Draw the key on your calculator that you would use to do each of the functions. ..... The winning pole-vault height given above was rounded to the nea...

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LESSON

Comparing Fractions

8 1

Math Message Write or . Be prepared to explain how you decided on each answer. 3 1. 5

4 5

4 2. 5

4 7

5 3. 9

3 7

7 4. 8

6 7

means is less than. means is more than.

Equivalent Fractions Cross out the fraction in each list that is not equivalent to the other fractions. 4 6 8 1 2 6. 4 , 8 , 20 , 24 , 32

2 4 18 20 5. 3 , 6 , 24 , 30

6 9 3 15 7. 5 , 10 , 20 , 25

Write or in each box. 3 8. 5

10 15

6 9. 8

16 24

15 10. 24

5 8

6 11. 14

2 7

means is not equal to.

Give three equivalent fractions for each fraction. 6 12. 9

,

7 14. 10

50 13. 100

, ,

,

15 15. 18

,

,

,

,

Fill in the missing number. 3 16. 4

19.

2 22. 5

36

3 17. 5

9

24 18

9 20. 12

6

23.

15

18.

20

5

21.

4

3 5

4 24. 9

2

16

8 1 0

16

Write or . 2 25. 5

248

5 10

3 26. 4

5 6

3 27. 8

2 7

3 28. 5

4 7

Date

Time

LESSON

Fraction Review

8 1

1 4

1. a.

Shade of the fraction stick.

b.

Use the fraction stick to 1 find equivalent fractions: 4

1 c. 4

2. a.

4.

16

1

b.

Is this more or less than 2 ?

c.

Is this more or less than 4 ?

1

1 8 1

Joe had 2 granola bars. He ate 1 2 bars. a.

Shade the part that he ate.

b.

Write the part he ate as a decimal.

Circle the decimal that is equivalent to each fraction. Use your calculator to help you. 1 a. 4

1 b. 10 2 c. 5

5.

3 Shade 8 of the fraction stick.

3 d. 8

3.

1 4

8

0.5

0.14

0.25

1.4

1.10

0.1

0.010

0.50

0.4

0.25

2.5

0.2

Lucy had 16 beads. Half the beads were red. One fourth were blue. The rest were white. a.

1 1 Color 2 of the beads red and 4 blue.

b.

What fraction of the beads are white?

c.

Lucy put away all the white beads. What fraction of the remaining beads are red?

249

Date

Time

LESSON

Math Boxes

8 1

Make a circle graph of the survey results.

1.

title

Favorite After-School Activity Activity

Students

Eat Snack

18%

Visit Friends

35%

Watch TV

22%

Read

10%

Play Outside

15%

126 127

Write each numeral in number-and-word notation.

2.

a. b. c. d.

3.

43,000,000 607,000

Multiply. 3 a. 8

5 b. 7

6 11

3 4

2 5

7 6

4 5

c.

1 3

d.

2 1

3,000,000,000 72,000

7 9

26 e. 4

8 6

4

Complete the “What’s My Rule?” table and state the rule. in

Rule

5.

out

Find the area of the rectangle. Area b º h

3 8

14 cm

40 8 cm

4.

76–78

1 2

50 4

20

Area: (unit)

231 232

250

189

Date

Time

LESSON

Adding Fractions

8 2

Math Message Add. Write the sums in simplest form. 3 1. 5

1 5

3 2. 8

1 8

3 4. 7

5 7

7 5. 10

1 7. 6

2 3

2 8. 3

7 10

2 5

2 3. 3

2 3

2 3

5 6. 9

5 9. 6

7 9 5 8

Adding Mixed Numbers Add. Write each sum as a whole number or mixed number. 3 5

1

10.

1 2

1

11.

1 5

3 4

1 2

1

1 4

2

12.

3

Fill in the missing numbers. 12 7

13.

5 6

16.

4 5

5 3

5

3

8 5

14.

7

17.

12 13

11 6

3 5

6

5 4

15.

2 3

18.

9 10

21.

3

13 10

4

10

Add. Write each sum as a mixed number in simplest form. 19.

2 3

3 2 3

5

20.

6 7

4 4 7

2

4 9 8 9

6

251

Date

Time

LESSON

Adding Mixed Numbers

8 2

continued

To add mixed numbers in which the fractions do not have the same denominator, you must first rename one or both fractions so that both fractions have a common denominator. 3 5

2 3

Example: 2 4 ? 3 5

2 3

Find a common denominator. The QCD of and is 5 3 15. Write the problem in vertical form, and rename the fractions. 3 5

2 4 3

∑

Add. 19 15

9 15

2

2

Rename the sum. 6 6

0 4 1

15 9 6 1 15 15 4 15 15

4 15

4 15

6 1 7

Add. Write each sum as a mixed number in simplest form. Show your work. 1 3

1 4

2.

5 2

1 3

4 9

4.

1 4

1 4

5 6

6.

3 3

1.

2 3

3.

6 2

5.

