# Enrichment Workbook - LessonPaths

[PDF]Enrichment Workbook - LessonPaths7b4f2bc0ee4c8a468310-a3943345f87d97050e2a25dbf3db3bf2.r70.cf1.rackcdn.co...

1–1

Name

Date

Enrich Place Value Through Billions

This puzzle is similar to a crossword puzzle. Instead of writing letters in the boxes, write one digit in each box to form numbers. Use the clues below. A

B

C

A

D E

F G

A. the greatest possible number using each of the digits 0–9 once with a zero in the tens place

A. the greatest possible 12-digit number using an equal number of 6s, 7s, 8s, and 9s

E. the least possible 9-digit number with a 2 in the hundred millions, hundred thousands, and hundreds places

B. the least possible 10-digit number using 5 as the first and last digit C. the least possible number using each of the digits 0–9 once

F. 10 million more than 7 billion, 470 million, 100

D. 1 million more than 99 million

G. 1 thousand more than 55 billion, 50 million, 5 thousand Look at the clue and number you wrote for B Down. Write two different clues for the same number.

12

Chapter 1

Down

Across

1–2

Name

Date

Enrich Chapter Resources

Compare and Order Whole Numbers and Decimals Each star below has a number next to it. Find the stars with a number greater than zero and less than 100 million. Connect the stars in order from least to greatest. Blast off!

11 thousand, 5 203 million, 4

127,054,762

200,000 + 30,000 + 4,000

8,000 + 900 + 3

500 million, 370

55 billion 243 thousand 8 million, 9 thousand, 300

2 thousand, 340 1,000 + 200 + 3

500,000 + 50

1,545 50,000,000 + 30,000

6

What could you do to make it easier to connect the stars in order?

17

Chapter 1

1–3

Name

Date

Enrich Summer Jobs

Solve. Use the four-step plan and the data from the table. You may use a calculator for exercises that require computation. Earnings of Four Students During Summer Vacation Summer Job Sabrina’s Tammi’s Ned’s Earnings Earnings Earnings Babysitting \$620 \$230 \$140 Gardening \$140 \$20 \$340 Tutoring \$0 \$440 \$220 Other \$90 \$240 \$160

Allen’s Earnings \$140 \$260 \$0 \$150

2. From what job did Ned earn the least money?

3. Which student earned the most money from gardening?

4. List Tammi’s jobs from greatest earnings to least earnings.

5. Who earned more money in all, Sabrina or Tammi?

6. List the students in order from the student with the least earnings to the student with the greatest earnings.

7. Write a problem that could be solved by comparing 3 or more numbers. Then give the problem to another student to solve.

22

Chapter 1

1. Which student earned the most money from tutoring?

1–4

Name

Date

Enrich Chapter Resources

Grid Design

The grid area below is made up of 4 10-by-10 grids. Each 10-by-10 grid represents 1. Use three different color pencils or crayons to make a design on the grids. Color the grids completely.

Write a decimal to tell what area you shaded with each color. Remember, 100 boxes (one grid) represent 1. Color

Decimal

When was it necessary to write a decimal that included a whole number?

27

Chapter 1

1–5

Name

Date

Enrich Decimal Place Value

Part 1 Read each clue. Write the decimal, one digit on each answer line. Look carefully at the position of the decimal point. Circle the digit in the hundredths place. C. the least possible decimal using each of the digits 5–9 once

A. the greatest possible decimal using each of the digits 5–9 once

_____ _____ . _____ _____ _____

_____ _____ _____ . _____ _____

I. the least possible decimal using each of the digits 0–5 once

E. the greatest possible decimal using each of the digits 0–5 once

_____ _____ _____ . _____ _____ _____

_____ _____ . _____ _____ _____ _____

M. the greatest possible decimal

L. the least possible decimal greater than zero

_____ . _____ _____ _____ _____

_____ . _____ _____ _____

_____ . _____ _____ _____ _____

_____ _____ . _____ _____ _____

T. a decimal equivalent to 0.7770

P. a decimal equivalent to 3.4600

_____ . _____ _____ _____

_____ . _____ _____ _____

Part 2 Use the problems above to solve a riddle. Match each digit you circled with one in the box below. Write the letter before the clue above the matching digit. On what mountain would you expect to find a mathematician? On D _____ _____ _____ _____ _____ _____ 2 8 4 9 5 0

_____ _____ _____ _____ _____ 6 1 4 3 7

Look at the clue for I. How did you find out the least possible decimal?

32

Chapter 1

O. the decimal with one fewer thousandth than 6.3118

N. the decimal with one more tenth than 15.237

Name

1–6

Date

Enrich Chapter Resources

Compare and Order Rearrange the digits in each number in the given statement to make a new true statement. Example:

3,427 or 2,734

< >

3,825 2,385

can become or

7,342 2,347

> <

5,382 5,823

1. 585 > 597 2. 4,268 > 2,684 3. 23,627 < 24,745 4. 313,546 < 331,645 Using all of the digits given, write a decimal number to make each statement true. Use each digit only once in each number. Use 5, 6, 8, 9, and 0.

5. 0.8659 < 6. 5.698 >

< 0.8956 > 5.6809

7. 68.509 <

< 68.950

8. 8.6950 >

> 8.6095

Use 1, 2, 3, 4, and 0. 9. 0.2341 <

< 0.2431

10. 3.0124 <

< 3.1042

11. 4.1023 >

> 4.0132

12. 14.023 <

< 14.203

13. List your answers for exercises 5–12. Order the numbers from greatest to least.

37

Chapter 1

1–7

Name

Date

Enrich Hurdling the Competition

Use the data from the table to solve.

Year 1980 1984 1988 1992 1996 2000 2004

Men’s Olympic 400-Meter Hurdles Gold Medal Winner Time (in seconds) Volker Beck 48.70 Edwin Moses 47.75 Andre Phillips 47.19 Kevin Young 46.78 Derrick Adkins 47.54 Angelo Taylor 47.50 Felix Sanchez 47.63 2. Which gold medal winner has the fastest time in the 400-meter hurdles?

3. How much less time did it take Angelo Taylor in 2000 than it took Derrick Adkins in 1996?

4. Which athlete has the slowest time?

6. What are the athlete’s names in order from slowest time to fastest time?

5. In 1976, Edwin Moses won a gold medal in the 400-meter hurdles with a time of 47.64 seconds. How much faster was his time in 1976 than in 1984?

7. Who had a time 0.25 second faster than Edwin Moses had in 1984?

8. In what year did an athlete have a gold-medal-winning time of 0.19 second more than 47 seconds?

9. What is the difference between the fastest time and the slowest time?

10. How many years after Andre Phillips won a gold medal did Felix Sanchez win a gold medal?

42

Chapter 1

1. List Andre Phillips, Kevin Young, and Derrick Adkins from fastest to slowest.

1–8

Name

Date

Enrich Chapter Resources

Benchmark Numbers Use the benchmark number on the left to estimate the number in the picture on the right. 1.

2.

________ hats

________ keys

Use the benchmark number to draw each item described. 3. The pickle barrel below holds 300 pickles. Draw a pickle barrel that could hold 900 pickles.

4. The necklace below has 50 beads. Draw a necklace that is long enough to hold 100 beads.

47

Chapter 1

2–1

Name

Date

Enrich Speeds of Planets

Mercury has the fastest orbit of all the planets. It circles the Sun at about 30 miles per second. At this speed, it takes about 88 Earth days for the planet to orbit the Sun. The table below shows the average orbital speeds of the five fastest planets, rounded to the nearest tenth. Orbital Speed (miles/second) 18.5 8.1 14.5 29.8 21.8

Planet Earth Jupiter Mars Mercury Venus

Source: Book of World Records 2006

Circle the most reasonable orbital speed for each planet.

29.70 mi/s

29.75 mi/s

29.85 mi/s

2. Earth 17.95 mi/s

18.05 mi/s

18.51 mi/s

18.55 mi/s

3. Venus 20.80 mi/s

21.18 mi/s

21.74 mi/s

21.76 mi/s

4. Jupiter 8.01 mi/s

8.12 mi/s

8.17 mi/s

8.21 mi/s

5. Mars 14.51 mi/s

14.56 mi/s

15.04 mi/s

15.40 mi/s

1. Mercury 29.08 mi/s

6. Which is a more reasonable description of the time it takes Mercury to orbit the Sun: 88.76 Earth days or 87.96 Earth days? 7. It takes Jupiter about 11.9 Earth years to complete one orbit around the Sun. Which is a more reasonable description of this time: 11.862 Earth years or 11.849 Earth years?

12

Chapter 2

2–2

Name

Date

Enrich Chapter Resources

Estimate Sums and Differences Cut out the number cards and the decimal-point cards below. • Arrange the cards to show two decimal numbers. Each number can have up to three decimal places. Round the numbers. Estimate the sum and difference of the two numbers. Show your work. • Now move each decimal-point card left or right. Try to make the greatest possible change in your sum or difference. Round the numbers. Estimate the new sum or difference.

Example 1

Example 2

1.236 + 78.594

9.824 - 3.157

→123.6 + 7,859.4

→982.4 - 315.7 greatest change

greatest change

17

Chapter 2

Name

2–3

Date

Enrich Emmy

In 1882, a mathematician who was known as Emmy was born in Germany. Albert Einstein described her as “the most significant creative mathematical genius thus far produced since the higher education of women began.” For many years, she taught at universities in Germany without any pay. She was a kind teacher and taught her students with great enthusiasm. She escaped Germany when the Nazis took over and taught in America for several years. This was the first time in her life that she was paid a full professor’s salary and accepted as a full faculty member. She died unexpectedly in 1935. Estimate each sum or difference by rounding each number to the nearest ten. 1. A = 16 + 37

2. E = 118 - 52

3. H = 94 - 11

4. I = 24 + 69

5. L = 286 - 244

6. M = 75 + 29

Estimate each sum or difference by rounding each number to the nearest whole number. 8. O = 9.02 - 1.3

7. N = 0.79 + 2.65

10. T = 46.77 + 10.991

Look for each solution below. Write the corresponding letter on the line above the solution. If you have estimated correctly, the letters will spell Emmy’s full name.

60

110

60

50

90

70

8

70

58

80

70

EMMY

4

49

22

Chapter 2

9. R = 56.61 - 8.234

2–4

Name

Date

Enrich Chapter Resources

Add and Subtract Whole Numbers A math palindrome is a number that reads the same when it is reversed. Use the flowchart to make palindromes.

981 ← starting number + 189 ← first reversal ______ 1170 + 0711 ← second reversal _______ 1881 ← palindrome Find the palindrome for each number. 1. 5,382

2. 3,136

3. 8,096

4. 15,682

5. 26,853

6. 234,567

Look back at the regrouping you did as you added in problems 1–6. When will the sum of a number and its reversal result in a palindrome?

27

Chapter 2

2–5

Name

Date

Enrich Over and Under

An underestimate is an estimate that is less than the exact answer. You can make an underestimate by rounding down factors or addends.

An overestimate is an estimate that is greater than the exact answer. You can make an overstimate by rounding up factors or addends.

436 + 797 + 856

436 + 797 + 856

400 + 700 + 800 = 1,900

500 + 800 + 900 = 2,200

Use an underestimate, an overestimate, or an exact answer to solve each problem. Tell which kind of answer you used. 2. A minor-league baseball team is planning a fan appreciation night. Each fan will be given a souvenir. The team has 860 mugs, 690 caps, and 862 posters to give away as souvenirs. A crowd of 2,500 is expected. Does the team have enough souvenirs?

3. WBGB is a public radio station that has three fundraising drives each year. This year, the first two drives raised \$73,454 and \$72,200. WBGB wants the three drives to raise at least \$225,000. How much money must the third drive raise in order to meet the goal?

4. An art museum has operating costs of \$4,750 each week. This year, the museum has \$300,000 available to cover operating costs. Does the museum have enough money?

5. Write a problem that could be solved by using an underestimate. Write another problem that could be solved by using an overestimate. Then give the problems to another student to solve.

32

Chapter 2

1. The Primrose Place Theater produced a play called Secrets. The play cost \$13,900 to produce. A total of 720 people saw the play. Tickets cost \$22 each. Did ticket sales cover the cost of producing the play?

Date

Enrich The Hidden Message

Find each sum or difference. Match your sums and or differences with the numbers at right. Write the letter on the line next to the corresponding sum or difference. Read the letters from top to bottom to find the hidden message. Sum or Difference 1. 327.1 + 625.8

Y 2,183

2. 989.98 - 37.18

K 126.89

3. 126.7 + 43.3

C 952.9

4. 1,000 - 47.1

W 2,190

5. 87.64 + 39.25

U 169.89

6. 974 + 1,209

O 2,182.9

7. 412.6 + 1,770.3

R 170.01

8. 227.07 - 57.18 Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Matching Letter

H 952.8

9. 924.64 - 754.63

E 170

10. 1,246.31 + 943.69 11. 5,246.1 - 3,063.2 12. 895.07 - 725.06 13. 174.13 - 47.24 14. What is the message?

37

Chapter 2

Chapter Resources

2–6

Name

2–7

Name

Date

Play a game of alphabet addition.

Use the table to find each sum. 1. A + A =

2. A + B =

3. B + E =

4. E + A =

5. C + E =

6. C + C =

7. C + B =

8. (D + B) + C = 10. C + (B + B) =

11. (D + B) + B =

12. A + (D + C) =

13. In our number system, 0 is the additive identity. This means that for any number n, n + 0 = n. In the table above, which letter is the additive identity? Find each difference. Use what you know about the relationship between addition and subtraction. 14. D - A =

15. B - B =

16. E - B =

17. F - B =

18. A - B =

19. E - A =

20. In the addition table above, the letters A through G represent the values 0 through 6. Match each letter with a value. Make sure the values produce the sums shown in the table.

