Teaching the Lesson materials

Key ActivitiesStudents rename fractions as decimals and decimals as fractions. They also explore the relationship between fractions and division.

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 fraction notation and equal sharing to solve division problems.

[Operations and Computation Goal 4]

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

Ongoing Learning & Practice materialsStudents take a 50-facts test. They use a line graph to record individual and class scores. Then students find the median and calculate the mean of class scores.

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

Differentiation Options materials

Students make a design with base-10blocks, copy the design on a grid, and writea decimal and a fraction to describe whatpart of the grid is covered by the blocks.

Students color a 10-by-10 grid to representfractions and find the percent and decimal equivalents.

� Teaching Masters (Math Masters,p. 227)

� Teaching Aid Master (Math Masters,p. 442)

� base-10 blocks

ENRICHMENTREADINESS

3

� Math Journal 2, p. 204� Study Link Master (Math Masters,

p. 226)� Teaching Aid Masters (Math

Masters, pp. 412, 414, and 416)� pen or colored pencil

2

� Math Journal 2, pp. 203, 342, and343

� Student Reference Book, p. 46� Study Link 7�7 � Teaching Aid Master (Math

Masters, p. 426; optional)� Transparency (Math Masters,

p. 426)� base-10 blocks � calculator� slate� overhead base-10 blocks (optional)

1

Lesson 7�8 609

Objectives To provide experience with renaming fractions

as decimals and decimals as fractions; and to develop an

understanding of the relationship between fractions and division.

Technology Assessment Management System

Journal page 203, Problems 1–4,7, and 8See the iTLG.

610 Unit 7 Fractions and Their Uses; Chance and Probability

Getting Started

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

Sample answers:

�12� �

24�, �

36�

�14� �

28�, �1

32�

�13� �

26�, �

39�

�15� �1

20�, �1

35�

�15000� �1

50�, �

2550�

�34� �

68�, �1

92�

�69� �

23�, �

1128�

�58� �

1106�, �

5800�

�35� �1

60�, �1

95�

Math MessageWrite the following fractions as decimals:

�110� �1

3020� �1

70� �1

900�

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

Adjusting the Activity

� Math Message Follow-Up(Math Masters, p. 426)

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

Color or cover one column of the top grid.● What fractional part of the square is this? �1

10�

● How would you write �110� as a decimal? 0.1

Repeat with other fractions in tenths, including �130� and �1

70�.

ELL

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

110, or 0.1

WHOLE-CLASS

DISCUSSION

1 Teaching the Lesson

Name Date Time

Base-10 Grids

Math Masters, p. 426

Teaching Aid Master

Links to the Future

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

● What fractional part of the square is this? �1100�

● How would you write �1100� as a decimal? 0.01

Repeat with other fractions in hundredths, including �13020� and �1

900�.

Also, give students practice converting decimals into fractions; forexample, 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 convertingbetween 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 and Decimals as Fractions(Math Journal 2, pp. 203, 342, and 343; Math Masters, p. 426)

Students complete journal page 203. Discuss answers, using atransparency 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 forFractions table on journal pages 342 and 343.

Ongoing Assessment:Recognizing Student Achievement

Use journal page 203, Problems 1–4, 7, and 8 to assess students’ ability torename tenths and hundredths as decimals with the assistance of a visualmodel. Students are making adequate progress if they are able to name thenumber of tenths or hundredths shaded on the grid as a fraction and rename thefraction as a decimal. Some students may be able to solve Problems 5 and 6 onjournal page 203, which do not include a visual prompt.

[Number and Numeration Goal 5]

Journal page 203

Problems

1–4, 7, and 8�

INDEPENDENT

ACTIVITY

1100, or 0.01

�

Whole

large square

203

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

612 Unit 7 Fractions and Their Uses; Chance and Probability

� Renaming Fractions as Decimals with a Calculator(Math Journal 2, p. 203)

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

For the TI-15:

� Enter the fraction �14� (press 1 4 d .).

� Then press . 0.25

For the Casio fx-55:

� Enter the fraction �14� (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 . �17050�

For the Casio fx-55:

� Enter the decimal 0.75, then press . �34�

� Discussing Fractions and Division(Student Reference Book, p. 46)

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

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

Four dozen equals 4 � 12, or 48. The number models 48/8 � 6, 48 � 8 � 6, and �

488� � 6 fit this problem. The first and second

number models suggest “dealing out” the 48 cookies to the 8 clubmembers. Each member would get 6 cookies. The third numbermodel, �

488� � 6, suggests dividing each cookie into eighths and

giving �18� of every cookie to each person. Each person would end up

with 48 eighths. If the 48 eighths were reassembled, they wouldbe equivalent to 6 cookies.

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 atthe party. How much pizza is there for each person?

WHOLE-CLASS

DISCUSSION

F D

F D

dn

WHOLE-CLASS

ACTIVITY

Did You Know?The word fraction isderived from the Latinword frangere, whichmeans “to break.”Fractions are sometimescalled “broken numbers.”

Fractions and DivisionDivision problems can be written using a slash / instead of thedivision symbol �. For example, 21 � 3 can be written 21 / 3.