7 2

252

1 2

2 5

1 2

3 4

5 6

3 4

Date

Time

LESSON

Math Boxes

8 2

1.

3.

Add.

2.

1 a. 4

2 4

3 b. 8

1 4

1 c. 2

2 d. 3

1 6

2 e. 6

Use the patterns to fill in the missing numbers. a.

1, 2, 4,

,

b.

5, 14, 23,

,

c.

4, 34, 64,

,

d.

20, 34, 48,

e.

100, 152, 204,

1 8

2 6

68

3

The school band practiced 2 hours on 4 2 Saturday and 3 hours on Sunday. Was 3 the band’s total practice time more or less than 6 hours?

4.

Explain.

, ,

Make each sentence true by inserting parentheses. a.

18 11 3 10

b.

18 11 3 4

c.

14 7 5 1 13

d.

14 7 5 1 1

e.

14 7 5 1 3

71

5.

Solve. 5 a. 9

Solution

222

6.

x 18

Circle the congruent line segments. a.

8 b. 25

40 y

b.

6 c. 14

w 49

c.

28 d. z

7 9

d.

44 e. 77

4 v

230

108 109

155

253

Date

Time

LESSON

Subtracting Mixed Numbers

8 3

Math Message Subtract. 3 4 1 1 4

3

1.

2.

4 5

4 2

Renaming and Subtracting Mixed Numbers Fill in the missing numbers. 1 4

4.

5 4

6.

3

5 6

4

6

5.

65

7.

8

3

7 9

16 9

Subtract. Write your answers in simplest form. Show your work. 8.

1 3

8

3 5

5 2

1 4

3 4

11.

4 3

2 9

5 9

13.

10 5

10.

7 3

12.

6 4

254

9.

5 8

7 8

3 10

7 10

5 6 2 2 6

7

3.

Date LESSON

8 3

Materials

Time

Mixed-Number Spin Math Masters, p. 488 large paper clip

Players

2

Directions 1.

Each player writes his or her name in one of the boxes below.

2.

Take turns spinning. When it is your turn, write the fraction or mixed number you spin in one of the blanks below your name.

3.

The first player to complete 10 true sentences is the winner.

Name

Name

3

3

3

3

1

1

1 2

1

1

1

1

1

2

2

3

3

1

1

1 2

1

3

3

2

2

2

2

255

Date

Time

LESSON

Math Boxes

8 3

Make a circle graph of the survey results.

1.

title

Time Spent on Homework Time

Percent of Students

0–29 minutes

25%

30–59 minutes

48%

60–89 minutes

10%

90–119 minutes

12%

2 hours or more

5%

126 127

Write each numeral in number-and-word notation.

2.

a. b. c. d.

3.

Multiply. 8 a. 11

56,000,000

5 6

7 8

3 4

9 5

b.

1 3

c.

2 2

423,000 18,000,000,000

24 d. 5

9,500,000

9 10

e.

1 7

7 3

1 6

5 4

4

Complete the “What’s My Rule?” table and state the rule. in

Rule

5.

out

Find the area of the rectangle. Area b º h

48 40

5

1

1 8

12 m 6m

4.

76 78

0 16

2

Area: (unit)

231 232

256

189

Date

Time

LESSON

Exploring Fraction-Operation Keys

8 4

Some calculators let you enter, rename, and perform operations with fractions.

1.

Draw the key on your calculator that you would use to do each of the functions. Function of Key

Key

Give the answer to an entered operation or function. Enter the whole number part of a mixed number. Enter the numerator of a fraction. Enter the denominator of a fraction. Convert between fractions greater than 1 and mixed numbers. Simplify a fraction. Use your calculator to solve. 2 9

2 5

16 3

1 7

2.

5 6

3.

4 3

4.

26,342

2 7

5.

冢冣

6.

In any row, column, or diagonal of this puzzle, there are groups of fractions with a sum of 1. Find as many as you can, and write the number sentences on another piece of paper. The first one has been done for you.

Example: Number Sentence 2 6

2 8

1 6

1 4

1

7 2 8

14

2 6

1 6

3 6

1 4

2 5

5 6

2 4

2 8

2 10

2 8

2 4

1 2

3 6

1 4

1 6

1 4

2 3

3 4

1 6

4 8

1 4

1 4

1 6

1 4

1 3

2 4

2 10

2 6

2 3

1 3

5 12

1 4

1 5

3 6

1 4

3 8

257

Date

Time

LESSON

Math Boxes

8 4

1.

Add.

2.

1 a. 4

1 2

1 b. 4

4 c. 6

1 d. 2

1 e. 6

5 8 1 3 1 3 1 2

Use the patterns to fill in the missing numbers. a.

2.1, 4.2, 8.4,

,

b.

50, 25, 12.5,

,

c.

3.4, 10.2, 30.6,

d.

1.5, 7.5, 37.5,

e.

1, 4, 9,

, , ,

68

3.

3

Max worked for 3 hours on Monday and 4 1 6 hours on Tuesday. Did he work more 2 or less than 10 hours?

230

4.