42

Chapter 2

9. A + A + A =

2–8

Name

Date

Enrich Chapter Resources

Cut out the squares below and rearrange them in a 4 × 4 square so that every problem is adjacent to its solution. Try to use mental math strategies.

What message did you find? How did you use compensation to find 13.4 - 1.9 in W?

47

Chapter 2

3–1

Name

Date

Enrich Multiplication Patterns

Multiply the factors shown in the parentheses to complete these facts. 1. Adult great white sharks weigh about (2 × 800) and may grow to be about (4 × 5)

pounds

feet long.

2. The small mammal, a pygmy shrew, is only about (3 × 1) inches long from head to tail. 3. The largest mammal is the blue whale. Newborn calves weigh about (20 × 300)

caught weighed more than (50 × 7,000)

pounds.

4. The bat with the largest wingspan is the Bismarck flying fox. Its wingspan may be about (10 × 6)

inches long.

5. The largest carnivore, the polar bear, can weigh as many as (30 × 40)

pounds and have a nose-to tail length of

6. The fastest recorded speed of a kangaroo is (8 × 5)

miles

per hour. 7. In the 1950s, an Arctic tern flew the longest distance ever recorded for a bird, (700 × 20)

miles.

8. In 1989, scientists recorded an elephant seal diving about (7 × 700)

feet.

9. The largest game preserve in the world is Estosha National Park in Namibia. It covers about (50 × 800)

square miles.

10. The Monterey Bay Aquarium in California has more than (600 × 600)

specimens of animals and plants.

12

Chapter 3

Name

3–2

Date

Enrich Chapter Resources

The Distributive Property and Subtraction The Distributive Property can also be used to combine subtraction and multiplication. To multiply the difference of two numbers by a number, multiply each term in the parentheses by the number. Then subtract. 3 × (5 - 2) = (3 × 5) - (3 × 2)

Use the Distributive Property to rewrite the expression.

= 15 - 6

Multiply the numbers in parentheses.

=9

Subtract.

You can use the Distributive Property and subtraction to find a product like 2 × 79 mentally.

2 × 79 = 2 × (80 - 1)

Write 79 as 80 - 1.

= (2 × 80) - (2 × 1)

Distributive Property

= 160 - 2

Find 2 × 80 and 2 × 1 mentally.

= 158

Find 160 - 2 mentally.

Rewrite each expression using the Distributive Property. Then evaluate. 1. 3 × (20 - 1) 2. 2 × (10 - 1) 3. 5 × (30 - 2) Find each product mentally using the Distributive Property and subtraction. Show the steps that you used. 4. 2 × 29

5. 3 × 48

17

Chapter 3

3–3

Name

Date

Enrich Estimate Products

Choose a factor from the box to give each estimated product. You can use a number more than once. 224

789

17

322

72

9

495

914

3. 196 ×

4. 213 ×

5. 14 ×

6. 287 ×

7. 12 ×

8. 28 ×

9. 23 ×

About 18,000 11. 2 × 24 ×

×8

Look at the numbers in the box. 13. Which two factors would give the least product? 14. Which three factors would give the greatest product?

22

Chapter 3

Name

3–4

Date

Enrich Chapter Resources

The Greatest Product Game The goal of this game is to make up the greatest product. Get Ready! Players: 2 to 4 You Will Need: 10 index cards Get Set! • Write a different digit from 0 to 9 on each card. • Mix up the cards. Then place the cards in a pile facedown. • Each player should draw four boxes on a piece of paper as shown.

×

Go! • Each player takes a turn choosing a card. • The player writes the digit on the card in one of the boxes on his or her paper. Players may not move digits after they have placed them in a box. • When all the boxes are full, players should find their products. • The player with the greatest product is the winner.

27

Chapter 3

Name

3–5

Date

Enrich Exponents

While working on a family tree project to trace his family’s roots, Tim wanted to know how many great-great-grandparents he has. Family Members Number

Parents

Grandparents

Great-grandparents

Great-great-grandparents

2

2×2=4

2×2×2=8

2 × 2 × 2 × 2 = 16

So, Tim has 2 × 2 × 2 × 2 or 16 great-great-grandparents. When a product like 2 × 2 × 2 × 2 has identical factors, you can use an exponent to write the product. An exponent describes how many times a number is used as a factor. 2 factors 2×2=2

3 factors 2

Exponent is 2.

4 factors

2 × 2 × 2 = 23

2 × 2 × 2 × 2 = 24

Exponent is 3.

Exponent is 4.

Rewrite each product using an exponent. Then evaluate. 2. 5 × 5 × 5

3. 4 × 4 × 4 × 4 × 4

4. 2 × 2 × 2 × 2 × 2 × 2 × 2

1. 3 × 3 × 3 × 3

Rewrite each as a multiplication expression. Then evaluate. 5. 9 2

6. 6 5

7. 10 3

8. 3 6

ALGEBRA Find each missing number. 9. 7 = 49 11. 13.

5 1

10.

2

= 64

= 32

12. 5 = 625

= 15

14. 12 = 1,728

32

Chapter 3

Date

Enrich Multiply by Two-Digit Numbers

Play a multiplication game with a partner. How to Play • Choose a number from one of the circles and from one of the squares. Use the numbers to write a number sentence to fit each description below. Then find the product of the numbers. • Work quickly. Your partner will record the time you used to finish the exercise. • Switch roles. The player who uses less time wins the game. 1. the least product

532 83

2,178

2. the greatest product

57

9 357

3. two different products with a zero in the ones place 921 Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

4. the greatest product with an 8 in the ones place 28 5. the least product with a 9 in the ones place 6 6. the product with a 3 as the first and last digit 7,059 7. two different products between 30,000 and 40,000

72

8. the product closest to 60,000 42,133

45

9. the product closest to 300,000 26,041

37

Chapter 3

Chapter Resources

3–6

Name

Name

3–7

Date

Enrich Multiplication Properties

Write two number sentences to show the Commutative Property of Multiplication. Then shade the grids to show the number sentences you wrote.

5

4

4

5

Write a number sentence to show the Identity Property of Multiplication. Then shade the grid to show the number sentence you wrote.

1 17

Write a number sentence to show the Distributive Property. Then shade the grid to show the number sentence you wrote.

3 10

+

42

4

Chapter 3

Name

3–8

Date

Enrich Chapter Resources

Extending Multiplication

Find each product to decode a secret message.

D

W

E

A

\$5.70 × 34

\$4.21 × 9

875 × 63

563 ×70

L

U

I

Y

\$5.66 × 13

\$7.19 × 34

89 × 876

123 × 342

P

C

N

M

\$52.88 × 644

\$32.99 × 211

65 × 65

\$7.66 × 55

O

H

S

G

\$12.44 × 555

2,233 × 155

\$1.39 × 45

29 × 34

T

I

O

T

75 × 78

\$45.85 × 25

\$6.75 × 555

129 × 75

Match the letter in each box with one of the products below the lines. Write the letter on the line.

\$37.89 \$193.80

55,125

42,066

9,675

77,964

346,115

\$6,960.89 \$1,146.25 \$421.30

\$3,746.25

346,115

5,850

986

\$244.46

55,125

39,410

\$34,054.72 \$6,904.2

47

55,125

77,964

\$73.58

\$62.55

5,850

4,225

9,675

Chapter 3

3–9

Name

Date

Enrich

Extra or Missing Information Use the chart to solve the problems. If there is not enough information to solve, write not enough information and tell what information is needed. If you can estimate the missing information, write estimate, and explain your estimate. If there is too much information, write too much information and tell what information you need to solve the problem.

Sports Caps Color Number of Students Red 4 Blue 12 Black 16 White 8

Rebecca’s school will order sports caps with the school name. She is taking color requests from her classmates. She has 40 requests so far. 1. Rebecca plans to take 10 more requests. What fraction of the requests did she already have for red caps?

2. Rebecca just added 8 more requests. Now what fraction of the total requests are for black caps? Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

3. If Rebecca takes 50 requests, how many will be for white caps?

4. The blue and the red caps costs \$1.50 more than the black and the white caps. What is the total cost of the blue caps requested?

5. The blue caps cost \$5.50 each and the black caps cost \$4.00 each. What is the total cost of the black caps requested so far?

52

Chapter 3

4–1

Name

Date

Enrich A Game of Basic Facts

Play a game with a partner. Take Turns. Player 1 uses

.

Player 2 uses

.

How to Play • Player 1 looks for three numbers that form a basic division fact. • Player 2 looks for three numbers that form a basic multiplication fact. The players should look across or down. Circle the numbers. • The player with the greater number of circles wins the game.

What method did you use to find the division facts?

12

Chapter 4

Name

4–2

Date

Enrich Chapter Resources

Estimating Quotients Using Mental Math The numbers in the rectangles are dividends. The numbers in the circles are divisors. 572 4,325

157,000 782

62

316 843

30,824

58

86 262,000

4,748

Write the dividend and divisor that will give each estimated quotient in Exercises 1–6. Then write a division sentence that shows how you made each estimate. You may use a number more than once. The first exercise has been done for you. 1. Estimated quotient: 5 316 ÷

58

300 ÷ 60 = 5

2. Estimated quotient: 70

÷

3. Estimated quotient: 40 ÷

4. Estimated quotient: 200 ÷

5. Estimated quotient: 8 ÷

6. Estimated quotient: 3,000 ÷

17

Chapter 4

Name

4–3

Date

Enrich Divide and Assemble

Solve each division problem on the shapes. Cut out the shapes. Match the sides with the same quotients to complete the puzzle. What shape did you make?

8 3

20,113 ÷ 4

÷

1,017 ÷ 5

79 R6

3,453 R4

24,175 ÷ 7

2,625 ÷ 3

507 R1

2.

3 25

7

R7

203 R2

÷

85 5

÷

9

1,012 ÷ 3

875 1, 12

337 R1

8 77

5,028 R1

717 ÷ 9

2,153 R7

R1

7 89 1,

8 52

6 ÷

R7

6

10

2,547 ÷ 6

5

02

1, ÷ 19,384 ÷ 9

4,057 ÷ 8

424 R3

22

Chapter 4

4–4

Name

Date

Enrich Chapter Resources

Division Crossword This puzzle is similar to a crossword puzzle. Instead of using letters to form words, you use digits to form numbers. Use the clues below to complete the puzzle. A

B E

G

H

K

C

D

F I

J

L

M

N Q

R

S

T

O

P

Down

A. 8,025 ÷ 25

A. 9,030 - 5,616

C. 224 × 4

B. the remainder in 9,645 ÷ 56

E. 3,604 - 327

C. 1,758 ÷ 2

G. 696 ÷ 58

D. 8,148 ÷ 84

I. 1,653 ÷ 87

F. 10,293 ÷ 47

J. the remainder in 52 ÷ 12

H. 1,075 ÷ 5

K. 5 × 823 + 4

L. 6 × 12 × 19

N. 2,226 ÷ 42

M. 131 × 30

O. 282 ÷ 3

P. 71 × 6

Q. the remainder in 3,821 ÷ 72

Q. 1,881 ÷ 33

R. 83 × 4

R. the remainder in 1,618 ÷ 36

S. 23,616 ÷ 32 T. 32,886 ÷ 81 Grade 5

27

Chapter 4

4–5

Name

Date

Enrich Divisibility

Who was the first American woman in space? To find out, follow the directions below.

1

2

3

4

5

6

7

8

9

1. Write an I above number 2 if 219 is divisible by 9. 2. Write a Y above number 5 if 249 is divisible by 3. 3. Write a D above number 4 if 215 is divisible by 3 and 9. 4. Write a G above number 6 if 390 is divisible by 3, 9, and 10. 5. Write an A above number 2 if 76,540 is divisible by 2, 5, and 10. 6. Write a D above number 9 if 1,299 is divisible by 3 and 9. 7. Write an I above number 6 if 1,112 is divisible by 2, 3, and 9. 8. Write an S above number 1 if 9,000 is divisible by 2, 3, 5, 9, and 10. Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

9. Write a D above number 8 if 1,140 is divisible by 2, 3, and 6. 10. Write an R above number 6 if 1,377 is divisible by 3 and 9. 11. Write an L above number 4 if 504 is divisible by 2, 3, and 6. 12. Write an N above number 1 if 18,242 is divisible by 2, 3, and 9. 13. Write an A above number 5 if 1,204 is divisible by 4 and 8. 14. Write an L above number 7 if 2,479 is divisible by 3 and 9. 15. Write an A above number 3 if 35,469 is divisible by 3, 5, and 9. 16. Write an I above number 7 if 11,235 is divisible by 3 and 5. 17. Write an E above number 9 if 15,872 is divisible by 2, 4, and 8. 18. Write an L above number 3 if 60,000 is divisible by 2, 3, 5, and 10.

