eToolkitePresentations Interactive Teacher’s

Lesson Guide

Algorithms Practice

Family Letters

CurriculumFocal Points

www.everydaymathonline.com

AssessmentManagement

EM FactsWorkshop Game™

Common Core State Standards

Lesson 7� 8 609

Advance Preparation

Teacher’s Reference Manual, Grades 4–6 pp. 62, 63, 153, 154

Key Concepts and Skills• Read and write decimals through

hundredths. 

[Number and Numeration Goal 1]

• Represent a shaded region as a fraction

and a decimal. 

[Number and Numeration Goal 2]

• Rename fractions with 10 and 100

in the denominator as decimals. 

[Number and Numeration Goal 5]

• Use equal sharing to solve division

problems. 

[Operations and Computation Goal 4]

Key ActivitiesStudents rename fractions as decimals and

decimals as fractions. They also explore the

relationship between fractions and division.

Ongoing Assessment: Recognizing Student Achievement Use journal page 203.  [Number and Numeration Goal 5]

MaterialsMath Journal 2, pp. 203, 342, and 343

Student Reference Book, p. 46

Study Link 7� 7

Math Masters, p. 426 (optional)

transparency of Math Masters, p. 426 �

base-10 blocks � calculator � slate �

overhead base-10 blocks (optional)

Math Boxes 7� 8Math Journal 2, p. 204

Students practice and maintain skills

through Math Box problems.

Study Link 7� 8Math Masters, p. 226

Students practice and maintain skills

through Study Link activities.

READINESS

Creating Base-10 Block DesignsMath Masters, p. 442

base-10 blocks

Students make a design with base-10 blocks,

copy the design on a grid, and write a

decimal and a fraction to describe what

part of the grid is covered by the blocks.

ENRICHMENTFinding Fractions, Decimals, and Percents on GridsMath Masters, p. 227

Students shade a 10-by-10 grid to represent

fractions and find the percent and decimal

equivalencies.

ENRICHMENTDesigning a Baseball Cap Rack Math Masters, pp. 227A and 227B

Students use fractions with denominators

of 10; 100; or 1,000 to design a baseball

cap rack.

EXTRA PRACTICE

Taking a 50-Facts TestMath Masters, pp. 412 and 414; p. 416

(optional)

pen or colored pencil

Students take a 50-facts test. They use a

line graph to record individual and optional

class scores.

Teaching the Lesson Ongoing Learning & Practice Differentiation Options

Fractions and DecimalsObjectives To provide experience with renaming fractions

as decimals and decimals as fractions; and to develop an

understanding of the relationship between fractions and division.

a

��������

609_EMCS_T_TLG2_G4_U07_L08_576906.indd 609609_EMCS_T_TLG2_G4_U07_L08_576906.indd 609 3/3/11 2:50 PM3/3/11 2:50 PM

610 Unit 7 Fractions and Their Uses; Chance and Probability

Adjusting the Activity

Name Date Time

Base-10 Grids

Math Masters, p. 426

Teaching Aid Master

Getting Started

Mental Math and Reflexes Write a fraction on the board. Students write an equivalent fraction on their slates. Suggestions:

Sample answers:

1

_ 2 2

_ 4 ,

3

_ 6

1

_ 4 2

_ 8 ,

3

_ 12

1

_ 3 2

_ 6 ,

3

_ 9

1

_ 5

2

_ 10

, 3

_ 15

50

_ 100

5

_ 10

, 25

_ 50

3

_ 4

6

_ 8 ,

9

_ 12

6

_ 9 2

_ 3 ,

12

_ 18

5

_ 8 10

_ 16

, 50

_ 80

3

_ 5

6

_ 10

, 9

_ 15

Math MessageWrite the following fractions as decimals:

1

_ 10 32

_ 100

7

_ 10

9

_ 100

Study Link 7�7 Follow-UpHave students compare answers and share the name-collection boxes they created.

1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASSDISCUSSION

(Math Masters, p. 426)

Display a transparency of Math Masters, page 426 as you discuss the answers. Remind students that the square is the “whole.” You can color the grid sections to show fractional parts or cover them with base -10 blocks.

Color or cover one column of the bottom grid.

● What fractional part of the square is this? 1 _ 10

110, or 0.1

● How would you write 1 _ 10 as a decimal? 0.1

Repeat with other fractions in tenths, including 3 _ 10 and 7 _ 10 .

Provide students with base-10 blocks and a copy of Math Masters,

page 426, so they can model the decimal numbers at their desks.