Make each sentence true by inserting parentheses. a.

100 15 10 4

b.

4 24 / 4 2

c.

8 24 / 4 2

d.

10 4 / 2 3 24

e.

10 4 / 2 3 1

Explain.

222

71

5.

Solve.

Solution

6.

45 50

m a. 10

56 b. 64

k c. 48

4 d. 30

2 e. 18

a.

b.

c.

d.

7 n 3 8

12 p

a 180

108 109

258

Circle the congruent angles.

155

Date

Time

LESSON

Number-Line Models

8 5

Math Message

0

1

2

3

Use the number line above to help you answer Problems 1–10. 1

1.

What is 2 of 3?

3.

What is 4 of 2?

5.

What is 2 of 2 ?

7.

What is 2 of 4 ?

9.

What is 4 of 4 ?

11.

3 1

1

1

3

1

1

1

2.

What is 4 of 2?

4.

What is 3 of 3?

6.

What is 2 of 4 ?

8.

What is 4 of 2 ?

10.

What is 2 of 8 ?

1 1

1

1

1

1

3

Explain how you figured out the answer to Problem 10.

Solve. 2 12. 3

of 12?

13.

2 5

of 25?

2 14. 3

of 90?

15.

3 4

of 16?

3 16. 4

of 28?

17.

3 5

of 100?

2 18. 3

of 18?

19.

3 4

of 100?

3 20. 5

of 50?

21.

5 8

of 64?

259

Date

Time

LESSON

Paper-Folding Problems

8 5

Record your work for the four fraction problems you solved by paper folding. Sketch the folds and shading. Write an X on the parts that show the answer. 1 1. 2

of is

1 3. 4

of is

260

1 2

2 3

.

.

2 2. 3

of is

1 2

3 4. 4

of is

1 2

.

.

Date

Time

LESSON

8 5

Paper-Folding Problems

continued

Solve these problems by paper folding. Sketch the folds and shading. Write an X on the parts that show the answer. 1 5. 3

of is

3 4

.

1 6. 8

of is

1 2

.

5 7. 8

of is

1 2

.

3 8. 4

of is

3 4

.

261

Date LESSON

8 5

Time

Fraction Spin

Materials

Math Masters, p. 471 large paper clip

Players

2

Directions 1.

Each player writes his or her name in one of the boxes below.

2.

Take turns spinning. When it is your turn, write the fraction you spin in one of the blanks below your name.

3.

The first player to complete 10 true sentences is the winner.

Name

262

Name

1

1

1

1

1 2

1 2

1

1

1 4

1 4

1

1

1 4

1 4

3 4

3 4

1 2 1 2

1 4 1 4

1 4 1 4 3 4 3 4

Date

Time

LESSON

Math Boxes

8 5

1.

Complete.

2.

a. 2 3

— — 24 36

b. 1 8

a.

16 (3 5) 18

— — 24 32

b.

(4 2) 5 30

c. 2 5

12 — —

c.

100 (25 25) 5 7

d. 1 6

d.

15 4 3 2 35

e.

(40 22) 6 6

25 3

—

4

—

108 109

3.

4.

Write true or false for each number sentence.

Use the grid on the right to locate the following objects on the map. The first one has been done for you.

222 223

6 5

D4

a.

Fifth grader

b.

Boat

3

c.

Car

2

d.

House

1

e.

Tree

4

A

Circle any triangles that look like equilateral triangles.

5.

144

C

D

E

F

208

The soup can and cereal box below represent geometric solids. Name each of these solids. a.

Write a definition of an equilateral triangle.

B

b.

CEREAL

147–149

263

Date

Time

LESSON

Fraction Multiplication

8 6

Math Message 1.

Use the rectangle at the right to sketch how you would fold paper 1 2 to help you find of . 3

1 3

3

2 3

What is of ?

2.

Use the rectangle at the right to sketch how you would fold paper 1 3 to help you find of . 4

1 4

5

3 5

What is of ?

3.

3 Rewrite 2 of using the multiplication symbol .

4.

Rewrite the following fraction-of-fraction problems using the multiplication symbol .

3

4

1 a. 4

of

1 3

4 b. 5

of

1 c. 6

of

1 4

3 d. 7

of

264

2 3

2 5

Date

Time

LESSON

8 6

1.

An Area Model for Fraction Multiplication 2 3

3 4

Use the rectangle at the right to find . 2 3

3 4

Your completed drawing in Problem 1 is called an area model. Use area models to complete the remaining problems. 2.

3.

2 3

1

3 4

5

5.

4.

2 5

6.

3 8

3 5

1 4

5 6

5 6

4 5

7.

1 2

5 8

Explain how you sketched and shaded the rectangle to solve Problem 7.

265

Date

Time

LESSON

An Algorithm for Fraction Multiplication

8 6

1.

Look carefully at the fractions on journal page 265. What is the relationship between the numerators and the denominators of the two fractions being multiplied and the numerator and the denominator of their product?

2.

Describe a way to multiply two fractions.

3.