32

Chapter 4

4–6

Name

Date

Enrich Chapter Resources

Moon Riddles Riddle: What is the value of the moon? To solve the riddle, find the quotient for each division exercise. Then write the matching letter from the box next to the exercise. Read the letters from top to bottom. Quotient and Remainder

Matching Letter

1. 562 ÷ 23

R 75 R8

2. 98,309 ÷ 34

Q

301 R11

3. 6,784 ÷ 92

L

139 R32

4. 4,433 ÷ 59

U 73 R68 T

19

O

2,891 R15

6. 6,054 ÷ 82

F

24 R10

7. 52,128 ÷ 67

A 778 R2

5. 12,954 ÷ 43

8. 3,458 ÷ 46

S

3,026 R8

E

19 R2

9. 703 ÷ 37 10. 1,484 ÷ 78 11. 5,708 ÷ 76 12. 72,632 ÷ 24 Divide to answer this riddle: How does the moon feel after dinner? Quotient and Remainder

Matching Letter

13. 1,666 ÷ 69 14. 5,835 ÷ 79 15. 4,758 ÷ 34 16. 12,125 ÷ 87

37

Chapter 4

4–7

Name

Date

Enrich Divide Decimals by Whole Numbers

• Write a division problem that meets the criteria described in each Exercise. • Have your partner use a calculator to solve the problem. • Take turns writing and solving the problems. 1. Divide a decimal number between 3 and 4 by 2.

2. Divide a decimal number between 5 and 6 by 3.

3. Divide a decimal number between 4 and 5 by 3. The quotient should contain three odd numbers.

4. Divide a decimal number between 6 and 7 by 3. The quotient should contain three even numbers.

6. Divide a decimal number between 9 and 10 by 4. The quotient should contain three even numbers.

7. Divide a decimal number between 6 and 8 by 6.

8. Divide a decimal number between 6 and 8 by 6. The quotient should contain three different digits.

42

Chapter 4

5. Divide a decimal number between 5 and 6 by 4.

Date

Enrich More Mental Math with Division

A restaurant bill comes to \$158.90. If ten people split the bill evenly, how much will each person pay, not including the tip? Using a calculator, you find that 158.90 ÷ 10 = 15.89. So, each person will pay \$15.89. You can divide numbers by 10, 100, 1,000, and so on by using patterns and mental math. 158.90 ÷ 1 = 158.90 158.90 ÷ 10 = 15 8.90 = 15.89

1 zero in 10: Move the decimal point 1 place to the left.

158.90 ÷ 100 = 1 5 8.90 = 1.589

2 zeros in 100: Move the decimal point 2 places to the left.

158.90 ÷ 1,000 = 1 5 8.90 = 0.1589

3 zeros in 1,000: Move the decimal point 3 places to the left.

So, to divide by numbers like 10, 100, and 1,000, count the number of zeros in the divisor. Then move the decimal point in the dividend to the left that many places.

Find each quotient by using mental math. 1. 60.4 ÷ 10

2. 485 ÷ 100

3. 355.1 ÷ 1,000

4. 0.81 ÷ 10

5. 9,200 ÷ 100

6. 73.4 ÷ 1,000

7. 0.22 ÷ 1,000

8. 1,006 ÷ 10,000

9. Nevaeh ran in a 10-kilometer race to raise money for cancer research. She raised \$426.50 in all. How much did she earn per kilometer?

10. It cost the Gates family \$12 to make 100 flyers advertising their garage sale. How much did it cost per flyer?

47

Chapter 4

Chapter Resources

4–8

Name

5–1

Name

Date

Enrich Explore Addition and Subtraction Expressions

1. Evaluate each expression for n = 2.35 31.95 - n

1.35 + n

19.85 + n

8.75 + n

20.85 - n 28.25 - n

12.45 + n 35.65 - n

5.05 + n

What is the sum of each row, column, and diagonal? 2. Let n equal 10. Write the new value of each expression from above in the table below.

3. Rewrite each expression above so that, when n = 10, each row, column, and diagonal has the sum of 55.5.

12

Chapter 5

How did you decide how to rewrite the expressions?

Check the sum of each row, column, and diagonal. What do you notice?

Name

5–2

Date

Enrich Chapter Resources

Problem-Solving Strategy: Solve a Simpler Problem Solve a Simpler Problem The diagram shows an artist’s design for the layout of the family room in a house. Use data from the diagram to solve the problems. Remember: The area of a rectangle is equal to its length times its width. 25 ft 15 ft

8 ft 4 ft

C

12 ft 4 ft

B

4 ft

D

H 2 ft

G

2 ft 6 ft

4 ft

2 ft

A

E

F

8 ft

17 ft

1. How many square feet of the room is section B?

2. How many square feet of the room are sections D and H?

3. How many square feet of the room is section E?

4. How many square feet of the room are sections A and F ?

5. How many square feet of the room are sections C and G?

6. How many square feet of the room are sections D and G?

7. How many square feet of the room are sections B and E?

8. How many square feet of the room are sections A, C, and F ? Grade 5

17

Chapter 5

5–3

Name

Date

Enrich Explore Multiplication and Division Expressions

Match each phrase in Column A to a phrase in Column B to make a true sentence. Then write the letters above each exercise number to solve the riddle in the box. Column A

Column B

1. If n = 12, then

O. n ÷ 4 = 0.8.

2. If n = 20, then

I. 1 _14_n = 3 _18_.

3. If n = 14, then

E. _n7_ = 0.7.

4. If n = 6, then

O. 3n = 36.

5. If n = 3.5, then

n W. ___ = 7. 12

6. If n = 2 _12_, then

A. 1 _12_n = 9.

7. If n = 3.2, then

V. n ÷ 1 _34_ = 12.

8. If n = 84, then

n N. ___ = 40. 0.5

9. If n = 2.1, then

A. 6n = 12.6. R. n ÷ _78_ = 16.

11. If n = 4.9, then

S. _34_ n = 12.

12. If n = 16, then

D. 2.4n = 8.4.

10. If n = 21, then

Where do disc jockeys surf? _____ _____ 1 2

_____ _____ _____ _____ _____ 3 4 5 6 7

_____ _____ _____ _____ _____ 8 9 10 11 12

22

Chapter 5

Date

Enrich Multiplication and Division Equations

Evaluate each expression if a = 3, b = 15, c = 9, and d = 20 . Circle each solution in the maze below. Then trace the path through the maze from Start to Finish. 1. 2d + 8

2. 10b + 5d

3. d - 2c

4. 2b - d

5. 3b ÷ c

6. 3c - 3a

7. 8d + 7b

8. 12a ÷ c

9. 6d ÷ b

10. 3d - 5c 12. 5a - 2

11. 4c

17 48

25 259

20

32

7

30 75 72 3 13

Finish

Start

100

27

Chapter 5

Chapter Resources

5–4

Name

5–5

Name

Date

Would you give an estimate or an exact answer? Explain, then solve. 1. Suppose a mint makes 2,300,000 nickels per day. At that rate, can they make at least 60,000,000 nickels in 32 days?

2. A private coin company makes commemorative coins with famous singers on them. The coins are sealed in individual boxes. The total weight of one coin and one box is 4 ounces. The individual boxes are packed in large boxes. How many coins are there in a large box that weighs 45 pounds?

3. A commemorative coin company has 39,485,500 new coins for sale. If 11,890,500 coins have already been sold, about how many coins does the company still have in stock? Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

4. A magazine has a circulation of 18,000,000. Suppose 5,000 magazines are printed every hour for 3 days. Will the magazine print enough magazines in 3 days to cover their circulation?

5. The circulation of a magazine has increased by 5,325,000 from last year. The circulation was 12,937,500 last year. What is the new circulation of the magazine?

6. It costs \$0.41 to mail a letter. If there are 3,480 letters, will \$900 cover the postage?

32

Chapter 5

5–6

Name

Date

Enrich Chapter Resources

Function Tables All the figures are made of toothpicks. For each exercise, draw the next two figures in the sequence. Record the number of polygons and the number of toothpicks in each figure. Then write the function rule that describes the relationship between the number of toothpicks and the number of polygons. 1.

Number of triangles (t)

1

Number of toothpicks (n)

3

Equation: 2.

Number of squares (s)

1

Number of toothpicks (n) Equation: 3.

Number of pentagons (p)

1

Number of toothpicks (n) Equation: Suppose a sequence of figures like those above was made using octagons. What function rule do you think would describe the relationship between the number of toothpicks (n) and the number of octagons (o)? Explain your thinking.

37

Chapter 5

5–7

Name

Date

Enrich Number Sentences

Write a numerical expression that has a value equal to each number from 1 through 30. In each expression, use each of four consecutive digits exactly once. You may use any operation and 2-digit numbers. Here are some examples. Numbers used: 1, 2, 3, 4 1 = (3 × 1) - (4 - 2)

Numbers used: 3, 4, 5, 6 4 = 36 ÷ (4 + 5)

Numbers used: 2, 3, 4, 5 5 = 4 + (3 - 2)

11 =

21 =

2=

12 =

22 =

3=

13 =

23 =

4=

14 =

24 =

5=

15 =

25 =

6=

16 =

26 =

7=

17 =

27 =

8=

18 =

28 =

9=

19 =

29 =

10 =

20 =

30 =

42

1=

Chapter 5

Name

6–1

Date

Enrich Riddle Fun

Find each solution. A. a + 18 = 43; a =

K. k + 98 = 203; k =

B. b + 2 = 4; b =

O. 55 = o + 37; o =

C. c + 46 = 98; c =

P. p + 45 = 100; p =

D. 79 = d + 55; d =

R. r + 87 = 505; r =

E. 12 = e + 5; e =

S. s + 240 = 343; s =

F. f + 98; = 142; f =

T. 21 = t + 16; t =

H. h + 7 = 22; h =

U. 497 = u + 78; u = W. 14 = w+ 10; w =

I. 73 = i + 19; i =

Find each solution below. Write the letter of the exercise above the matching solution to find out the answer to the riddle. Riddle: Why did the boy eat his math homework?

2

7

52

25

419

103

7

5

15

7

5

7

25

52

15

7

418

103

25

54

54

5

4

25

103

25

55

54

7

24

52

7

44

52

25

105

7

12

Chapter 6

Name

6–2

Date

Enrich Chapter Resources

Multiplication and Division Equations The Vice President takes over if the President cannot fulfill the term of office. But who takes over should the Vice President leave office before completing the term of office?

To find the answer, solve each equation. Write the capital letter that is before the equation on the line above the answer at the bottom of the page. H

8n = 40

n=

S

3c = 36

c=

R

3y = 6

y=

P

10k = 140

k=

O

3d = 12

d=

U

9y = 72

y=

V

9r = 27

r=

N

3t = 33

t=

T

4t = 40

t=

I

87t = 87

t=

E

6n = 36

n=

F

4a = 60

a=

K

2a = 18

a=

A

13d = 52

d=

10

2

6

5

6

12

10

5

6

14

2

6

12

14

6

4

9

6

5

4

8

12

6

6

11

17

10

4

2

4 4

10

1

15

15 3

6

12

Chapter 6

6–3

Name

Date

Enrich Functions

Complete the table. Write an equation to show the relationship. Tell what each variable in the equation represents. 1.

Pattern Number Picture Number of Dots

2.

Pattern Number Picture

3 •• • •• • • 7

1

2

Number of Sections 2

4

Pattern Number Picture Number of Dots

4.

2 •• •• • 5

1 •• • •• 5

2 ••• • ••• 7

Pattern Number Picture

1

2

Number of Squares

1

4

3

3 •••• • ••••

3

22

4 •••• •••• • 9

5 ••••• ••••• •

4

4 ••••• • •••••

4

5 •••••• • ••••••

5

Chapter 6

3.

1 • • • 3

Date

Enrich Geometry: Ordered Pairs

Graph the ordered pairs. Connect the points. Record the length, width, and perimeter of the rectangle. Remember, the perimeter is found by adding the measures of all the sides. 1. ( 3, 2), (3, 8), (7, 8), (7, 2)

2. (7, 1), (4, 1), (4, 10), (7, 10) y 9 8 7 6 5 4 3 2 1

y 9 8 7 6 5 4 3 2 1 O

=

O

1 2 3 4 5 6 7 8 9 x

w=

P=

=

3. (9, 9), (9, 2), (2, 2), (2, 9)

=

w=

P=

4. (7, 9), (7, 1), (1, 1), (1, 9)

y 9 8 7 6 5 4 3 2 1 O

1 2 3 4 5 6 7 8 9 x

y 9 8 7 6 5 4 3 2 1 O

1 2 3 4 5 6 7 8 9 x

w=

P=

=

1 2 3 4 5 6 7 8 9 x

w=

P=

Compare the length and width of each rectangle to the coordinates you graphed.

27

Chapter 6

Chapter Resources

6–4

Name

6–5

Name

Date

Enrich Algebra and Geometry: Graph Functions

Complete. 1. Graph the ordered pairs (2, 2), (0, 4), (2, 6), and (4, 4). Connect the points in the order given. Then reverse the x- and y-coordinates in the ordered pairs. Graph the new set of points and connect them in the order given.

0

2. Graph the ordered pairs (0, 0), (0, 3), (3, 3), (3, 5), and (4, 4). Connect the points in the order given.

1 2 3 4 5 6

0

3. Graph the ordered pairs (1, 1), (3, 0), (3, 2), (3, 5), and (6, 6). Connect the points in the order given.

6 5 4 3 2 1

Then reverse the x- and y-coordinates in the ordered pairs. Graph the new set of points and connect them in the order given.

1 2 3 4 5 6

6 5 4 3 2 1

Then reverse the x- and y-coordinates in the ordered pairs. Graph the new set of points and connect them in the order given.