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

EM3cuG4TLG2_610-614_U07L08.indd 610EM3cuG4TLG2_610-614_U07L08.indd 610 1/20/11 9:11 AM1/20/11 9:11 AM

Links to the Future

�

Whole

large square

Fractions and DecimalsLESSON

7�8

Date Time

61

1.

�120� of the square is shaded.

How many tenths?

�120� � 0. 2

2

2.

�12� is shaded.

How many tenths?

�12� � � 0.

105

5

3.

�15� is shaded.

How many tenths?

�15� � � 0.

102

2

4.

�25� is shaded.

How many tenths?

�25� � � 0.

104

4

5. �35� � � 0.

10

6. �45� � � 0.

108

6

�1100� , or 0.01

7.

�14� is shaded.

�14� � � 0.

10025

8.

�34� is shaded.

�34� � � 0.

10075

�110�, or 0.1

� �

�

� �

5

6

8

25 75

42

Math Journal 2, p. 203

Student Page

Lesson 7�8 611

Next, color (or cover) one small square of the top grid on the transparency.

● What fractional part of the square is this? 1 _ 100

1100, or 0.01

● How would you write 1 _ 100 as a decimal? 0.01

Repeat with other fractions in hundredths, including 32 _ 100 and 9 _ 100 . Also, give students practice converting decimals into fractions; for example, 0.3 and 0.25.

Tell students that in this lesson they will use a base -10 grid as a tool to help them rename fractions as decimals.

Do not be concerned with reducing fractions to simplest form when converting

between decimals and fractions. At this stage, it is enough for students simply

to make the conversions. Naming fractions in simplest form is a Grade 5 Goal.

� Renaming Fractions as Decimals INDEPENDENTACTIVITY

and Decimals as Fractions(Math Journal 2, pp. 203, 342, and 343; Math Masters, p. 426)

Students complete journal page 203. Discuss answers, using a transparency of Math Masters, page 426. For each problem, ask by which number the numerator and denominator were multiplied to obtain the second fraction.

Ask students to record the decimals in the Equivalent Names for Fractions table on journal pages 342 and 343.

Ongoing Assessment: Recognizing Student Achievement

Journal page 203

Problems

1–4, 7, and 8 �

Use journal page 203, Problems 1–4, 7, and 8 to assess students’ ability to

rename tenths and hundredths as decimals with the assistance of a visual

model. Students are making adequate progress if they are able to name the

number of tenths or hundredths shaded on the grid as a fraction and rename the

fraction as a decimal. Some students may be able to solve Problems 5 and 6 on

journal page 203, which do not include a visual prompt.

[Number and Numeration Goal 5]

EM3cuG4TLG2_610-614_U07L08.indd 611EM3cuG4TLG2_610-614_U07L08.indd 611 1/20/11 9:11 AM1/20/11 9:11 AM

612 Unit 7 Fractions and Their Uses; Chance and Probability

Math Boxes LESSON

7�8

Date Time

4. ∠ART is an acute (acute or

obtuse) angle.

The measure of ∠ART is

40 ° .

2. A bag contains

8 blue blocks,

2 red blocks,

1 green block, and

4 orange blocks.

You put your hand in the bag and, without

looking, pull out a block. About what

fraction of the time would you expect to

get a red block?

2 __ 15

3. Use pattern blocks to help you solve

these problems.

a. 1 _ 3 + 1 _

3 =

b. 2 _ 6 + 2

_ 3 =

c. 5

_ 6 - 1 _ 6 =

d. 4 _ 6 - 1

_ 2 =

51

55–57

130

93 142143

45

RT

A

5. There are 252 pages in the book Ming is

reading for his book report. He has two

weeks to read the book. About how many

pages should he read each day?

18 pages

6. Tell if each of these is closest to 1 inch,

1 foot, or 1 yard.

a. the height of the door 1 yard b. the width of your journal

c. the length of

your largest toe

d. the length of your shoe 1 foot

1 inch

1 foot

6 _ 6 ,

3

_ 3 , or 1

4 _ 6 , or 2 _

3

1 _ 6

2 _ 3

1. Complete the name-collection box.

4 _ 5

3 _ 5 + 1 _

5

0.8

8 __ 10

9 __ 10 - 1 __

10

80%

Sample answers:

185-218_EMCS_S_MJ2_G4_U07_576426.indd 204 1/27/11 10:51 AM

Math Journal 2, p. 204

Student Page

STUDY LINK

7�8 Fractions and Decimals

61

Name Date Time

Write 3 equivalent fractions for each decimal.