Multiply the following fractions using the algorithm discussed in class. 1 a. 3

1 5

3 c. 10

4.

7 10

2 b. 3

1 3

5 d. 8

1 4

3 e. 8

5 6

2 f. 5

4 g. 5

2 5

4 h. 9

2 i. 4

4 8

3 j. 7

7 k. 9

2 6

2 l. 7

5 12 3 7 5 9

9 10

Girls are one-half of the fifth-grade class. Two-tenths of these girls have red hair. Red-haired girls are what fraction of the fifth-grade class?

266

Date

Time

LESSON

Math Boxes

8 6

1.

The digit in the hundreds place is a square number, and it is odd. The digit in the tens place is 1 more than the square root of 16. 1 The digit in the hundredths place is 0.1 larger than of the digit in the hundreds place. 1 0 30 The digit in the thousandths place is equivalent to . 5 The other digits are all 2s. . Write this number in expanded notation.

4

2.

Write 3 equivalent fractions for each number.

3.

1

Jon spent 24 hours reading in March and 4 1 15 hours reading in April. How many more 2 hours did he spend reading in March?

2 a. 5

4 b. 7

Number model:

1 c. 2

Answer:

40 d. 50

25 e. 75

71 72

59

4.

5.

Complete. 10 a. 100

10

8 b. 100

25

5 c. 20

1

10 d. 12

5

Use your Geometry Template to draw a trapezoid.

How does the trapezoid you’ve drawn differ from other quadrangles on the Geometry Template?

108 109

134–136

267

Date

Time

LESSON

A Blast from the Past

8 7

1.

From Kindergarten Everyday Mathematics: This slice of pizza is what fraction of the whole pizza?

2.

From First Grade Everyday Mathematics: Write a fraction in each part of the diagrams below. Then color the figures as directed. a.

b.

3 4

Color . 3.

c.

2 3

Color .

From Second Grade Everyday Mathematics: a.

b.

1 Color 4 of the beads.

4.

1 Color 8 of the beads.

From Third Grade Everyday Mathematics: 1 a. 2

5.

2 2

Color .

1 4

of

1 b. 8

1 2

of

From Fourth Grade Everyday Mathematics: 5 6

Cross out of the dimes.

268

1 c. 2

1 8

of

Date

Time

LESSON

Area Models

8 7

Draw an area model for each product. Then write the product as a fraction or as a mixed number. Example:

2 3

1 1. 3

4

1 2. 4

3

3.

2

4 , 3

or 1 13

3 5

2

3 4. 8

3

269

Date

Time

LESSON

Using the Fraction Multiplication Algorithm

8 7

An Algorithm for Fraction Multiplication a b

c d

ac bd

The denominator of the product is the product of the denominators, and the numerator of the product is the product of the numerators. 2 3

Example: 2 2 3

2 2 3 1 22 31 4 1 , or 1 3 3

2

2 1

Think of 2 as . Apply the algorithm. Calculate the numerator and denominator.

Use the fraction multiplication algorithm to calculate the following products. 3 1. 4

3 3. 10

5.

7 2. 8

6 5

Use the given rule to complete the table. in ( )

Rule

3 5

º

1 2

2 4 5 3 4

3

270

out ( )

3 4 5

4.

6

6.

What is the rule for the table below?

Rule

in ( ) out ( ) 2 3 3 4 7 8

3

2 6 3 8 7 16 1 1 2

Date

Time

LESSON

Math Boxes

8 7

1.

Complete. 1 a. 5

4

30

2 b. 3

10

9

5 c. 8

25

24

32

4 d. 7

3.

2.

42

A bird in C2.

b.

A fish in D6.

c.

A turtle in E3.

d.

A snake in F1.

a.

5 (6 3) (5 6) (5 3)

b.

(2 102) (1 101) (6 100) 2,160

1 c. 2

5 6

1 3

1 3

1 2

5 6

d.

16 (4 8 2) / 2 3

e.

106 1 billion

108 109

On the grid, draw each animal whose location is given below. a.

Write true or false for each number sentence.

6

222 223

Lake

5 4 3 2 1

e.

4.

A frog in F4.

208

A

Draw an isosceles triangle.

5.

B

C

D

E

F

The shapes below represent geometric solids. Name the solids.

Write a definition of an isosceles triangle.

a.

144

b.

147–149

271

Date

Time

LESSON

Review Converting Fractions to Mixed Numbers

8 8

Math Message You know that fractions larger than 1 can be written in several ways.

Whole Rule

Example:

hexagon

If a

is worth 1,

what is

worth? 5

5

5

The mixed-number name is 3 6 (3 6 means 3 6 ). 23

The fraction name is 6 . Think sixths:

5

5

23

3 6 , 3 6 , and 6 are different names for the same number. Write the following mixed numbers as fractions. 3

1.

2 5

3.

1 3

2

7

2.

4 8

4.

3 4

6

Write the following fractions as mixed or whole numbers. 7 5. 3

18 7. 4

6 6. 1

9 8. 3

Add. 7

9.