6 5 4 3 2 1

0

32

1 2 3 4 5 6

Chapter 6

6-6

Name

Date

Enrich Chapter Resources

Functions and Equations Follow the directions to write other addition equations. For each new equation, change only one number. Look at the example if you need help. Record the solution of each equation you write. Directions

Equations

Solutions

x + 12 = 43 or x + 9 = 40

x = 31

1. Write an equation that has a solution that is 1 more than the solution of 30 = b + 20.

___________________

__________

2. Write an equation that has a solution that is twice the solution of 9 + d = 10.

___________________

__________

3. Write an equation that has a solution that is 5 less than the solution of n + 2 = 30.

___________________

__________

4. Write an equation that has a solution that is half the solution of 16 = p + 6.

___________________

__________

5. Write an equation that has a solution that is 3 less than the solution of h + 4 = 24.

___________________

__________

6. Write an equation that has a solution that is 3 times the solution of 17 = k + 16.

___________________

__________

7. Write an equation that has a solution that is 20 more than the solution of 7 + s = 16.

___________________

__________

8. Write an equation that has a solution that is one fourth the solution of 29 = r + 1.

___________________

__________

9. Write an equation that has a solution that is 6 less than the solution of 7 + z = 26.

___________________

__________

___________________

__________

Example Write an equation that has a solution that is 3 more than the solution of x + 12 = 40. (x = 28, so the solution should be 31.)

10. Write an equation that has a solution that is 7 more than the solution of 17 = 5 + c.

What do the solutions of all the equations you wrote have in common?

37

Chapter 6

6–7

Name

Date

A magic square is a square of numbers in which each row, column, and diagonal has the same sum. Use counters to find if each is a magic square. If so, give the magic sum. 1.

2. 4

10

0

8

1

6

6

2

2

3

5

7

4

6

8

4

9

2

Magic Square: Yes or No?

Magic Square: Yes or No?

Use counters to complete these magic squares. 4.

3. 2

14

9

5

12

8 10

5

4

7

4

18

11

17 8

15

13

19

9

12

16

3

Sum:

Sum:

Sum of the four middle squares:

Sum of the four middle squares:

Sum of the four corners:

Sum of the four corners:

42

3

7

Chapter 6

Name

7–1

Date

Enrich Median and Mode

Use the numbers in the box to complete problems 1—7. Once you have used a number, cross it out. You may not use it again. 1

2

6

5

1

6

4

7

9

5

10

98

96

79

96

25

75

32

53

50

71

22

81

76

97

44

36

20

72

36

31

40

50

49

18

29

74

96

42

34

198

173

367

379

988

637

724

706

251

600

546

468

809

343

702

706

867

331

828

615

When you have completed Exercises 1—7, compare your answers with a classmate. For each of Exercises 1–6, give one point to the person who comes closer to the goal. For Exercise 7, give one point for each person who finds the mode of the data.

2. Choose six numbers.

Goal: greatest range

Goal: least mean

Numbers:

Numbers:

Range:

Range:

3. Choose eight numbers.

4. Choose five numbers.

Goal: least median

Goal: greatest range

Numbers:

Numbers:

Median:

Range:

5. Choose seven numbers.

1. Choose seven numbers.

6. Choose nine numbers.

Goal: least range

Goal: greatest range

Numbers:

Numbers:

Range:

Median:

7. Find the mode of the remaining numbers. 8. Describe one strategy you used in this game.

12

Chapter 7

Name

7–2

Date

Enrich Chapter Resources

Leisure Reading This pictograph is supposed to show the types and numbers of magazines in a library. Some parts of the graph are missing. Use the clues to complete the graph. Magazines at Branch Library

Sports Fashion Science

News

Key: Each Clues • • • • • •

stands for

magazines.

The library has:

40 fashion magazines 20 travel magazines 25 news magazines 10 more business magazines than travel magazines 40 more sports magazines than fashion magazines a total of 270 magazines

Use the completed pictograph to find each. Tell how you find each answer. Mode:

Median:

17

Chapter 7

Name

7–3

Date

Enrich Every Word Counts

Use a favorite fiction book or story. Count the number of words in each of the first 25 sentences. Record your findings in the table below. Number of Words in Sentences

Number of Words

Tally

Total

1 2 3 4 5 6 7 8

10 more than 10 Use your data to make a line plot. Number of Words in Sentences

1

2

3

4

5

6

7

8

9

10

more than 10

Write a sentence that describes your data.

22

Chapter 7

9

7–4

Name

Date

Enrich Chapter Resources

Tally the Score Work with a partner to play a kind of miniature golf. Take turns. You’ll need two number cubes, 1 red and 1 green. • Each player rolls the number cubes and reads the game grid to find out how many strokes it took to get the ball into the hole. • Record the number of strokes on your tally sheet. • The player with the fewest number of strokes after 18 holes is the winner. In miniature golf, low scores are better than high scores.

GREEN CUBE

If you roll a 3 on the red cube and a 2 on the green cube, you will get a Poor Putt and score 3 strokes. That means it took you 3 strokes to get the ball into the hole. After you play, make a frequency table showing the number of holes for each number of strokes. RED CUBE

1

2

3

4

5

6

1

Hole In One! (1)

Out of Control (5)

Poor Putt (3)

Stuck Under Windmill (4)

Out of Control (5)

Stuck Under Windmill (4)

2

Poor Putt (3)

Hole In One! (1)

Poor Putt (3)

Perfect Putt (2)

Perfect Putt (2)

Poor Putt (3)

3

Stuck Under Windmill (4)

Stuck Under Windmill (4)

Hole In One! (1)

Stuck Under Windmill (4)

Missed by a Mile (5)

Out of Control (5)

4

Out of Control (5)

Poor Putt (3)

Missed by a Mile (5)

Hole In One! (1)

Poor Putt (3)

Perfect Putt (2)

5

Out of Control (5)

Perfect Putt (2)

Poor Putt (3)

Perfect Putt (2)

Hole In One! (1)

Perfect Putt (2)

6

In the Water (6)

Perfect Putt (2)

Poor Putt (3)

Poor Putt (3)

Perfect Putt (2)

Hole In One! (1)

Miniature Golf Tally Sheet

HOLE 1 2 3 4 5 6 7 8 9 Grade 5

Player 1

Player 2

HOLE

Player 1

Player 2

10 11 12 13 14 15 16 17 18 TOTAL

27

Chapter 7

7–5

Name

Date

Enrich Relative Scale

Make a table to determine how much of a certain item is needed for a pool party you are having. Assume that 10 people will attend your party. In addition to a sandwich and a drink for everyone, you will also need to provide pool supplies for some of your guests.

After you have created your table, answer the following questions: 1. What item will most of your guests need you to provide?

2. What item will the least number of guests need you to provide?

32

Chapter 7

7–6

Name

Date

Enrich Chapter Resources

Jaguar Season Complete the graph to show the scores of the eight football games playes by the Jaguars in one season. Use the information in the table. Points Scored in Football Games 40

Jaguars

Points Scored

Opponents 30 20 10

0

Game 1

Game 2

Game 3

Game 4

Use your completed graph to answer these questions. 1. How many games did the Jaguars win?

2. In which game did the Jaguars win by the most points?

3. By how many points did the Jaguars lose in Game 2?

4. In how many games did the Jaguars score at least 20 points?

5. About how many more points altogether did the Jaguars score than their opponents in the 5 games that they won?

37

Chapter 7

7–7

Name

Date

Enrich Use Graphs to Identify Relationships

A meteorologist measures snowfall every 2 hours during a snowstorm. The points on the graph below show the measurements. The dashed line comes closest to connecting the points. Use the graph to solve Exercises 1—3.

1. The dashed line shows the relationship between time and snowfall. For each hour that passes, about how many centimeters of snow accumulate?

2. About how many centimeters of snow do you think will have accumlated by 3 P.M.? Explain your answer.

3. Suppose the snow continues falling at about the same rate. What time will it be when the accumulation reaches 24 cm?

4. As Mr. Sanders drives, he checks his odometer each hour. At 3 P.M., the odometer says 948 miles. At 4 P.M., it says 1,000 miles. At 5 P.M., it says 1,055 miles, and at 6 P.M., it says 1,100 miles. Plot these points. Draw the dashed line that comes closest to connecting the points.

5. Describe the relationship between hours and number of miles driven.

42

Chapter 7

7–8

Name

Date

Enrich Chapter Resources

Make an Appropriate Graph Six students took a music survey in their school. They tallied the results in the table below. Favorite Types of Music Survey Sandra’s Results

Trevor’s Results

Rap

12

Rap

6

Rap

15

Rock

5

Pop

14

Jazz

4

Pop

9

Country

3

Pop

11

Erin’s Results

Arlan’s Results

Anya’s Results

Juan’s Results

Rap

12

Jazz

12

Rap

7

Rock

5

Rap

5

Rock

4

Blues

3

Pop

9

Country

6

Pop

9

Classical

1

Pop

2

1. The students decide to combine the results of their survey and display them in a graph. They want no more than 5 categories represented. How can they group their data to best reflect the results within a limit of 5 categories?

2. Make a table to show the data in 5 categories.

3. Which type of graph would you use to display the data in the table you made? Explain. Then make the graph.

47

Chapter 7

7–9

Name

Date

Enrich Methods of Persuasion

Use the data from the chart to solve Exercises 1–5. A bus company records the number of passengers along each route. It is considering adding more buses to each route.

Number of Passengers 2,800 2,300 2,400

Route Northeast Northwest North

1. The bus company orders six new buses. You think each route should get two new buses. Make a bar graph to support your argument.

Bus Line Riders Number of Passengers

3. Suppose you think that the Northeast Route should get 4 new buses, leaving the other two lines with 1 new bus each. Make a bar graph to support that argument.

Bus Line

Northeast

Northwest

North

Route

5. The two graphs that you drew show the same data, but they look different. Explain how you made them look different and why.

Number of Passengers

Bus Line Riders

Northeast

Northwest

North

Route

52

Chapter 7

4. Explain why the graph supports your argument.

8–1

Name ____________________________ Date ________________

Enrich Fractions and Division

2. Some of the triangles have exactly two corners that are on the large triangle. Draw a dot in each of these small triangles.

3. Some of the triangles have exactly one corner that is on the large triangle. Draw an X in each of these small triangles.

4. Some of the triangles have no corners that are on the large triangle. Draw a star in each of these small triangles.

5. What fraction of the small triangles is shaded?

6. What fraction of the small triangles has a dot?

7. What fraction of the small triangles has an X?

8. What fraction of the small triangles has a star?

9. What fraction of the small triangles has at least one corner that is on the larger triangle?

12

Chapter 8

1. The large triangle is made of four rows of small triangles. Some of the small triangles have three corners that are on the large triangle. Shade each of these small triangles.

Name ____________________________ Date ________________

8–2

Enrich Chapter Resources

Understanding Fractions Match each improper fraction below a blank to a mixed number with a letter below. Write the letter in the blank to complete a quote by Willy Wonka from the book Charlie and the Chocolate Factory by Roald Dahl. “A little nonsense now and then

17 _ 3

22 _ 6

26 _ 8

49 _ 5

6

34 _ 4

22 _ 9

13 _ 3

26 _ 8

20 _ 3

26 _ 8

21 _ 10

44 _

21 _ 10

17 _ 3

19 _ 4

21 _ 10

13 _ 3

17 _ 3

50 _ 8

26 _ 8

26 _ 8

17 _ 3

22 _ 9

8 _ 5

3 N = 1_ 5

2 S = 5_ 3

2 M = 6_ 3

3 W = 4_ 4

1 H = 4_ 3

4 T = 2_ 9

2 E = 3_ 8

4 L = 9_ 5

4 R = 3_ 6

2 Y = 8_ 4

1 I = 2_ 10

2 D = 6_ 8

2 B = 7_ 6 2 How did you change 3_ into an improper fraction? 8

17

Chapter 8

8–3

Name ____________________________ Date ________________

Enrich Egyptian Fractions

The ancient Egyptians wrote numbers using different symbols than those we use today. The ancient Egyptian symbols for 100, 10, and 1 are shown below.

The Egyptian symbol for the number 215 is shown at the right. A unit fraction has 1 as its numerator. Ancient Egyptians wrote all fraction as unit fractions. To show a fraction, they used the symbol for a mouth above the denominator. The ancient 1 ___ Egyptian symbol for 12 is shown at the right.

Write the ancient Egyptian symbol for each number. 1. 16

2. 24

3. 131

Write the ancient Egyptian symbol for each fraction. 1 4. _ 3

1 5. _ 10

1 6. _ 17

1 7. _ 25

1 8. _ 110

1 9. _ 201

Write each Eyptian fraction as it would be written today. 10.

11.

12.

22

13.