Example:

0.8

1. 0.20

2. 0.6

3. 0.50

4. 0.75

Write an equivalent decimal for each fraction.

5. 3

_ 10

6. 63

_ 100

7. 7

_ 10

8. 2

_ 5

9. Shade more than 53

_ 100

of the square and less than

8

_ 10

of the square. Write the value of the shaded part

as a decimal and a fraction.

Decimal:

Fraction:

10. Shade more than 11

_ 100

of the square and less than

1

_ 4 of the square. Write the value of the shaded part

as a decimal and a fraction.

Decimal:

Fraction:

Sample answers:

0.3 0.63 0.7 0.4

0.70Sample answer:

Sample answer:0.2

11. = 78 ∗ 9 12. 461 ∗ 7 = 13. = 39 ∗ 259753,227702

Practice

8 _ 10

4 _ 5

80 _ 100

2

_ 10 1

_ 5 20

_ 100

6

_ 10 3

_ 5 60

_ 100

5

_ 10

1

_ 2 50

_ 100

6

_ 8 3

_ 4 75

_ 100

2

_ 10

70

_ 100

203-246_EMCS_B_MM_G4_U07_576965.indd 226 1/25/11 9:58 AM

Math Masters, p. 226

Study Link Master

� Renaming Fractions as WHOLE-CLASS ACTIVITY

Decimals with a Calculator(Math Journal 2, p. 203)

Use Problem 7 on journal page 203 to model renaming fractions as decimals on a calculator.

For the TI-15:

� Enter the fraction 1 _ 4 (press 1 n 4 dd ).

� Then press F D . 0.25

For the Casio fx-55:

� Enter the fraction 1 _ 4 (press 1 4).

� Then press . 0.25

Use Problem 8 to model renaming a decimal as a fraction.

For the TI-15:

� Enter the decimal 0.75, then press F D. 75 _ 100

For the Casio fx-55:

� Enter the decimal 0.75, then press . 3 _ 4

� Discussing Fractions and WHOLE-CLASSDISCUSSION

Division(Student Reference Book, p. 46)

Read and discuss “Fractions and Division” on page 46 of the Student Reference Book. Have students apply their understanding of division to equal-sharing division problems. For example:

� Nina and her mother baked 4 dozen cookies for the book club meeting. The club has 8 members. How many cookies are there for each member?

Four dozen equals 4 ∗ 12, or 48. The number models 48/8 = 6, 48 ÷ 8 = 6, and 48 _ 8 = 6 fit this problem. The first and second number models suggest “dealing out” the 48 cookies to the 8 club members. Each member would get 6 cookies. The third number model, 48 _ 8 = 6, suggests dividing each cookie into eighths and giving 1 _ 8 of every cookie to each person. Each person would end up with 48 eighths. If the 48 eighths were reassembled, they would be equivalent to 6 cookies.

NOTE 48

_

8 is called an improper fraction because the numerator is greater than

the denominator. Improper fractions have numerators that are greater than or

equal to their denominators.

Also discuss problems in which the divisor is greater than the dividend. For example:

� Adam ordered 3 pizzas for a party. There will be 5 people at the party. How much pizza is there for each person?

610-614_EMCS_T_TLG1_U07_L08_576906.indd 612610-614_EMCS_T_TLG1_U07_L08_576906.indd 612 1/27/11 3:39 PM1/27/11 3:39 PM

Lesson 7�8 613

Name Date Time

LESSON

7�8 Designing a Baseball Cap Rack

Karen plans to design and construct two identical horizontal racks to display her

baseball cap collection. She has 12 different caps to hang on pegs. Karen’s

sister suggested that she add extra pegs for caps she may get in the future.

Karen measured the width of some caps and decided that the pegs need to be

2 decimeters ( 2

_ 10

meter) apart. Also, in order to fit on her wall, each rack cannot

be more than 160 centimeters long.

Help Karen design one of the identical racks. Use metric units. Fill in the blanks

below as you create the design. Sample answers are given.

1. Each of Karen’s racks will have 8 pegs for hats.

2. The total length of the rack will be 160 centimeters.

3. The first peg will be 10 centimeters from the edge of the rack.

4. In the space below, draw a rough sketch of the rack. Include the measurements

in your sketch.

