying Getting to OneStudent Reference Book, p. 248

calculator

Students apply their proportional reasoning

skills and their understanding of the concept

of ONE.

ENRICHMENTFinding the ONEMath Masters, p. 232

Students determine how a candy bar

was divided.

Teaching the Lesson Ongoing Learning & Practice

132

4

Differentiation Options

The ONE for FractionsObjective To guide students as they find the whole, or the ONE,

for given fractions.f

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eToolkitePresentations Interactive Teacher’s

Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

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622 Unit 7 Fractions and Their Uses; Chance and Probability

NOTE The blocks that make up the ONE

can often be arranged in several ways.

Investigating various arrangements is worth-

while, but in this lesson, it does not matter

how the blocks in the ONE are arranged.

1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASSDISCUSSION

Discuss students’ answers. For Problem 2, have volunteers describe 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 to WHOLE-CLASS ACTIVITY

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

● If is 1 _ 2 , then what is the ONE? 1 wide rhombus or equivalent

● If is 3 _ 4 , then what is the ONE? 2 wide rhombuses or equivalent

● If is 2 _ 3 , then what is the ONE? 3 trapezoids or equivalent

● If is 1 _ 3 , then what is the ONE? 6 squares

● If is 1 _ 2 , then what is the ONE? 4 wide rhombuses

Getting Started

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

Study Link 7�9 Follow-UpHave students share how they know the fractions in Problems 3 and 4 are equivalent. Encourage students to use a model to explain.

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 decimals on 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:

34

_ 100

0.34

80 _

100 0.80, or 0.8

0.6 6

_ 10

0.3 3

_ 10

132

_ 100

1.32

206

_ 100

2.06

1.99 199

_ 100

or 1 99

_ 100

65.79 6,579

_ 100

, or 65 79

_ 100

5

_ 100

0.05

9 _

100 0.09

0.03 3

_ 100

0.065 65

_ 1,000

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Adjusting the Activity

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

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 �1

5� 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

16

25

16

15

Math Journal 2, p. 209

Student Page

Adjusting the Activity

� Using Counters to Find the ONE WHOLE-CLASS ACTIVITY

Pose more problems in which part of a collection of objects is given and students are to find the ONE. Display beans, pennies, or other counters on the overhead projector. Tell and write what fraction is represented. Ask students to use their slates to write the number of counters in the ONE. Suggestions:

● If is 1 _ 2 , then what is the ONE? 6 counters

● If is 1 _ 3 , then what is the ONE? 9 counters

● If is 2 _ 5 , then what is the ONE? 10 counters

● If is 2 _ 3 , then what is the ONE? 6 counters

● If is 1 _ 4 , then what is the ONE? 8 counters

Draw boxes around counters to create a visual representation

of the problems.

Example 1:

12

ONE

If 3 counters is 1

_ 2 , then what is the ONE?

Example 2:

15

15

ONE

If 4 counters is 2

_ 5 , 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?” PARTNER ACTIVITY

Problems(Math Journal 2, pp. 208 and 209)

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

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

ELL

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BBBBBBBBBBBBBBBBBBBB EEELEMMMMMMMOOOOOOOOOBBBLBLBLBLBLBROOOOROROROROROROROROROO LELELELEEEEEELEEMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRGGGLLLLLLLLLLLLLVINVINVINVINNNVINVINVINNVINVINVINVINVINV GGGGGGGGGGGOLOOOLOOOLOLOO VINVINVVLLLLLLLLLVINVINVINVINVINVINVINVINVINVINVINVINNGGGGGGGGGGGOOOLOLOLOLOLOLOOO VVLLLLLLLLLLVVVVVVVVOSOSOOSOSOSOSOSOSOSOOSOSOSOSOSOOOOOSOSOSOSOSSOOSOSOSOSOSOSOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVVVLLLLLLVVVVVVVLLLVVVVVVVLLLLLLLLVVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSSSS GGGGGGGGGGGGGGGGGOOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIISOLVING

ELL

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Date Time

Insect Data continuedLESSON

7�10

Use the line plot on journal page 209A to answer the questions. Write a number model

to summarize each problem.

1. a. What is the maximum insect length? 1

3

_ 4 in. The minimum?

3 _ 8 in.

b. What is the range of the data set? 1

3

_ 8 in. Number model: 1

3

_ 4 –

3

_ 8 = 1

3

_ 8

2. a. What is the median of the data set? 7 _ 8 in.

b. How much longer is the median length than the minimum length? 4

_ 8 , or

1

_ 2 in.

Number model: 7

_ 8 –

3

_ 8 =

1

_ 2

3. a. What is the mode of the data set? 7 _ 8 in.

b. How much longer is the maximum length than the mode length? 7 _ 8 in.

Number model: 1 3

_ 4 –

7

_ 8 =

7

_ 8

4. Two insects have the maximum length. What is the difference

in length between these insects and the next-longest insects? 1

_ 4 in.

Number model: 1

3

_ 4 – 1 1 _

2 = 1

_ 4

5. There are three insects in Veronica’s collection that are from 1 _ 2 inch to

3

_ 4 inch long.

If these three insects were placed end to end, how long would the line of insects be?

in. Number model: 5

_ 8 +

5

_ 8 +

3

_ 4 = 2

6. How long would the line of insects be if all the

insects less than 1 _ 2 inch long were placed end to end?

in.

Number model: 3

_ 8 +

3

_ 8 =

3

_ 4 in.

7. Make up and solve your own problem about the insect data.

Answers vary.

Number model:

Sample number models are given.