Chapter 8

8–4

Name ____________________________ Date ________________

Enrich Chapter Resources

A Maze of Mixed Numbers Solve A–N by rounding to the nearest whole number. Then find your way through the maze to reach the dot. When you come to a letter, choose the number that matches your answer. Follow the path until you reach the next intersection. 7 A. 2 _ 8

1 B. 6 _ 7

3 C. 3 _ 4

2 D. 8 _ 10

7 E. 9 _ 9

5 F. _ 6

5 G. 12 _ 7

5 H. 20 _ 7

2 I. 18 _ 10

7 J. 16 _ 9

3 K. 7 _ 20

4 L. 1 _ 5

8 N. 14 _ 10

2 M. 5 _ 14 START

8

D

F

6 1

B 7

J

0 7

17

9

10

11

18

E

N 13 12 16

A

3

15

G

2

I 19 18

20

C 5

H 4

5

6

21

M

7

K

L 4

27

2

Chapter 8

8-5

Name

Date

Enrich Unit Rates

A unit rate is a comparison of two quantities by division in which the denominator is 1. Description riding a bicycle 23 miles in 2 hours

Rate

Unit Rate

23 miles _ 2 hours

11_12_ miles _ = 1 hour 2 hours ÷ 2

23 miles ÷ 2 __

= 11_21_ miles/hour reading 14 pages in 8 minutes

14 pages _ 8 minutes

1_34_ pages _ = 1 minute 8 minutes ÷ 8

14 pages ÷ 8 __

= 1_34_ pages/minute earning \$33 for babysitting 5 hours

\$33 ÷ 5 __

\$33 _ 5 hours

\$6.60 =_ 1 hour 5 hours ÷ 5 = \$6.60/hour

Find each unit rate. 1. 52 gallons of water for 5 fish 2. typing 111 words in 2 minutes 3. canoeing 49 miles in 4 days 4. a total weight of 78 pounds for 9 boxes 5. earning \$350 for working 40 hours 6. An SUV can go 230 miles on one tank of gas. The gas tank holds 25 gallons. What is the SUV’s gas mileage in miles per gallon? 7. A messenger delivers 8 packages in 3 hours. At that rate, how many packages can she deliver in 15 hours? Grade 5

32

Chapter 8

Name

8–6

Date

Enrich Chapter Resources

Greatest Possible Error When you measure a quantity, your measurement is more precise when you use a smaller unit of measure. But no measurement is ever exact—there is always some amount of error. The greatest possible error (GPE) of a measurement is one half the unit of measure. 1 unit of measure: _ inch 8 3 length of line segment: 1 _ inches INCHES 1 2 18 1 GPE: half of _ inch, or _ inch 8 16 3 6 _ _ Since 1 = 1 , the actual measure of the line segment may range 8 16 5 7 anywhere from 1 _ inches to 1 _ inches. 16 16

Use the GPE to give a range for the measure of each line segment. 2.

1. INCHES

1

INCHES

2

3.

1

2

4. INCHES

1

2

CM 1

5. Using this scale, the weight of a bag

2

3

4

5

6. Using this container, the amount of a

of potatoes is measured as 3 pounds.

liquid is measured as 20 milliliters.

What is the range for the actual

What is the range for the actual amount

weight of the potatoes?

of the liquid?

0 3

pounds

50 mL 40 mL

1

30 mL

2

20 mL 10 mL

37

Chapter 8

8–7

Name

Date

Enrich Choose the Operation

Solve. 1 1. A box is _ inch tall. If 5 of the boxes are stacked on top of each 2 other, how tall is the stack of boxes?

3 3 2. Darlene needs _ yard of fabric to cover a chair. She has _ yard of 4 8 fabric. How much more fabric does she need?

3. Mr. Montgomery is a chef. He has created 250 new recipes. He 3 plans to donate _ of them to the school library. How many recipes 5 does he plan to donate?

4. The art department received a shipment of 6 boxes of clay. Each 3 box weighed _ pound. How many pounds of clay were in the 4 shipment?

2 5. A sculptor has a steel tube that is _ foot long. To create a longer 3 5 tube, he attaches it to another steel tube that is _ foot long. How 6 long is the new steel tube?

2 6. Marcel was in a triathalon, a race with 3 events. He ran 4 miles in _ 3 13 hour. He bicycled 5 miles in _ hour, and he swam 880 yards in _ 4 2 hour. What was his total race time?

42

Chapter 8

9–1

Name

Date

Enrich Let Them Eat Cake

You can use a strategy called the cake method to find the GCF of a pair of numbers. Find the GCF of 30 and 36.

5

Use the cake method to find the factors of 30 and 36.

3 3  9

3  15

18 2 

30 2 

36 2 

Divide each number by a small prime number. Divide the quotients by another small prime number until the quotient is a prime number. Circle the common factors.

30 = 2 × 3 × 5 36 = 2 × 2 × 3 × 3

Find the product of the common factors. 2 × 3 = 6 Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

6 is the GCF of 30 and 36.

Use the method shown above to find the GCF of each pair of numbers. 1. 18 and 42

2. 16 and 72

GCF:

GCF:

3. 56 and 84

4. 45 and 144

GCF:

GCF:

12

Chapter 9

Date

Enrich Number Patterns

Mathematicians have found interesting patterns among prime and composite numbers. Complete each table. See what pattern you find. 1. Prime number Remainder when divided by 6

11

23

37

41

59

67

73

83

89

97

83

89

97

2. What do you notice about remainders when prime numbers are divided by 6? 3. Try three prime numbers of your choice. Divide by 6. Does the pattern continue? Explain. 4. Prime number Remainder when divided by 4

11

23

37

41

59

67

73

5. What do you notice about remainders when prime numbers are divided by 4? 6. Try three prime numbers of your choice. Divide by 4. Does the pattern continue? Explain. 7. Find out if a similar pattern exists when dividing prime numbers by other 1-digit numbers. Make tables like those above to find out what happens when you divide by 3, by 5, by 7, by 8, and by 9. Describe your findings.

A perfect number is a composite number whose factors, not including the number itself, add up to the number. The first perfect number is 6. The factors of 6 are 1, 2, and 3. 6 = 1 + 2 + 3 8. Find the next perfect number. Show the number as a sum of its factors.

17

Chapter 9

Chapter Resources

9–2

Name

9–3

Name

Date

Enrich Fraction Boxes

Arrange each set of digits in the boxes to make each equivalent fractions. 1. 15, 1, 5, 3

_ _

2. 1, 4, 3, 12

_ _

3. 1, 8, 4, 2

_ _

4. 20, 4, 16, 5

5. 6, 2, 3, 9

_ _

6. 3, 18, 6, 9

_ _

9. 4, 12, 8, 6,

_ _

_ _

8. 3, 20, 4, 15

10. 6, 4, 3, 12

_ _ Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

7. 16, 3, 8, 6,

_ _

_ _

11. How did you solve problem 10?

22

Chapter 9

Date

Enrich Simplify!

Shade in the boxes that contain fractions that are in simplest form.

7 _

20 _

2 _

11 _

5 _

1 _

3 _

20 _

11 _

3 _

9 _

1 _

9 _

3 _

10 _

3 _

16 _

6 _

6 _

4 _

9 _

15 _

16 _

8 _

8 _

12 _

4 _

5 _

1 _

2 _

7 _

21 _

1 _

10 _

3 _

4 _

15 _

1 _

14 _

8 _

12 _

21 _

20 _

8 _

6 _

3 _

12 _

3 _

2 _

5 _

2 _

12 _

5 _

27 _

9 _

8 5

60 35 8

24 12 15 14 4

5 7

32 50 30

44 50 24 35 9

9 8 5 4 3

3

42 7

30 6

5

33 8

12 15

24 18 8

21 15

12 9

12 42 12

20 24 25 54 40

25 30 6

27 10

What word is formed?

5 _

4 _

3 _

6 _

6 _

1 _

9 _

40 _

1 _

6 _

14 _

4 _

7 _

7 _

4 _

16 _

6 _

1 _

5 _

9 _

2 _

3 _

1 _

10 _

11 _

10 _

3 _

1 _

14 _

4 _

13 _

2 _

6 _

3 _

2 _

20 _

6 _

17 _

16 _

1 _

5 _

8 _

1 _

4 _

2 _

1 _

3 _

15 _

5 _

12 _

1 _

12 _

6 _

1 _

2 _

8 7 5 4 5

15 14 20 12 4

10 42 22 50 10

54 12 30 36 60

11 21 13 32 17

2 8 9

64 24

14 12 15 3

25

60 10 48 35 40

8

36 39 24 18

7 3

57 30 6

19 6

12 6 4

What word is formed?

27

Chapter 9

Chapter Resources

9–4

Name

9–5

Name

Date

Enrich Fraction and Decimal Fun

Find a decimal in Box B that matches a fraction in Box A. When you find a match, cross out both numbers and the letters next to them. Box A

Box B

M

29 _

F

1 _

U 0.28

H

7 _

Y

7 _

I 0.07

A 0.625

R

2 _

B

37 _

P 0.29

T 0.15

G

1 _

D

3 _

C 0.7

M 0.12

O

1 _

X

5 _

D 0.125

H 0.63

I

7 _

N

3 _

L 0.36

Y 0.62

E

13 _

T

49 _

I 0.18

E 0.58

Z

24 _

S

63 _

N 0.65

K 0.96

A

39 _

C

13 _

S 0.5

F 0.48

1 _

P

3 _

B 0.25

G 0.74

10 5 8 5

20 20 25

100 4

25 25 50 5 8 4

50

100 25 20

R 0.6

W

50

Now write the letters that remain in each box. Unscramble each group of letters to spell a math word. Box A Box B How did you find the decimal for

1 _ ? 8

32

Chapter 9

Date

Enrich Fractions as Repeating Decimals

You can write fractions as decimals by dividing.

Write

3 _ as a decimal by finding 3 ÷ 4.

4 0.75   4 3.00

Write

3 0.666

3  2.000

28 ______

–18 _____ 20 – 18 ____ 20 – 18 ____ 2

20 20 _____ 0 3 So, _ = 0.75. 4

So,

2 _ as a decimal by finding 2 ÷ 3. If you keep dividing, you keep getting 6 in the quotient.

When you subtract, you get the same number.

2 _ = 0.666…. 3

When you divide 3 by 4, the quotient is a terminating decimal because the quotient terminates, or ends. When you divide 2 by 3, the quotient does not end. This is called a repeating decimal. You can write a repeating decimal by drawing a bar over the digit or digits that repeat. − 2 _ = 0.6666666666… = 0.6

− 1 _ = 0.1111111111… = 0.1

−− 5 _ = 4545454545… = 0.45

− 19 _ = 1.0555555555… = 1.05

3

9

11

18

Write each fraction as a decimal. Tell whether it is a terminating or repeating decimal. 1.

3 _

2.

2 _

3.

1 _

4.

15 _

5.

7 _

6.

5 _

7.

16 _

8.

1 _

9.

7 _

5

11 9

9 4 8

37

3 6

12

Chapter 9

Chapter Resources

9–6

Name

9–7

Name

Date

Enrich Calendar Math Camp Ringing Rocks Calendar

Camp opens July 1 and runs for the entire month. Mark the schedule on the calendar.

S

M

T

W

T

F

S

• On the first day, they have all the activities 1

2

3

4

5

6

7

• Orchestra every day

8

9

10

11

12

13

14

• Writing every two days

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

• Drama every three days • Pottery every four days • Chorus every six days

2. On which days will campers have only one activity available?

3. Julia’s favorite activity is drama. What factional part of the camp season will she be able to participate in this activity?

4. How many days will campers have orchestra, writing, drama, and chorus available on the same day?

5. On which days will campers have all five activities available?

6. Which activities are available on the tenth day? On the twentieth day?

7. A new activity is to added. When should it be available? Why?

42

Chapter 9

1. Which activities are available on the fourth?

9–8

Name

Date

Enrich Chapter Resources

Fractions in Ancient Rome The Romans used words rather than numbers to indicate fractional parts of a whole. The uncia was an ancient Roman unit equal to one twelfth of the Roman pound. The table below shows the Roman words that represented parts of a whole. Fraction of Roman Pound

Word

Fraction of Roman Pound

Word

11 _

deunx

5 _

quincunx

12 10 _ 12 9 _ 12 8 _ 12 7 _ 12 6 _ 12

12 4 _ 12 3 _ 12 2 _ 12 1 _ 12

dextans dodrans bes septunx

semis

Use the table given above. Write the fraction represented by each word in simplest form. If the fraction is already in simplest form, write simplified. 1. dextans

2. semis

3. quandrans

4. septunx

5. uncia

6. bes

A pound in the customary system has 16 ounces. Use the table below.

15 _ Fraction of Customary Pound

16 7 _ 16

14 _ 16 6 _ 16

13 _

12 _

16 5 _ 16

16 4 _ 16

11 _ 16 3 _ 16

10 _ 16 2 _ 16

9 _ 16 1 _ 16

8 _ 16

7. Which fraction in the table is equal to half of a pound? 1 8. Which do you think represents a greater amount of a whole: _ 12 1 or _? Explain. 16

47

Chapter 9

9–9

Name

Date

Enrich More Fraction Boxes

Arrange each set of digits in the boxes to make each statement true. 1. 3, 1, 7, 5

_<_

2. 1, 8, 4, 2

_=_

3. 6, 9, 5, 4

_>_

4. 2, 3, 7, 6

_>_

5. 8, 3, 1, 5

_<_

6. 4, 6, 5, 3

_<_

_<_<_

8. 4, 2, 8, 6, 5, 1

_<_<_

9. 7, 1, 8, 3, 2, 9

_<_<_

10. 3, 5, 2, 6, 4, 7

_<_<_

7. 1, 3, 4, 5, 7, 9

11. How did you solve problem 10?

52

Chapter 9

10–1

Name ____________________________ Date ________________

Enrich Fraction Pyramid!

In this triangle, the number in each blank circle is equal to the sum of the fractions in the two circles above it. Add to find the missing fractions to complete the triangle. Do not write your answers in simplest form. 1 25 1 25

1 25

1 25

1 25

1 25

1 25

1 25

1 25 1 25

1 25

1 25

1 25

1 25

1 25

How many fractions less than 1 can you simplify in the triangle? Write the fractions in simplest form. How many fractions in the triangle are greater than 1? Write the fractions in simplest form.

12

Chapter 10

Name ____________________________ Date ________________

10–2

Enrich Chapter Resources

Fraction Puzzles In the puzzles below, the sum of the fractions in each row is the same as the sum of the fractions in each column. Use your knowledge of adding and subtracting fractions to find the missing fractions. Hint: Remember to check the fractions for like denominators before adding.