2 dm10 cm

160 cm

5. Write a fraction addition number sentence to show the total length of the rack.

Sample answer: 10

_ 100 + 2 _ 10 + 2 _ 10 + 2 _ 10 + 2 _ 10 + 2 _ 10 + 2 _ 10 + 2 _ 10 +

10

_ 100 = 160

_ 100 m, or 160 cm

6. Could there be 9 pegs on the rack? Explain your answer.

No. Nine hats would require about 200 cm, and the rack can

only be 160 cm long.

227A-227B_EMCS_B_MM_G4_U07_576965.indd 227A 3/3/11 10:44 AM

Math Masters, p. 227A

Teaching Master

Name Date Time

Designing a Baseball Cap Rack continuedLESSON

7�8

Use your answers to Problems 1 and 2 on Math Masters, page 227A to fill in

the blanks in the sentence below. Sample answers:

Each rack is 160 centimeters long and has 8 pegs.

At the lumberyard, Karen discovered she could spend less if she was willing to

glue leftover pieces of wood together instead of using one long piece. She

measured several boards and wrote down the lengths:

7

_ 10

meter 85

_ 100

meter

35

_ 100

meter 3

_ 10

meter

20

_ 100

meter 9

_ 10

meter

8

_ 10

meter 55

_ 100

meter

75

_ 100

meter 15

_ 100

meter

7. Can Karen use these pieces to create two racks of the length you planned?

Explain why or why not. Show your work.

Pegs come in two different packages:

5-pack for $3.79 or 2-pack for $1.99

8. Explain how Karen can purchase the pegs for her racks, spending as little

money as possible.

Karen needs 16 pegs. She should buy three 5-packs and

one 2-pack for $13.36 because this is cheaper than

buying two 5-packs and three 2-packs for $13.55.

Yes. Rack one: 7

_ 10 meter and

9

_ 10 meter;

7

_ 10 +

9

_ 10 =

16

_ 10 m,

or 160 cm

Rack two: 75

_ 100 meter,

55

_ 100 meter, and

3

_ 10 meter;

75

_ 100 +

55

_ 100 +

3

_ 10 =

160

_ 100 m, or 160 cm

Sample answers are given.

227A-227B_EMCS_B_MM_G4_U07_576965.indd 227B 3/23/11 12:43 PM

Math Masters, p. 227B

Teaching Master

Point out that this problem and the cookie problem are both about sharing. The main difference is that in this problem, each share is less than one whole pizza. Draw 3 pizzas on the board or on the overhead transparency, and divide each one into fifths for the 5 people. If Adam’s guests are named Bob, Charles, Darryl, and Ed, the pizzas could be shared in the following way:

A BC

DE

A BC

DE

A BC

DE

Help students see how the number model 3 / 5 = 3 _ 5 fits this problem. The left side, 3 / 5, suggests dividing 3 pizzas among 5 people. The right side, 3 _ 5 , tells how much each person would get.

Explain that in high school and beyond, the symbol ÷ is almost never used for division. Division is usually shown with a slash (/) or a fraction bar (—).

2 Ongoing Learning & Practice

� Math Boxes 7�8 INDEPENDENTACTIVITY

(Math Journal 2, p. 204)

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

Writing/Reasoning Have students write a response to the following: Explain how you solved Problem 2. Sample answer: There are 15 blocks in the bag, and 2 of them are red. So the chance of getting a red block is 2 _ 15 .

� Study Link 7�8 INDEPENDENTACTIVITY

(Math Masters, p. 226)

Home Connection Students rename decimals as fractions and fractions as decimals. They color fractional parts of a base-10 grid and write the value of the shaded part as a decimal and a fraction.

610-614_EMCS_T_TLG2_G4_U07_L08_576906.indd 613610-614_EMCS_T_TLG2_G4_U07_L08_576906.indd 613 3/24/11 2:39 PM3/24/11 2:39 PM

614 Unit 7 Fractions and Their Uses; Chance and Probability

LESSON

7�8

Name Date Time

Fraction, Decimal, and Percent Grids

227

Sample answers:Fill in the missing numbers. Shade the grids.

1. 2.

Fraction: 1

_ 8 = Fraction:

1

_ 3 =

100 100

Decimal: 0.125 Decimal: 0.333

Percent: 12.5 % Percent: 33

1

_ 3 %

3. 4.