2 8

11.

3 5

272

3

3

10.

1 4

12.

1 6 2 3

Date

Time

LESSON

Multiplying Fractions and Mixed Numbers

8 8

Using Partial Products Example 1: 1

Example 2:

1

1

1

1

2 3 2 2 (2 3 ) (2 2 )

2

1

2

3 4 5 .(3 4 ) 5 2

6

22

4

3 5 . 5

2 2

1

1

1 4

1 3

2

2 3

1 3

1 1 2 6

1

1 5

2 1 2 5 . 20 1 0 3

1 10

5

5 6

Converting Mixed Numbers to Fractions Example 4:

Example 3: 1

1

7

5

2 3 2 2 3 2

1

2

13

2

3 4 5 4 5

35 5 6 5 6

6 3 26 20 1 2 0 1 10

Solve the following fraction and mixed-number multiplication problems. 1

1

3

1

1.

3 2 2 5

2.

10 4 2

3.

The back face of a calculator has an area of about

4.

The area of this sheet of notebook paper is about

in2. 5.

5

58 "

1

10 2 "

in2.

7 28 "

8"

The area of this computer disk is about

6. 5

36 "

in2. 7.

ACMECALC INC. Model# JETSciCalc Serial# 143

The area of this flag is about

1 32 "

1

2 3 yd

yd2.

3

3 5 yd

Is the flag’s area greater or less than that of your desk? 273

Date LESSON

8 8

Time

Track Records on the Moon and the Planets

Every moon and planet in our solar system pulls objects toward it with a force called gravity. 2

In a recent Olympic games, the winning high jump was 7 feet 8 inches, or 7 3 feet. The winning pole vault was 19 feet. Suppose that the Olympics were held on Earth’s Moon, or on Jupiter, Mars, or Venus. What height might we expect for a winning high jump or a winning pole vault? 1.

On the Moon, one could jump about 6 times as high as on Earth. What would be the height of the winning … high jump? About

2.

feet 3

pole vault? About

feet

pole vault? About

feet

1

On Venus, one could jump about 1 7 times as high as on Earth. What would be the height of the winning … feet

pole vault? About

feet

Is Jupiter’s pull of gravity stronger or weaker than Earth’s? Explain your reasoning.

Try This 6.

feet

2

high jump? About 5.

feet

On Mars, one could jump about 2 3 times as high as on Earth. What would be the height of the winning … high jump? About

4.

feet

On Jupiter, one could jump about 8 as high as on Earth. What would be the height of the winning … high jump? About

3.

pole vault? About

The winning pole-vault height given above was rounded to the nearest whole 1 number. The actual winning height was 19 feet 4 inch. If you used this actual measurement, about how many feet high would the winning jump be … on the Moon?

on Jupiter?

on Mars?

on Venus?

274

Date

Time

LESSON

Finding Fractions of a Number

8 8

One way to find a fraction of a number is to use a unit fraction. A unit fraction is a fraction with 1 in the numerator. You can also use a diagram to help you understand the problem. 7

32

Example: What is 8 of 32? 1 8

7

of 32 is 4. So 8 of 32 is 7 4 28. ?

Solve. 1 1. 5

of 75

2 2. 5

of 75

4 3. 5

of 75

1 4. 8

of 120

3 5. 8

of 120

5 6. 8

of 120

Solve Problems 7–18. They come from a math book that was published in 1904. 1

2

First think of 3 of each of these numbers, and then state 3 of each. 7.

9

8.

10.

3

11.

6 21

1

9.

12

12.

30

3

First think of 4 of each of these numbers, and then state 4 of each. 13.

32

14.

40

15.

12

16.

24

17.

20

18.

28

19.

Lydia has 7 pages of a 12-page song memorized. Has she memorized more 2 than 3 of the song? 1

20.

A CD that normally sells for $15 is on sale for 3 off. What is the sale price?

21.

Christine bought a coat for 4 off the regular price. She saved $20. What did she

1

pay for the coat? 22.

Seri bought 12 avocados on sale for $8.28. What is the unit price, the cost for 1 avocado?

275

Date

Time

LESSON

Math Boxes

8 8

1. a.

Write a 7-digit numeral that has

5 in the ten-thousands place, 6 in the tens place, 9 in the ones place, 7 in the hundreds place, 3 in the hundredths place, and 2 in all the other places. b. Write this numeral in expanded notation.

4

2.

Write 3 equivalent fractions for each number.

3.

2 a. 7

Ellen played her guitar 2 1 hours on 3 Saturday and 1 1 hours on Sunday. How 4 much longer did she play on Saturday? Number model:

3 b. 5

Answer:

5 c. 8 20 d. 30 25 e. 50 59

4.

5.

Complete. 8 a. 20

5

4 b. 50

25

6 c. 20

3

2 d. 18

1

Use your Geometry Template to draw a scalene triangle.

How does the scalene triangle differ from other triangles on the Geometry Template?

108 109

276

71

134

Date

Time

LESSON

8 9

1.