3 _ 20

9 _ 20

2 _

20

20

25

3 _ 25

4 _

0 _

2 _

7 _

20

20

25

7 _

8 _

1 _

2 _ 16

7 _

2 _ 16

16

25

3 _ 25

25

1 _ 25

15

15

16

16

6 _

3 _

12 _

0 _ 16

25

4 _

15

2 _

2 _

25

2 _ 16

16

25

15

1 _ 15

11 _

2 _

15

15

6 _

2 _

15

15

7 _

20

20

6 _

20

4 _

3 _

3 _

15

2 _

2 _

9 _

2 _ 16

4 _ 16

6 _ 16

CHALLENGE Create your own fraction puzzle using a box of 5 rows and 5 columns.

17

Chapter 10

Name ____________________________ Date ________________

10–3

The fractions in the squares are addends. Write the pair of addends that will give each sum.

3 _ 5

2 _ 3

3 _ 4

3 _ 8

7 _ 10

1 _ 16

1 _ 12

5 _ 6

2 _ 5

7 _ 8

+

3 = 1_ 10

2.

+

11 = 1_ 40

3.

+

5 = 1_ 12

4.

+

15 =_ 16

5.

+

7 = 1_ 20

6.

+

23 =_ 24

7.

+

1 = 1_ 15

8.

+

7 =_ 16

9.

+

11 = 1_ 12

10.

+

11 = 1_ 30

22

1.

Chapter 10

10–4

Name ____________________________ Date ________________

Enrich Chapter Resources

Subtract Unlike Fractions Play “Five-in-a-Row“ with a partner. You will need a coin. Player 1 selects any two fractions on the game board. Then the player tosses the coin. If the coin lands heads up, the player finds the sum of the fractions. If the coin lands tails up, the player finds the difference.

Player 2 checks Player 1’s sum or difference. If it is correct, Player 1 writes an X in each box containing the fractions added or subtracted

Player 2 takes a turn and writes an O in each box.

The player who marks five Xs or five Os in row wins. If no more boxes can be marked, the player who marked more boxes is the winner.

1 _ 10

3 _ 5

7 _ 8

1 _ 4

4 _ 5

3 _ 4

1 _ 2

5 _ 12

1 _ 8

7 _ 20

5 _ 6

3 _ 8

1 _ 6

3 _ 10

1 _ 5

1 _ 12

2 _ 3

2 _ 5

5 _ 6

1 _ 2

5 _ 8

1 _ 4

7 _ 10

3 _ 8

1 _ 3

27

Chapter 10

10–5

Name ____________________________ Date ________________

Enrich Dr. Ken’s Computer Cures

Use the data from the advertisement to solve the problems. Explain your answers. —Dr. Ken’s Computer Cures— Repairs at Ken’s: \$49 per hour House calls: \$75 flat fee, plus \$79 per hour Web Site Design: \$55 per hour Computer Tutoring: \$40 per hour Network Design and Setup: \$65 per hour Home Computer Setup: \$200 1. On Monday, Dr. Ken’s schedule lists 3 home computer setups and 4 hours of Web site design. Dr. Ken estimates that he will earn \$1,000. Is his estimate reasonable?

3. The Computer Whiz charges \$46 per hour for Web site design. The Computer Whiz spends 22 hours designing a Web site for Regina. Regina estimates that she saved \$400 by using The Computer Whiz instead of Dr. Ken. Is Regina’s estimate reasonable?

4. Dr. Ken tutors a group of 3 people for 4 hours. He charges a group rate of \$32.50 per person per hour. Dr. Ken estimates that he earns \$200 more than he would have if he had tutored just one person for the same amount of time at his regular rate. Is his estimate reasonable?

32

Chapter 10

2. Dr. Ken makes a house call to Leah. He spends 3 hours fixing her computer. Leah estimates that her bill will be about \$315. Is her estimate reasonable?

10–6

Name ____________________________ Date ________________

Enrich Chapter Resources

Estimate Sums and Differences

Round each mixed number to the nearest whole number. Then find three paths of four parts each. The estimated sums and differences of the mixed numbers on the paths must match the estimates at the finish lines. Do not use a number more than once.

Start

Start

Start

7 6 ___ mi 10

9 5 ___ mi 20

9 _87_ mi

3 + 5 ___ mi 16

3 + 5 ___ mi 10

- 2 _83_ mi

11 - 1 ___ mi 12

3 - 4 ___ mi 20

9 + 7___ mi 10

11 + 8 ___ mi 16

+ 8 _52_ mi

1 + 3 _ mi 6

Finish

Finish

Finish

37

Chapter 10

Name

10–7

Date

Find the sums for the problems in the squares. Shade pairs of adjacent squares that have the same answer to find a path through the maze.

Start 7 3 48 + 8

1 1 216 + 1 8 5 7 28 + 28

1 3 2 16 + 3 16

5 5 68 + 18

7 5 2 16 + 5 16

7 3 18 + 78

5 5 3 12 + 12

4

1

7 + 1 10

4

13

+

9 10

1 7 3 20 + 1 20 1 1 22 + 12

1 1 46 + 2 6 7

13 9 2 16 + 2 16

7

2 10 + 1 10 5

3 9 1 16 + 1 16 7 3 3 16 + 1 16

2 10 + 2 7 1 1 12 + 1 12

5 5 16 + 6

42

11

4 2 3 6 + 13

3 16 1 5 + 2 20

1 16 + 2 16 9 10

11

3 12 + 3 12 4 2 26 + 33

4 1 6 16 + 7 4 13

1 10 + 8 5

1

3 20 + 2 5 9 10

8

14 7 1 20 + 1 10 3 9 3 10 + 1 10

16

110 + 1 5

18 3 2 20 + 5 10

1 5 3 16 + 2 16 5 5 16 + 16

Finish Chapter 10

11

4 8 5 5 + 2 20

3 7 3 8 + 18

1 7 10 + 2 11

9 17 4 20 + 2 20

1 3 3 20 + 2 20

1 12 + 1 12

1 11 2 16 + 4 16

13 7 8 16 + 16

5 5 2 12 + 2 12

7 9 2 20 + 1 20

14 7 4 16 + 1 8

1 17 4 20 + 2 20

7 7 48 + 2 8

15 13 4 16 + 16

3 1 39 + 33

10–8

Name

Date

Enrich Chapter Resources

Subtract Mixed Numbers Play this game with a partner. You will need a counter. • Together choose a whole number from 5 through 10. Write it in the square at that bottom right of the game board. Place your counter on Start. Then move it one square in any direction. Find the sum or difference of the numbers in the starting square and the square you moved to. If fractions don’t have like denominators, try using an equivalent fraction to find the sum or difference. Record it on a separate sheet of paper. • Players alternate turns. On each turn, move one square. Add or subtract the number in that square to or from your previous sum or difference and record your answer. You cannot return to a square. • The winner is the first player who reaches the target square with a sum or difference equal to the target number.

Start 1 2_ 2

1 1_ 6

5 3_ 8

1 2_ 8

1 4_ 2

1 1_ 3

1 3_ 4

2 2_ 5

2 1_ 3

1 1_ 4

4 1_ 5

1 2_ 4

2 3_ 3

7 1_ 8

1 3_ 2

7 1_ 10

1 1_ 2

5 2_ 6

3 1_ 4

3 1_ 8

2 _

5 _

3 _

3 _

1 1_ 2

3 2_ 10

1 _

1 _

1 _

3 _

1 5_

3 2_

1 _

1 _

1 _

Target Number

4

4

3

8

4

5

6

8

47

5

2

8

4

3

Chapter 10

10–9

Name

Date

Enrich Multi-step Problems

Solve. 1. The outer edge of a picture frame forms a square. The square picture frame has sides of 18 inches. The width of the frame is 1 inch. What is the area of the picture within the frame? Remember, area is found by multiplying length times width.

1 1 2. Sammy has a 42 _ - inch-long board. He cuts three 6 _ inch long 2 2 pieces of wood from the board. Does Sammy have enough wood left to make a 24 inch long shelf? Explain.

1 3. Theresa made a stack of cubes. Three of the cubes were _ inch 2 1 on each side. Three of the cubes were 1 _ inches on each side. 2 1 After Theresa removed a cube, the height of the stack was 4 _ inches. 2 Which kind of cube did Theresa remove?

4. Mark was paid \$10,000 to do some carpentry. He spent half of that money on suppplies and \$1,000 to pay a helper. How much money did Mark earn for himself?

52

Chapter 10

10–10

Name

Date

Enrich Chapter Resources

More Mixed Numbers Find a path through the maze. Shade the spaces that connect two equivalent numbers. (Hint: Rename fractions if you get stuck!)

2 3_ 5

1 4_ 4 5 3_ 9

7 2_ 5

19 20

15 _ 119 _ 1 3_ 4 12 _

3 3_ 10

1 7_ 2

18 _ 11 _ 3 3_ 5

27 _ 7 2_ 10

36 _

1 5_ 2

27 _ 100

4 1_ 5

51 _

10

3 5_ 10 5 2_ 11

57

5

53 _

20

1 5_ 5

18 _

53

1 10 _ 2

10

5 1_ 16

10 _

2

27 _

5

1 6_ 4

11 _

5

20

11 2_ 20

4

9 1_ 20 29 _

3

7 _

2

8

2 6_ 3

1 1_ 5

2

8

23 _

15 _

4

21 _

4

1 1_ 4

13 _

5

3 _

3

5 _

7 2_ 8 5 2_ 8

20 _

25

1 6_ 2

3 4_ 4

1 6_ 3 44 _

4

8

1 4_ 4

25

3 3_ 8 19 _

4

19 4_ 25

4

3 2_ 5

1 4_ 2 19 _

4_

3 3_ 4

3 3_ 4

3 3_ 5 3 3_ 10

Chapter 10

11–1

Name

Date

Enrich Measure It!

1. Measure the line segment below.

Refer to the line segment above to answer questions 2–6. 2. How long is a line segment that is twice as long? 3. How long is a line segment that is half as long? 1 4. How long is a line segment that is 1 _ inches longer? 2 5. How long is a line segment that is

1 _ inch shorter? 2

1 6. How long is a line segment that is 1 _ times as long? 2 7. Measure the line segment below. Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Refer to the line segment above to the answer questions 8–12. 8. How long is a line segment that is twice as long? 9. How long is a line segment that is half as long? 10. How long is a line segment that is

1 _ inch longer?

11. How long is a line segment that is

1 _ inch shorter?

2 2

12. How long is a line segment that is 3 times as long?

12

Chapter 11

11–2

Name

Date

Enrich Chapter Resources

Another Customary Unit The inch, foot, yard, and mile are the most commonly used customary units of length. Another customary unit of length is called a rod. Customary Units of Length 1 rod (rd) = 16.5 feet 1 rod = 5.5 yards 1 mile = 320 rods Complete. 1. 6 rd = 3. 22 yd =

5. 2 mi =

2. 9 rd =

yd

ft

4. 165 ft =

rd

rd

6. 880 rd =

rd

7. 750 rd =

mi

rd

9. 645 rd =

mi

ft

8. 20 ft =

mi rd

10. 8 rd 3 ft =

ft ft

11. For which object listed below could you use a rod to measure the length? Explain your reasoning. • big-screen T.V. • cruise ship • dog house

12. Which is a more reasonable estimate for the length of a bedroom: 1 rod or 4 rods? Explain.

13. The lengths of two skateboard ramps are shown in the table. Which ramp is the longer one?

Ramp A B

Length 2 rd 5 ft 40 ft

14. How many inches is 2.4 rods?

17

Chapter 11

11–3

Name

Date

Enrich Customary Length and Weight

Use what you know about customary units for measuring capacity and weight to complete the crossword.

Across Number of: B. inches in 5 feet

A B

C. feet in 24 yards 3 E. ounces in 5 _ pounds 4 1 F. inches in 12 _ feet 2 1 _ G. ounces in 3 pounds 8 7 _ H. ounces in 1 pounds 8 I. inches in 80 feet Down

C

D

E

F

G H I Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Number of: A. feet in 54 yards D. feet in 70 yards 1 E. pounds in 4 _ tons 2 1 _ G. pounds in ton 4 1 H. ounces in 2 _ pounds 4 How did you decide what clue to write for I Across?

22

Chapter 11

Date

Enrich Units of Capacity

Work with a partner. Cut out the 16 squares below. The object of the game is to be the first to arrange the smaller squares into a new larger square in which the measures that touch are equal to one another.

27

Chapter 11

Chapter Resources

11–4

Name

11–5

Name

Date

Enrich Time

Choose the best answer for each problem. Write the letter of your answer above the Exercise number at the bottom of the page to find out about a unit of time. 2. One million days is about

1. How many seconds are in 3 hours 5 minutes 30 seconds?

K. 3,000 months L. 19,000 months M. 2,700 years

N. 11,130 seconds O. 11,100 seconds P. 510 seconds 3. One million seconds is about

4. One million hours is about

.

R. 12 hours S. 12 days T. 12 months

6. 4 hours 22 minutes afer 6:48 A.M. is

.

8. Which time span is longest?

X. 12:05 A.M. Y. 12:45 A.M. Z. 12:45 P.M.

A. from 11:05 P.M. to 12:43 A.M. B. from 10:37 P.M. to 12:12 A.M. C. from 1:48 A.M. to 3:14 A.M.

9. The movie ended at 5:10 in the afternoon. If it lasted 1 hour 47 minutes, at what time did it start?

10. You are 3 years 8 months older than your friend. If your friend is 8 years 6 months old, how old are you?

S. 4:57 P.M. T. 4:23 P.M. U. 3:23 P.M.

5

J. 11 years 2 months K. 11 years 11 months L. 12 years 2 months

8

4

3

=1

2

6

32

10

10

5

1

1

6

9

2

Chapter 11

7. 2 hours 47 minutes after 9:58 P.M. is

.