Division problems can also be written as fractions. One of themany uses of fractions is to show divisions. The example belowshows that 21 � 3 can be written as the fraction �

231�.

Fractions

ExampleExample 21 � 3 � 7 Show that �231� � 7 also.

This is the whole, or ONE. This is the whole after dividing it into 3 equal parts. Each part is �

13� of the whole.

The picture below shows that 21 thirds make 7 wholes. So, �231� � 7.

You can rename any fraction by dividing on your calculator. To rename �

231�, think of it as a division problem and divide:

Press 21 3 . The answer in the display will show 7,which is another name for �

231�.

21 � 3 � 21 / 3

and

21 � 3 � �231�

Fractions less than 1 can also be thought of as divisions.

ExampleExample Show that 3 � 4 � �34�.

Think of 3 � 4 as an equal-sharing problem. Suppose 4 friends want to share 3 oranges. They could cut or divide each orange into 4 equal parts.

Each person gets �34� of an orange. So, 3 � 4 � �

34�.

Student Reference Book, p. 46

Student Page

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

Help students see how the number model 3 / 5 � �35� fits this

problem. The left side, 3 / 5, suggests dividing 3 pizzas among 5 people. The right side, �

35�, tells how much each person would get.

Explain that in high school and beyond, the symbol � is almostnever used for division. Division is usually shown with a slash (/)or a fraction bar (—).

� Taking a 50-Facts Test(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 andclass results.

� Math Boxes 7�8(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 6previews 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 �1

25�.

� Study Link 7�8(Math Masters, p. 226)

Home Connection Students rename decimals as fractionsand 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.

INDEPENDENT

ACTIVITY

INDEPENDENT

ACTIVITY

WHOLE-CLASS

ACTIVITY

2 Ongoing Learning & Practice

A BC

DE

A BC

DE

A BC

DE

204

Math Boxes LESSON

7�8

Date Time

4. �ART is an (acute orobtuse) angle.

The measure of �ART is °.40

acute

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, withoutlooking, pull out a block. About whatfraction of the time would you expect toget a red block?

�125�

3. Use pattern blocks to help you solve these problems.

a. �13� � �

13� �

b. �26� � �

23� �

c. �56� � �

16� �

d. �46� � �

12� �

51

55–57

130

93 142143

45

R T

A

5. There are 252 pages in the book Ming isreading for his book report. He has twoweeks to read the book. About how manypages should he read each day?

pages18

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

a. the height of the door

b. the width of your journal

c. the length of your largest toe

d. the length of your shoe 1 foot

1 yard

1 inch1 foot

�66�, �

33�, or 1

�46�, or �

23�

�16�

�23�

1. Complete the name-collection box.

�45

�

�35� � �

15�

0.8�180�

�190� � �1

10�

80%

Sampleanswers:

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. �130� 6. �1

6030� 7. �1

70� 8. �

25�

9. Shade more than �15030� of the square and less than

�180� of the square. Write the value of the shaded part

as a decimal and a fraction.

Decimal:

Fraction:

10. Shade more than �11010� of the square and less than

�14� of the square. Write the value of the shaded part as a decimal and a fraction.

Decimal:

Fraction:

�180� �

45� �1

8000�

Sample answers:

�68� �1

7050�

�15000�

�16000�

�12000�

0.3 0.63 0.7 0.4

�17000�

0.70Sample answer:

Sample answer:�120�

0.2

11. � 78 º 9 12. 461 º 7 � 13. � 39 º 259753,227702Practice

�150�

�15�

�35�

�12�

�34�

�160�

�120�

Math Masters, p. 226

Study Link Master

Lesson 7�8 613

614 Unit 7 Fractions and Their Uses; Chance and Probability

Name Date Time

Decimal:

Fraction:

Decimal:

Fraction:

Decimal:

Fraction:

Decimal:

Fraction:

Base-10 Block Designs

Math Masters, p. 442

Teaching Aid Master

� Creating Base-10 Block Designs(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 cubesand then copy the design onto one of the grids shown on MathMasters, page 442. Students determine how much of the flat iscovered by their design and express this number as a decimal anda fraction. Students may choose to exchange as many cubes aspossible for longs, which would result in a certain number of longs(tenths) and cubes (hundredths).

� Finding Fractions, Decimals,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�18�, �

13�, �

16�, and �

46�. Encourage students to discuss patterns they

see and strategies they used. Ask: How could you have found the percent equivalent for �

46� without shading the grid? Sample

answer: Use the answer for �16� and multiply by 4.

15–30 Min

PARTNER

ACTIVITYENRICHMENT

Decimal:

Fraction:

0.2424100

30+ Min

INDEPENDENT

ACTIVITYREADINESS

3 Differentiation Options

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: �18� � Fraction: �

13� �

100 100

Decimal: Decimal:

Percent: % Percent: %

3. 4.

Fraction: �16� � Fraction: �

46� �

100 100

Decimal: Decimal:

Percent: % Percent: %

0.6660.166

12.50.3330.125

61 62

12�12� 33�

13�

16�46� 66�

46�

33�13�

16�46� 66�46�

Math Masters, p. 227

Teaching Master