Finding a Percent of a Number

The Madison Middle School boys’ basketball team has played 5 games. The table at the right shows the number of shots taken by each player and the percent of shots that were baskets. Study the example. Then calculate the number of baskets made by each player. Example: Bill took 15 shots. He made a basket on 40% of these shots. 40

4

, or 40% 100 10 4 º 15 4 4 15 60 of 15 6 10 º 1 10 10 1 10

Bill made 6 baskets. 2.

On the basis of shooting ability, which five players would you select as the starting lineup for the next basketball game?

Shots Taken

Percent Made

Baskets

Bill

15

40%

6

Amit

40

30%

Josh

25

60%

Kevin

8

75%

Mike

60

25%

Zheng

44

25%

André

50

10%

David

25

20%

Bob

18

50%

Lars

15

20%

Justin

28

25%

Player

Explain your choices.

3.

Which player(s) would you encourage to shoot more often? Why?

4.

Which player(s) would you encourage to pass more often? Why?

277

Date

Time

LESSON

8 9

Calculating a Discount

Example: The list price for a toaster is $45. The toaster is sold at a 12% discount 12 (12% off the list price). What are the savings? (Reminder: 12% = 100 0.12) Paper and pencil: 12% of $45

12 12 4 5 45 100 100 1 540 12 45 100 100 1

$5.40 Calculator A: Enter 0.12 Calculator B: Enter 0.12

Æ

45 45

and interpret the answer of 5.4 as $5.40. and interpret the answer of 5.4 as $5.40.

First use your percent sense to estimate the discount for each item in the table below. The discount is the amount by which the list price of an item is reduced. It is the amount the customer saves. Then use your calculator or paper and pencil to calculate the discount. (If necessary, round to the nearest cent.)

Item

List Price

Percent of Discount

Clock radio

$33.00

20%

Calculator

$60.00

7%

Sweater

$20.00

42%

Tent

$180.00

30%

Bicycle

$200.00

17%

Computer

$980.00

25%

Skis

$325.00

18%

$29.99

15%

$110.00

55%

Double CD Jacket

278

Estimated Discount

Calculated Discount

Date

Time

LESSON

Math Boxes

8 9

1.

3.

Rename each fraction as a mixed number or a whole number. 79 a. 8

45 b. 9

111 c. 3

126 d. 6

108 e. 5

2.

Find the area of the rectangle. 6

3

5

Number model:

Answer:

62

Sam has 8 pounds of oats. A cup of oats is about 1 a pound. How many cups of 2 oats does Sam have?

4.

189

Julie makes $4.00 per week for washing dishes. She pays her sister Amy $0.75 each time Amy does the dishes for her. Is that fair? Explain.

79 80

5. a.

Plot the following points on the grid: (4,2); (2,4); (2,7); (6,7)

42

8 7

b.

Connect the points with line segments in the order given above. Then connect (6,7) and (4,2). What shape have you drawn?

6 5 4 3 2 1 0 0

1

2

3

4

5

6

7

8 208

279

Date

Time

LESSON

8 10

Unit Fractions and Unit Percents

Math Message 1.

?

12

1

If 12 counters are of a set, 5 how many counters are in the set? 2.

counters

1

If 15 counters are of a set, 7 how many counters are in the set?

counters

3.

Complete the diagram in Problem 1 to show your answer.

4.

If 31 pages are of a book, 8 how many pages are in the book?

Number model:

If 13 marbles are 1% of the marbles in a jar, how many marbles are in the jar?

Number model:

If $5.43 is 1% of the cost of a TV, how much does the TV cost?

Number model:

If 84 counters are 10% of a set, how many counters are in the set?

Number model:

5.

6.

7.

8.

9.

1

After 80 minutes, Dorothy had read 120 pages of a 300-page book. If she continues reading at the same rate, about how long will it take her to read the entire book? Eighty-four people attended a school concert. This was 70% of the number expected to attend. How many people were expected to attend?

280

Answer:

Answer:

Answer:

Answer:

pages

marbles

dollars

counters

Number model: Answer:

min

Number model: Answer:

people

Date

Time

LESSON

8 10

1.

Using Units to Find the Whole

Six jars are filled with cookies. The number of cookies in each jar is not known. For each clue given below, find the number of cookies in the jar. Clue

Number of Cookies in Jar

1 a. jar contains 31 cookies. 2 3 b. jar contains 36 cookies. 5 2 c. jar contains 10 cookies. 8 3 d. jar contains 21 cookies. 8 4 e. jar contains 64 cookies. 7 3 f. jar contains 45 cookies. 11

2.

3.

Use your percent sense to estimate the list price for each item. Then calculate the list price. Sale Price

Percent of List Price

Estimated List Price

Calculated List Price

$120.00

60%

$180.00

$200.00

$100.00

50%

$255.00

85%

$450.00

90%

Use the given rule to complete the table.

Rule

in

out

44

out 25% of in

25 64

4.

Find the rule. Then complete the table.