I. 11:10 A.M. J. 11:00 A.M. K. 10:10 A.M.

C. 470 weeks D. 108 months 1 E. 4 _ years 2

7

.

Q. 1,114 months R. 114 years S. 1,114 years

5. Suppose you sleep an average of 9 hours each night. How long would you have slept by the age of 12 years?

1,000

.

Name

11–6

Date

Enrich Chapter Resources

Not Much Time Over the course of history, scientists have developed more and more accurate measurements of time. The Sun was first used to measure days. Then mechanical devices, such as pendulums, were used to measure hours, minutes, and seconds. In the twentieth century, atomic clocks, which are based on the vibrations of atoms, were developed. These clocks are so accurate that they do not gain nor lose a second in more than 60 million years! Units of time that are smaller than seconds are used in fields such as computer science and laser technology. Four of these units are listed in the table. Units of Time 1 1 1 1

second second second second

= = = =

1,000 milliseconds 1,000,000 microseconds 1,000,000,000 nanoseconds 1,000,000,000,000 picoseconds

Source: [email protected]

Use the table given above. 1. How many milliseconds are there in 1 minute? 2. How many nanoseconds are there in 1 millisecond? 3. How many picoseconds are there in 3 microseconds? 4. Light travels 186,000 miles in 1 second. About how many microseconds does it take light to travel 1 mile? 5. The time it takes a compter to locate a single piece of information for processing is called the access time. Compare the access times of the disk drive and DRAM chip described in the table.

Personal Computer Speeds Fastest Access Device Time disk drive 9 milliseconds DRAM chip 50 nanoseconds Source: webopedia.com

37

Chapter 11

Name

11–7

Date

Enrich Elapsed Time

The contiguous United States (all the states excluding Hawaii and Alaska) is divided into four time zones. The map below shows the time zones of the contiguous United States.

Pacific

Mountain

Central

Eastern

N E

W S

The time zones are one hour apart, with Eastern Time being the later time. So, when it is 6 A.M. in California, it is 9 A.M. in New York. From March to October most states go on Daylight Savings Time to save energy. During Daylight Savings Time, the clocks are set ahead 1 hour. However, Arizona and most of Indiana remain on Standard Time throughout the year. Solve. Use the map. 1. When it is 11:45 A.M. in Seattle, WA, what time is it in Boston, MA? 2. When it is 12:05 P.M. in Dallas, TX, what time is it in Reno, NV? 3. When it is 10:06 P.M. in Sacramento, CA, what time is it in Minneapolis, MN? 4. When it is 2:38 A.M. in Miami, FL, what time is it in Albuquerque, NM? 5. When it is 5:20 P.M. Daylight Savings Time in Denver, CO, what time is it in Phoenix, AZ? 6. Name two states that have more than one time zone. Grade 5

42

Chapter 11

Time Zones of the Contiguous United States

12–1

Name

Date

Enrich Explore Metric Length

Complete. Each square is 1 cm in length. Begin at Start. Move in the directions indicated in order and draw the distances along the grid. Do not lift your pencil off the paper until you finish. N W

E S

1. 105 mm West

7. 25 mm West

13. .57 mm East

19. 1 cm East

2. 6 cm North

8. 22 mm North

14. 45 mm North

20. 45 mm South

3. 7 mm East

9. 28 mm East

15. 1 cm East

21. 6 mm East

4. 2 cm North

10. 42 mm South

16. 5 mm South

22. 6 cm South

5. 23 mm East

11. 2 cm East

17. 24 mm East

23. 55 mm West

6. 20 mm North

12. 20 mm South

18. 5 mm North

12

Chapter 12

Start

12–2

Name

Date

Enrich Chapter Resources

Check for Reasonableness This diagram shows plans for part of a park. Use the diagram to decide if each estimate is reasonable. Explain your answers. Sample answers are given.

1. Sarah estimates that the spiral slide is about 4 feet high. Is her estimate reasonable?

2. The swing set area is covered by material that protects children from getting hurt if they fall. The swing set area extends 3 feet in each direction from the edge of the swing set. Howard estimates that the distance around the swing set area is about 108 yards. Is his estimate reasonable?

3. Roger estimates that the area of the sandbox is 70 square feet. Is his estimate reasonable? (Hint: Area of a rectangle = length × width)

4. The sandbox requires 2 cubic feet of sand for each square foot of area. Roger estimates that he needs about 200 cubic feet of sand for the sandbox. Is Roger’s estimate reasonable?

17

Chapter 12

12–3

Name

Date

Enrich Metric Mass

Camille has forgotten her locker combination. She asked Mr. Chen to write it out for her again and he did, but Mr. Chen wrote it in code. Mr. Chen’s note is printed below. Help Camille find out her locker combination. Circle the measurement in each column that is not equal to the others. Write the number, without the metric unit, on the blank below each column. Find the sums and the differences and you will soon have your locker combination. Good luck! RIGHT 1.5 g

4,000 g

37,500 mg

1,500 mg

400 kg

0.0375 kg

15 mg

4,000,000 mg

375 g

+

-

=

LEFT 16 mg

280 g

4,392 mg

1,600 g

280,000 mg

439.2 g

0.000016 kg

2,800 kg

0.4392 kg

+

-

=

left

RIGHT 26,000 mg

291 kg

5.7 kg

26 g

29.1 mg

570 g

2.6 kg

291,000 g

570,000 mg

+

-

=

right

The combination to Camille’s locker is Grade 5

.

22

Chapter 12

12–4

Name

Date

Enrich Chapter Resources

Cubic Conversions Did you know that 1 hollow centimeter cube will hold 1 milliliter of water? 1 centimeter cube 1 mL of water To find out how much water will fit in a container, find out how many centimeter cubes will fit in the container. Multiply the number of cubes in each layer times the number of layers. cubes in one layer ↓

×

number of layers ↓

(5 × 3)

×

4

15

×

4 = 60 cubes

The container will hold 60 centimeter cubes, so it will hold 60 mL of water. It has a capacity of 60 mL. Find the capacity of each container. Each cube represents a centimeter cube. 1.

2.

3.

Make a drawing of a container with each capacity. Let each cube in your drawings represent a centimeter cube. 4. 32 mL

5. 42 mL

6. 0.02 L

How did you decide what to draw for Exercise 5?

27

Chapter 12

12–5

Name

Date

Enrich Integers and the Number Line

Complete. Think carefully when you read statements that include the words and and or. (Hint: Think about how to compare whole numbers to help you compare integers.) Graph the integers that are greater than -5 and less than 3. -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0

1

2

3

4

5

6

7

8

9 10

7

8

9 10

Graph the integers that are greater than 3 or less than -5. -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0

1

2

3

4

5

6

Complete. Graph each set of integers. 1. Graph the integers that are greater than -1 and less than 10. -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0

1

2

3

4

5

6

7

8

9 10

2. Graph the integers that are greater than 0 or less than -3. 1

2

3

4

5

6

7

8

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0

9 10

3. Graph the integers that are greater than -9 and less than -2. -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0

1

2

3

4

5

6

7

8

9 10

4. Graph the integers that are greater than 4 and less than -4. -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0

1

2

3

4

5

6

7

8

9 10

5. Graph the integers that are greater than -6 and less than 6. -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0

1

2

3

4

5

6

7

8

9 10

6. What is another way to describe the integers that are greater than -6 and less than 6?

32

Chapter 12

12–6

Name

Date

Enrich Chapter Resources

Temperature Try to find a Fahrenheit temperature in Box B that is a close estimate of each Celsius temperature in Box A. When you find a match, cross out both numbers and the letters next to them.

To estimate converting from Celsius to Fahrenheit, use the equation F = 2°C + 32. Then estimate the Fahrenheit equivalent of the Celsius temperature in Box A and look for it in Box B.

Now write the letters that remain in each box. Unscramble each group of letters to spell a weather word. Box A Box B How did you find a close estimate in degrees Fahrenheit for 42°C?

37

Chapter 12

12–7

Name

Date

Enrich Check for Reasonable Temperatures

Mr. Romero’s class collected temperature data for a week. The students recorded the data in a table. Use the data to determine if each answer is reasonable.

High Temperature (°F)

Low Temperature (°F)

Sunday

19°

-3°

Monday

13°

-12°

Tuesday

15°

-11°

Wednesday

14°

-12°

Thursday

18°

-5°

Friday

20°

-2°

Saturday

22°

-1°

Day

2. Quincy calculated that the low temperature changed by -7° from

3. Andrea calculated that the change in the

4. Li calculated the range in the temperatures on Friday to be 18°F. Is

Wednesday to Thursday. Is his answer reasonable? Explain.

high temperature from Sunday to Monday was -6°. Is her calculation reasonable? Explain.

her calculation reasonable? Explain.

5. Jerome calculated the range in the temperatures for Monday to be 25°F. Is his calculation reasonable? Explain.

42

Chapter 12

1. Maria calculated the range in the temperatures recorded for Wednesday to be 26°F. Is her calculation reasonable? Explain.

13–1

Name

Date

Enrich Basic Geometric Ideas

Tell whether each statement is always, sometimes, or never true. A. To draw a polygon, you must draw at least three line segments. E. Lines are part of a ray. I. A line segment that connects two vertices of a polygon is a side. I. A polygon has more vertices than sides. L. A line segment is longer than a ray. N. Vertical line segments have the same length. N. You can measure the length of a line. O. A closed figure is a polygon. P. An octagon is larger than a pentagon. R. A hexagon has fewer sides than an octagon.

Y. A point on a line is the endpoint of two rays. Write the letters of the problems whose answer is always, sometimes, or never. Then unscramble each group of letter to form a math word. Answers always sometimes never Choose one statement above that is never true. Rewrite it so that it is always true.

12

Chapter 13

T. Congruent line segments have a common endpoint.

Name

13–2

Date

Use the Clues Addison, Camryn, Juliana, Miles, and Steven each drew a pair of lines listed at the right. They each drew a different pair. 1. Addison and Miles drew lines that do not have endpoints. 2. Cameron’s lines are in the same plane but never intersect.

• • • • •

Pairs of Lines congruent line segments intersecting lines parallel lines parallel line segments perpendicular lines

3. Juliana’s lines are neither parallel nor perpendicular. 4. Miles and Addison are friends with the person who drew lines that form right angles. 5. Addison’s lines cross at a point. A. Use the clues to fill out the table below.

Congruent Line Segments

Intersecting Lines

Parallel Lines

Parallel Line Segments

Perpendicular Lines

Addison Camryn Juliana Miles Steven B. Describe the pair of lines that each person drew. Addison: Camryn: Juliana: Miles: Steven:

17

Chapter 13

Chapter Resources

Enrich

13–3

Name

Date

Enrich Triangles

∠ABC is an interior angle. ∠HAB is an exterior angle.

H

I A

Use a protractor to measure all of the interior and exterior angles of this figure. Record the measures on the figure. Then look for patterns.

G B 1. ∠BAC and ∠HAI are vertical angles. They have the same vertex, but they have no common sides. One angle is an F interior angle, and one angle is an exterior angle. Name the other pairs of vertical angles that are interior and exterior angles.

C D E

What do you notice about the measures of the angles in each pair?

2. ∠BAC and ∠IAC are adjacent angles because they are next to each other. One angle is an interior angle, and one angle is an exterior angle. Name two other pairs of adjacent angles that are interior and exterior angles. Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

What do you notice about the measures of the angles in each pair?

3. Besides the pairs of angles you listed in problem 1, what other pairs of angles have equal measures?

4. For each exterior angle, find two interior angles whose measures together equal the measure of the exterior angle. ∠HAB

∠CBF

∠ACD What do you notice about these groups of interior and exterior angles?

22

Chapter 13

Date

Follow these steps to complete the diagram below. The circles represent different quadrilaterals. 1. Add the names of each of the following quadrilaterals to the appropriate circle. Parallelogram

Trapezoid

Rectangle

2. Write the letter of each property in the appropriate part of the diagram. A. sum of the measures of the angles is 360º B. four right angles C. exactly one pair of parallel sides D. four sides E. four congruent sides F. four congruent sides and four congruent angles G. opposite sides parallel

Rectange

Square

H. opposite sides congruent

Rhombus

How did you decide where to write the letter E in the diagram?

27

Chapter 13

Chapter Resources

13–4

Name

13–5

Name

Date

1. Complete the table below. 108°

115°

108°

60°

65°

65° 115°

72°

136°

72°

89°

75°

Sum of Angle Measures 2. Use the pattern in the table above to determine whether the value of x in the figure at the right is 40˚, 60˚, 80˚, or 100˚. Explain your reasoning.

x 100° 100° 100°

3.

x

90°

4.

85°

95°

5.

84° 112°

87°

90°

112°

105°

x

x

6.

x

50°

7.

8.

57°

42°

x

112° 108°

113° 60°

22.3°

120°

x

32

Chapter 13

Find the measure of each unknown angle.

Date

Enrich Tessellations

A tessellation is an arrangement of repeated shapes that covers an area without any gaps or overlaps. One way to make a tessellation is by translating shapes. Tessellation

Not a Tessellation

There are no gaps or overlaps.

There are gaps in the arrangement.

Tell where a tessellation can be made by translating each shape. If so, draw a sketch of the tessellation using at least six of the shapes.

1.

2.

4.

3.

5. Refer to the shapes above that do not form tessellations. Can the shapes be moved in other ways so that they form tessellations? Explain.