16

__ 8 , or 2

6 _ 8 , or 3 _

4

185-218_EMCS_S_MJ2_G4_U07_576426.indd 209B 3/24/11 9:28 AM

Math Journal 2, p. 209B

Student Page

624 Unit 7 Fractions and Their Uses; Chance and Probability

Adjusting the Activity

Date Time

Insect DataLESSON

7�10

Veronica collected 15 insects for a science project. She measured the length of each

insect to the nearest 1 _ 8 inch. Her measurements are shown in the table below.

InsectLength

(to the nearest 1

_ 8 inch)

InsectLength

(to the nearest 1

_ 8 inch)

Darner dragonfly 1 1 _ 2 Red legged grasshopper 1 1

_ 8

Boreal firefly 3

_ 8 American cockroach 1 1 _ 2

Yellow bumblebee 3

_ 4 June beetle 5

_ 8

Damselfly 1 1 _ 4 Paper wasp 7

_ 8

Ground beetle 7 _ 8 Field cricket 7

_ 8

Green lacewing 1 Indian meal moth 3

_ 8

Lady bug 5

_ 8 Katydid 1 3

_ 4

Carolina mantid 1 3 _ 4

Plot the insect lengths on the line plot below. Then use the completed plot to answer

the questions on the next page.

Length (inches)

Insect Lengths

Nu

mb

er

of

Inse

cts

1 11

81

1

41

3

81

1

21

5

81

3

4

3

8

1

2

5

8

3

4

7

8

XX

XX

X XXX

X X X XX

XX

185-218_EMCS_S_MJ2_G4_U07_576426.indd 209A 3/24/11 9:28 AM

Math Journal 2, p. 209A

Student Page

2 Ongoing Learning & Practice

� Playing Fraction Top-It PARTNER ACTIVITY

(Student Reference Book, p. 247; Math Masters, p. 506)

Students play Fraction Top-It to practice comparing fractions.

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 for

the largest fraction and 2 points for the smallest fraction. The player with the

most 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

Math Masters

Page 506 �

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, and

write a number model to illustrate the comparison. Some students may be able

to compare fractions using only the numerical representations.

[Number and Numeration Goal 6]

� Plotting Insect Data INDEPENDENTACTIVITY

(Math Journal 2, pp. 209A and 209B)

Students plot insect lengths in fractions of an inch on a line plot. Then they use the line plot to solve fraction and mixed-number addition and subtraction problems.

� Math Boxes 7�10 INDEPENDENTACTIVITY

(Math Journal 2, p. 210)

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

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

ELL

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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 1

_ 4 . Draw each of the following:

Example: 3

_ 4 a. 1 b. 1

1

_ 2 c. 2

2. Suppose is 2

_ 3 . Draw each of the following:

a. 1

_ 3 b. 1 c.

4

_ 3 d. 2

Use counters to solve the following problems.

3. If 14 counters are 1

_ 2 , then what is the ONE?

28 counters

4. If 9 counters are 1

_ 3 , then what is the ONE?

27 counters

5. If 12 counters are 2

_ 5 , then what is the ONE? 30 counters

6. If 16 counters are 4

_ 9 , then what is the ONE? 36 counters

7. 3

_ 4 = 1

_ 4 +

1

_ 2 8.

1

_ 3 +

1

_ 6 =

3

_ 6 , or 1

_ 2

9. 3

_ 4 -

1

_ 4 =

2

_ 4 , or 1

_ 2 10. 3

_ 6 , or 1

_ 2 = 5

_ 6 -

1

_ 3

Practice

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Math Masters, p. 231

Study Link Master

Lesson 7�10 625

in out

55 0.846... When 55 is divided by the ONE, the result is a

decimal close to one. The ONE must be greater

than 55.

70 1.076... When 70 is divided by the ONE, the result is

greater 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.

LESSON

7�10

Name Date Time

A Whole Candy Bar

Two friends cut a large candy bar into equal pieces. Harriet ate 1

_ 4 of the pieces.

Nisha ate 1

_ 2 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.

Sample answer: I shaded 1 _ 4 of a

bar for Harriet. Then I divided the

remaining 3 _ 4 into 12 pieces because

6 is 1 _ 2 of 12. If 3 _ 4 = 12, then 4 _ 4 = 16.

16

Harriet Nisha

Sample answer:

203-246_EMCS_B_MM_G4_U07_576965.indd 232 1/25/11 9:58 AM

Math Masters, page 232

Math Boxes LESSON

7�10

Date Time

1. Name the shaded area as a fraction and

a decimal.

a. fraction:

27

___ 100

b. decimal:

0.27

31518 19

3. Write 6 fractions equivalent to 14

_

16

.

27 61

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

723

_

14

= 51 R9, or 51 9 __ 14

53 54

6. Compare.

a. 1 day is 12 times as long as 2 hours.

b. 6 years is 18 times as long as

4 months.

c. 3 gallons is 6 times as much as

8 cups.

d. 8 cm is 40 times as long as 2 mm.

e. 1 meter is 50 times as

long as 2 cm.

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

8,432 = 68 ∗ 124

22 2317949–51

Sample answers

7 _ 8 28

__

32

21

__ 24 70

__

80

35

__ 40 168

___

192

2. Which number sentence is true? Fill in the

circle next to the best answer.

A 5 _ 6 < 1 _

6

B 4 _ 10

> 4 _ 5

C 1 _ 7 > 1 _

100

D 2 _ 12

= 3 _ 6

185-218_EMCS_S_MJ2_G4_U07_576426.indd 210 1/27/11 10:51 AM

Math Journal 2, p. 210

Student Page

ENRICHMENT INDEPENDENTACTIVITY

� Finding the ONE 15–30 Min

(Math Masters, p. 232)

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

� Study Link 7�10 INDEPENDENTACTIVITY

(Math Masters, p. 231)

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

3 Differentiation Options

ENRICHMENT PARTNER ACTIVITY

� Playing Getting to One 5–15 Min

(Student Reference Book, p. 248)

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

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