Rule out

% of in

in

out

100

40

45

18

60

24

31

32

304 116

16 125

281

Date

Time

LESSON

Using Units to Find the WHOLE

8 10

continued

6

5.

Alan is walking to a friend’s house. He covered of the distance in 48 minutes. 10 If he continues at the same speed, about how long will the entire walk take?

6.

27 is of what number?

7.

3 8

8.

16 is 25% of what number?

9.

40 is 80% of what number?

3 4

3 4

is of what number?

The problems below are from an arithmetic book published in 1906. Solve the problems. 10.

11.

12.

2

If the average coal miner works of a month with 3 30 days, how many days during the month does he work?

days

1

A recipe for fudge calls for of a cake of chocolate. If a cake 4 costs 20¢, find the cost of the chocolate cake called for by the recipe.

¢

A collection of mail that required 6 hours for a postman to make with a horse and 5 wagon was made in an automobile in the time. How long did the automobile take? 12

hours 13.

How many corks per day does a machine in Spain make from the 1 bark of a cork tree if it makes of a sack of 15,000 corks in that time? 3

corks Source: Milne’s Progressive Arithmetic 14.

Alice baked a batch of cookies. 24 cookies are 40% of the total batch. Complete the table showing the number of cookies for each percent.

% Cookies 15.

282

10%

20%

30%

40%

50%

60% 70%

80%

90% 100%

24

Explain how you found 100% or the total number of cookies Alice baked.

Date

Time

LESSON

Math Boxes

8 10

1.

Solve the following problems. a.

2.

1

If there are 6 counters in of a set, 2 how many are there in the whole set?

Complete the table. Fraction

Percent

3 5

counters b.

Decimal

5%

3

9 counters in of a set. How many 4 are there in the whole set?

0.70 1 3

counters

0.625 c.

15 counters in the whole set. How many 2 are there in of the set? 3

74 75

counters 3.

Add. a.

89 90

4. 1 8

1 4

Grace ran 40 m in 8 seconds. At that speed, how far did she run in 1 second?

3 2 3 5

3 5

b.

5 4

c.

1 2

d.

3

e.

7 8

1 2

8 10

5 4

7 8

1 5

21 108 109

70

5.

Complete. 1 a. 2

hour

2 b. 6

hour

6.

Measure line segment IT below to the nearest tenth of a centimeter.

minutes I

1 2

minutes IT is about

c.

1 hours

d.

3 days

hours

e.

2 years

weeks

1 2

T

cm.

minutes

397

183

283

Date

Time

LESSON

8 11

1.

Class Survey

How many people live in your home? 1–2 people

2.

Spanish

Other:

Are you right-handed or left-handed? right-handed

4.

6 or more people

What language do you speak at home? English

3.

3–5 people

left-handed

How long have you lived at your current address? (Round to the nearest year.) years

5.

Pick one of the questions above. Tell why someone you don’t know might be interested in your answer to the question you picked.

6.

Fifteen percent of the 20 students in Ms. Swanson’s class were left-handed. How many students were left-handed?

7.

About 85% of the 600 students at Emerson Middle School speak English at home. Another 10% speak Spanish, and 5% speak other languages. About how many students speak each language at home? English: Spanish: Other:

8.

students

students students students

The government reported that about 5% of 148,000,000 workers do not have jobs. How many workers were jobless?

284

workers

Date LESSON

8 11

Time

Rural and Urban Populations

The U.S. Census Bureau classifies where people live according to the following rule: Rural areas are communities having fewer than 2,500 people each. Urban areas are communities having 2,500 or more people each. 1.

According to the Census Bureau’s definition, do you live in a rural or an urban area?

How did you decide?

Today more than three out of every four residents in the United States live in areas the Census Bureau defines as urban. This was not always the case. When the United States was formed, it was a rural nation. Work with your classmates and use the information in the Student Reference Book, pages 350, 351, and 376 to examine the transformation of the United States from a rural to an urban nation. 2.

My group is to estimate the number of people living in

areas in (rural or urban)

. (1790, 1850, 1900, or 2000) 3.

The total U.S. population in

was

.

(1790, 1850, 1900, or 2000) 4.

Estimate: The number of people living in

areas in (rural or urban)

was about

.

(1790, 1850, 1900, or 2000)

Make sure your answer is rounded to the nearest 100,000. 5.

Our estimation strategy was

.

285

Date

Time

LESSON

Rural and Urban Populations

8 11

6.

continued

Use the estimates from the groups in your class to complete the following table.

Estimated Rural and Urban Populations, 1790–2000 Year

Estimated Rural Population

Estimated Urban Population

1790 1850 1900 2000

7.

Is it fair to say that for more than half our nation’s history, the majority of the population lived in rural areas?

Vocabulary majority means more than one-half of a count

Explain your answer.

8.

About how many times larger was the rural population in 2000 than in 1790?

9.

About how many times larger was the urban population in 2000 than in 1790?

10.

286

In which decade do you think the urban population became larger than the rural population?

Date

Time

LESSON

Math Boxes

8 11

1.