37

Chapter 13

Chapter Resources

13–6

Name

13–7

Name

Date

Enrich Another Type of Transformation

When a figure is translated, reflected, or rotated, the size and shape of the figure does not change. There is another type of transformation in which the size of the figure does change. This type of transformation is y called a dilation. Use the triangle graphed at the right. 1. Name the ordered pairs of the three vertices.

2. Multiply the x- and y-coordinates of each ordered pair by 2. Name the new ordered pairs.

18 16 14 12 10 8 6 4 2 0

2 4 6 8 10 12 14 16 18

x

y

3. Graph the triangle formed by the new ordered pairs on the coordinate grid at the right. 4. Compare the size and shape of the two triangles.

0

2 4 6 8 10 12 14 16 18

x

6. Compare the side lengths of the new triangle with the side lengths of the original triangle.

7. Write about dilations that you can find in everyday life. Describe whether the figures are enlarged or reduced.

42

Chapter 13

5. Refer to the original triangle. Divide the x- and y-coordinates of the ordered pairs by 2. Name the new ordered pairs. Then graph the triangle that is formed on the coordinate grid at the right.

18 16 14 12 10 8 6 4 2

Name

13–8

Date

Combining Transformations

You can transform a figure by combining translations, reflections, and rotations. Some examples are shown below. Rotation and Reflection Rotate triangle A 180° to get triangle B. Reflect triangle B over a line to get triangle C.

Translation and Rotation Translate pentagon A to get pentagon B. Rotate pentagon B 90° to get pentagon C.

Translation and Reflection Translate figure A to get figure B. Reflect figure B over a line to get figure C. This coombination is called a glide reflection.

9 8 7 6 5 4 3 2 1

9 8 7 6 5 4 3 2 1

9 8 7 6 5 4 3 2 1

0

A

B C 1 2 3 4 5 6 7 8 9

0

C B 90°

A

1 2 3 4 5 6 7 8 9

0

A C B

1 2 3 4 5 6 7 8 9

Describe the combination of transformations used. 1.

2.

9 8 7 6 5 4 3 2 1 0

3

1

2

1 2 3 4 5 6 7 8 9

9 8 7 6 5 4 3 2 1 0

3.

1

2 3

1 2 3 4 5 6 7 8 9

9 8 7 6 5 4 3 2 1 0

3 2

1

1 2 3 4 5 6 7 8 9

4. A triangle has vertices at (8, 2), (10, 5), and (7, 3). The figure is translated 1 unit left and 3 units up. Then it is reflected across a vertical line. Name the ordered pairs of the new triangle.

47

Chapter 13

Chapter Resources

Enrich

13–9

Name

Date

Enrich Transformations

Play this game with a partner. Cut out the triangles. Take turns. Each player places a triangle at the start position on the game board. • Toss a number cube. • Move the triangle following the rules in the table. The first player to reach the center of the game board wins.

Number of Tossed 1 or 4 2 or 5 3 or 6

Number of Spaces 1 2 1

Kind of Movement Translation Rotation Reflection

52

Chapter 13

14–1

Name

Date

Enrich Perimeter of Rectangles

Play this game with a partner. Take turns. How to Play • Toss two 1–6 number cubes. Use the two numbers rolled to form a 2-digit number. • If possible, draw a rectangle on the grid below that has as many units in its perimeter as the two-digit number rolled. Write your initials in it. Your rectangle may not overlap another rectangle. • When the number cubes have been rolled four consecutive times without a rectangle being drawn, the game is over. The player who draws more rectangles wins.

Describe a strategy you and your partner used to play this game.

12

Chapter 14

Date

Enrich Perimeter and Area of Irregular Figures

You are a landscape designer. Your most recent project is a yard that measures 40 meters by 50 meters. You will include the features below. • • • • •

an irregularly-shaped pond that is between 100 and 200 square meters an irregularly-shaped vegetable garden that is between 50 and 100 square meters an irregularly-shaped flower garden that is between 50 and 100 square meters fences for the gardens a patio that is between 200 and 300 square meters.

Sketch your design on the grid below. Include a scale that explains what each square represents.

How many feet of fencing do you need for the gardens? Explain how you found your answers.

17

Chapter 14

Chapter Resources

14–2

Name

14–3

Name

Date

Enrich Areas of Polygons

Graph the ordered pairs. Connect the points. Record the length, width, and area of the rectangle. 1. (2, 3), (2, 7), (9, 3), (9, 7)

2. (2, 1), (2, 8), (7, 1), (7, 8) y

y

9 8 7 6 5 4 3 2 1

9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 x

0

=

w=

A=

=

3. (6, 1), (6, 6), (1, 1), (1, 6) y

A=

y

=

w=

4. (9, 8), (9, 1), (1, 1), (1, 8)

9 8 7 6 5 4 3 2 1 0

1 2 3 4 5 6 7 8 9 x

0

9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 x

w=

0

=

A=

1 2 3 4 5 6 7 8 9 x

w=

A=

Compare the length and width of each rectangle to the coordinates you graphed.

22

Chapter 14

Name

14–4

Date

Enrich Chapter Resources

Three-Dimensional Figures Complete the table for these three-dimensional shapes.

Figure

Number of Faces

Number of Vertices

Total Faces and Vertices

Number of Edges

A B C

D E F G H Look for a pattern in the table above. Then complete this statement. The sum of the number of faces and vertices is equal to the number of plus

.

Let f = number of faces, v = number of vertices, and e = number of edges. Write the statement you completed above as an equation.

Write a formula for the number of edges.

27

Chapter 14

14–5

Name

Date

Follow the directions to solve the problem. You may use cubes. The rectangular prism to the right is made of 1-inch cubes. The prism is 2 inches wide by 4 inches long by 3 inches high. 1. What is the total surface area of the prism?

3. Draw a model that shows what the figure would look like if you removed cube C. How would the surface area of the cube change if you removed cube C?

4. Name a cube that could be removed to give a surface area of 56 square inches.

5. Cube a is behind cube A, cube b is behind cube B, cube d is behind cube D, and so on. Name a pair of cubes that could be removed to give a surface area of 50 square inches.

32

Chapter 14

2. Label the front layer of cubes. Use the capital letters A through D to label the cubes in the first row, E through H to label the cubes in the second row, and I through L to label the cubes in the third row. Then draw a diagram that would show what the figure would look like if you removed cube D. How would the surface area of the cube change if you removed cube D?

14–6

Name

Date

Enrich Chapter Resources

Volume of Rectangular Prism Rectangular prisms of different shapes can have the same volume. These rectangular prisms have different shapes, but the volume of both prisms is 24 cm3. The table below shows the volumes of different rectangular prisms. For each volume, write as many different sets of three numbers that could represent a rectangular prism with that volume. One has been started for you.

32 in.3 1, 1, 32

40 m3

60 cm3

72 mm3

What strategy did you use to complete the table?

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14–7

Name

Date

Enrich Surface Areas of Prisms

Suppose that your job is to design boxes for a gift manufacturer. You know the name of an item and its dimensions. Your job is to draw a box to fit the item. Then you have to draw its corresponding net. You need to label the dimensions on the box and net and tell the surface area of the box. When designing a box, you also need to follow these guidelines: • Boxes must be rectangular prisms. • Boxes should be as small as possible. • The dimensions of each box must be in whole numbers of inches to allow room for packing materials. • You do not have to be concerned about sides of the boxes overlapping. Design a box for each item. 5 1 1 Item 1: A pottery giraffe that is 11_ in. tall, 5_ in. long, and 2_ in. wide 4

2

Box

8

Net

Surface area: 5 3 Item 2: A pyramid-shaped paperweight 4_ in. tall with a 3_ in. square base 4

8

Box

Net

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Chapter 14

14–8

Name

Date

Enrich Chapter Resources

Choose an Appropriate Tool and Unit Solve. 1. A punch is made from 3 pints of orange juice and 1 pint of lemonade. a. Will the punch fit in a punch bowl with a capacity of 2 quarts? Explain.

b. Will the punch fit in a bowl with a capacity of 7 cups? Explain. 3 5 1 2. A box is 9 _ inches long, 6 _ inches wide, and 2 _ inches deep. 4 2 8 5 3 1 a. Will a model that is 1 _ inches tall, 6 _ inches wide, and 9 _ 2 8 16 inches long fit inside the box? Explain.

5 3 3 b. Will a model that is 2 _ inches tall, 9 _ inches long, and 6 _ 4 4 8 inches wide fit inside the box? Explain.

3. Luisa and Dolores are running in a 100-yard race. a. What is an appropriate unit of measurement and measurement tool to use to measure their race times? Explain.

b. Is it likely that their race times will be recorded to the nearest minute? Explain.

4. A 7-year-old child visits a doctor for a checkup. a. What is an appropriate unit of measurement and measurement tool to use to measure the weight of the child? Explain.

b. What is an appropriate unit of measurement and measurement tool to use to measure the height of the child? Explain.

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14–9

Name

Date

Enrich Perimeter and Area Problem-Solving

Solve. Explain how you found your solution. 1. Nick builds the box shown at the right. The top of the box is mahogany. The sides and bottom are pine. How much mahogany does Nick use?

10 in. 8 in. 5 in.

2. Jenny’s pool is surrounded by square tiles that are each 2 feet by 2 feet. She needs a cover for her pool. How many square feet must the cover be? Explain.

Each

is 2 ft by 2 ft.

20 m

15 m

2m

4. A garden covers 36 square feet. What is the least amount of fence that could be used to enclose a garden of this size?

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Chapter 14

3. The park to the right is a field of grass with a diagonal path that is made of gravel. Workers have put gates at each end of the path. The rest of the park will be surrounded by a fence. How many meters of fencing are needed?

2m

Name

15–1

Date

Enrich Explore Probability

1. Suppose you were to toss two number cubes and find their sum. Complete the table to show all the possible outcomes.

1

2

3

4

5

6

1 2 3 4 5 6 2. How many different outcomes are possible? 3. Is each outcome equally likely to happen? Explain.

5. Which sum is most likely to happen? 6. Conduct an experiment. Toss two number cubes and record their sum in the table below. Repeat 25 times.

Sum Tally Frequency

2

3

4

5

6

7

8

9

10

11

12

7. Do the results of your experiment match the results of problems 4 and 5? Why or why not?

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4. Which sums are least likely to happen?

15–2

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Date

Enrich Chapter Resources

Positive Spin Design a spinner for each set of clues. Divide each spinner into as few sections as possible. Write a color word, letter, or number in each section. 1. The probability of spinning yellow is

3 _ . Spinning red is

8 equally likely as spinning yellow. The event spinning red, yellow, or blue is certain.

2. The probability of spinning a letter in the word certain is 1 The probability of spinning a vowel is _.

7 _ . 10

2 Spinning an o is more likely than spinning an e. The probability of spinning a letter in the word record is

6 _ . 10

3. The probability of spinning a factor of 12 is certain. The probability of spinning a number that is neither prime 1 nor composite is _. 3 4 The probability of spinning a prime number is _. 9 Spinning an odd number is twice as likely as spinning an even number. The probability of spinning a multiple of 3 is

17

5 _ . 9

Chapter 15

15–3

Name

Date

Enrich Predict to Win

The goal of this game is to predict the number of times that a particular event will occur.

Players: 2 to 4

You will need: number cube marked with the numbers 1 to 6, 4 index cards

• Write each of the following on one of the four index cards. • Even number • Number less than 5 • Number greater than 1 • Number divisible by 3 • Make a table like the one below to record the outcomes. Outcome

Number of Times

Total

2 3 4 5 6

• Shuffle the cards and place them facedown on the table. • Turn over the top card. Each player predicts the number of times the event shown on the card will occur in 30 tosses of the number cube. • Toss the number cube 30 times and record the outcomes in your table. • Count the number of times that the event occurred. The player or players whose prediction was the closest gets 1 point. • Repeat using the other three cards. The player with the greatest score is the winner. Grade 5

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Name

15–4

Date

Enrich

When the spinner at the right is spun, there are 3 possible outcomes: red, blue, and orange. Suppose the spinner is spun twice. This is called a compound event. How many outcomes are possible?

R

Number of Outcomes of Spin 2 ×

3

Spin 1

Spin 2

R

R B O

RR RB RO

B

R B O

BR BB BO

O

R B O

OR OB OO

All Possible Outcomes =

3

9

So, there are 9 possible outcomes. You can check this by making a tree diagram.

Find the number of possible outcomes.

5

B 1

G

Outcomes

2. spinning the spinner and tossing a coin

1. spinning each spinner once

R

B O

The counting principle states that the number of possible outcomes in a compound event equals the product of the number of possible outcomes for each simple event. Number of Outcomes of Spin 1

Chapter Resources

The Counting Principle

2

4

O

1 3

2

4. tossing two number cubes numbered 1–6

3. choosing a shirt and pants from 4 different shirts and 3 different pants

5. Suppose the spinners in Exercise 1 are each spun once. What is the probability of spinning blue and 1?

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Name

15–5

Date

Enrich Compound Events

When one event does not affect another event, those events are called independent events. You can use multiplication to find the probability of a pair of independent events. What is the probability of spinning blue and B when you spin each spinner once? To find the probability of two independent events, multiply the probability of one event by the probability of the other event. P(blue) = P(B) =

1 _ 3

1 _ 4

1 1 1 ×_ P(blue, B) = _ =_ 4 12 3 1 _ . 12

The probability of spinning blue and B is

Complete. 1. P(vowel) = P(4) = P(vowel, 4) =

×

=

2. P(blue) = P(even) = P(blue, even) =

×

=

3. P(square) = P(4 or 5) = P(square, 4 or 5) = Grade 5

×

=

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