Fraction: 1

_ 6 = Fraction:

4

_ 6 =

100 100

Decimal: 0.166 Decimal: 0.666

Percent: 16

4

_ 6 % Percent: 66

4

_ 6 %

61 62

16 4 _ 6 66 4 _

6

33 1 _ 3 12 1 _

2

203-246_EMCS_B_MM_G4_U07_576965.indd 227 1/25/11 9:58 AM

Math Masters, p. 227

Teaching Master

3 Differentiation Options

READINESS INDEPENDENTACTIVITY

� Creating Base-10 Block Designs 30+ Min

(Math Masters, p. 442)

To explore representing fractions and decimals on a base-10 grid, have students make a design on a base-10 block flat with cubes and then copy the design onto one of the grids shown on Math Masters, page 442. Students determine how much of the flat is covered by their design and express this number as a decimal and a fraction. (See margin.) Students may choose to exchange as many cubes as possible for longs, which would result in a certain number of longs (tenths) and cubes (hundredths).

ENRICHMENT PARTNER ACTIVITY

� Finding Fractions, Decimals, 15–30 Min

and Percents on Grids(Math Masters, p. 227)

To further investigate fraction, decimal, and percent equivalencies, have students shade a base-10 grid to show 1 _ 8 , 1 _ 3 , 1 _ 6 , and 4 _ 6 . Encourage students to discuss patterns they see and strategies they used. Ask: How could you have found the percent equivalent for 4 _ 6 without shading the grid? Sample answer: Use the answer for 1 _ 6 and multiply by 4.

ENRICHMENT PARTNER ACTIVITY

� Designing a Baseball Cap Rack 15–30 Min

(Math Masters, pp. 227A and 227B)

To further investigate the relationships among fractions with denominators of 10; 100; or 1,000, have students design two identical racks to display a baseball cap collection. Encourage students to work with a partner to complete the activity.

EXTRA PRACTICE SMALL-GROUP ACTIVITY

� Taking a 50-Facts Test 5–15 Min(Math Masters, pp. 412, 414, and 416)

See Lesson 3-4 for details regarding the administration of the 50-facts test and the recording and graphing of individual and optional class results.

Decimal:

Fraction:

0.24 24100

610-614_EMCS_T_TLG2_G4_U07_L08_576906.indd 614610-614_EMCS_T_TLG2_G4_U07_L08_576906.indd 614 3/3/11 3:15 PM3/3/11 3:15 PM

Copyrig

ht ©

Wrig

ht G

roup/M

cG

raw

-Hill

Name Date Time

227A

LESSON

7�8 Designing a Baseball Cap Rack

Karen plans to design and construct two identical horizontal racks to display her

baseball cap collection. She has 12 different caps to hang on pegs. Karen’s

sister suggested that she add extra pegs for caps she may get in the future.

Karen measured the width of some caps and decided that the pegs need to be

2 decimeters ( 2

_ 10

meter) apart. Also, in order to fit on her wall, each rack cannot

be more than 160 centimeters long.

Help Karen design one of the identical racks. Use metric units. Fill in the blanks

below as you create the design.

1. Each of Karen’s racks will have pegs for hats.

2. The total length of the rack will be centimeters.

3. The first peg will be centimeters from the edge of the rack.

4. In the space below, draw a rough sketch of the rack. Include the measurements

in your sketch.

5. Write a fraction addition number sentence to show the total length of the rack.

6. Could there be 9 pegs on the rack? Explain your answer.

227A-227B_EMCS_B_MM_G4_U07_576965.indd 227A227A-227B_EMCS_B_MM_G4_U07_576965.indd 227A 3/3/11 10:44 AM3/3/11 10:44 AM

Copyright

© W

right

Gro

up/M

cG

raw

-Hill

Name Date Time

227B

Designing a Baseball Cap Rack continuedLESSON

7�8

Use your answers to Problems 1 and 2 on Math Masters, page 227A to fill in

the blanks in the sentence below.

Each rack is centimeters long and has pegs.

At the lumberyard, Karen discovered she could spend less if she was willing to

glue leftover pieces of wood together instead of using one long piece. She

measured several boards and wrote down the lengths:

7

_ 10

meter 85

_ 100

meter

35

_ 100

meter 3

_ 10

meter

20

_ 100

meter 9

_ 10

meter

8

_ 10

meter 55

_ 100

meter

75

_ 100

meter 15

_ 100

meter

7. Can Karen use these pieces to create two racks of the length you planned?

Explain why or why not. Show your work.

Pegs come in two different packages:

5-pack for $3.79 or 2-pack for $1.99

8. Explain how Karen can purchase the pegs for her racks, spending as little

money as possible.

227A-227B_EMCS_B_MM_G4_U07_576965.indd 227B227A-227B_EMCS_B_MM_G4_U07_576965.indd 227B 3/23/11 12:43 PM3/23/11 12:43 PM