Rename each fraction as a mixed number or a whole number. 36 a. 8

36 b. 7

99 c. 13

13 d. 7

18 e. 6

Find the area of the rectangle.

8

6

4

Number model:

62

3.

2.

Rico is ordering 12 pizzas. How many people can Rico serve if each person 1 eats of a pizza?

189

Answer: 4.

Fran has $6.48. She buys a hamburger for $2.83. How much does she have left?

4

Number model: Explain your answer.

79 80

5.

34

Plot the following points on the grid: (0,1); (1,3); (4,3); (5,1)

8 7

Connect the points with line segments in the given order. Then connect (5,1) and (0,1). What shape have you drawn?

6 5 4 3 2 1 0

208

0

1

2

3

4

5

6

7

8

287

Date

Time

LESSON

Division

8 12

Math Message 1.

How many 2-pound boxes of candy can be made from 10 pounds of candy? boxes

2.

1 2

How many -pound boxes of candy can be made from 6 pounds of candy? boxes

3.

3

Sam has 5 pounds of peanut brittle. He wants to pack it in 4 -pound packages. How many full packages can he make?

full packages

Will any peanut brittle be left over?

How much?

pound

4.

0 inches

1

2

3

a.

How many 2-inch segments are in 6 inches?

b.

How many 2 -inch segments are in 6 inches?

c.

How many 8 -inch segments are in 4 of an inch?

4

5

segments

1 1

6

segments

3

segments

Common Denominator Division One way to divide fractions uses common denominators. Step 1 Rename the fractions using a common denominator. Step 2 Divide the numerators. This method can also be used for whole or mixed numbers divided by fractions. Examples: 3

3 4 ? 3

12

3

3 4 4 4 12 3 4

288

1 3 1 3

1

3

6 ? 1

2

3

18

3

3 5 5 5 5 1

6 6 6 212

18 3 6

Date

Time

LESSON

Common Denominator Division

8 12

continued

Solve. 4

1.

4 5

3.

3 3 6

5.

2 5

7.

6 5

1

5 2. 6

5

2

3

3 9. 5

1

6 5 2 10

6.

2 3

2

6 10. 5

3

2

3

4.

1 8. 2

1 1 0

1 1 8

1 8 3 1 0 1

3

11.

1 2 4

13.

Explain how you solved Problem 12.

14.

Chase is packing cookies in 2 -pound bags. He has 10 pounds of cookies.

12.

1

How many bags can he pack? 15.

4 5 5

bags

Regina is cutting lanyard to make bracelets. She has 15 feet of lanyard and 1 needs 1 2 feet for each bracelet. How many bracelets can she make? bracelets

16.

Eric is planning a pizza party. He has 3 large pizzas. He figures each person will 3 eat 8 of a pizza. How many people can attend the party, including himself? people

289

Date

Time

LESSON

Math Boxes

8 12

1.

Find the whole set. a. b.

2.

1 5

Fraction

10 is of the set. 12 is

3 4

2 7

Complete the table. Decimal

4 5

of the set.

0.125

c.

8 is

of the set.

d.

15 is of the set.

e.

9 is of the set.

11 20

5 8

2 3

66 % 0.857

3 5

74 75

3.

Add. a.

1 2

2 1 3 8

5.

5 6

1 5

2 3

6 3 1 8

14 8

d.

5

e.

4 6

3 10

1 2

19 20 108 109

70

Write a fraction or a mixed number for each of the following: a.

15 minutes

hour

b.

40 minutes

hour

c.

45 minutes

hour

d.

25 minutes

hour

e.

12 minutes

hour

6.

Measure the line segment below to the 1 nearest inch. 4

in.

62 63

290

A worker can fill 145 boxes of crackers in 15 minutes. At that rate, how many can she fill in 1 hour?

b. c.

89 90

4. 3 4

Percent

183

Date

Time

LESSON

8 13

1.

Math Boxes

Find the area of the rectangle.

2.

Draw a quadrangle with two pairs of parallel sides.

5 yd

Area b h

8 yd

Area: 3.

What kind of quadrangle is this? 189

Measure the dimensions of your calculator 1 to the nearest inch. Record your 4 measurements on the drawing below.

145 146

4.

A copy machine was used to copy the trapezoid ABCD. Are the trapezoids congruent? D

A On Off

Clear

Mode n

D

C

B

original

C

A

copy

B

?

Unit

n

Ud

n d

Frac

Simp

d

F

D

Fac

%

OP1

OP2

M MR/MC

Fix 1000.

(

)

7

8

9

4

5

1

2

3

+

0

.

(–)

ENTER

100. 10. 1.

Explain.

Int

%

6

–

0.1 0.01 0.001

=

183

5. a.

155

Plot the following points on the grid: (2,5); (4,7); (6,5); (4,1)

8 7

b.

6

Connect the points with line segments in the order given above. Then connect (4,1) and (2,5). What shape have you drawn?

5 4 3 2 1 208

0

0

1

2

3

4

5

6

7

8

291