school stops for summer—learning never...

5–6

Sum

mer B

ridge Math

RB

-904090

RB-904090

5–6

$8.95 U.S. Printed in the USA

Rainbow

Bridge P

ublishing

Education/Parenting

School Stops for Summer—Learning Never Should!

Bring the classroom home for the summer with Summer Bridge Math ! Summer is the perfect time to reinforce math skills and prepare for the grade ahead. Great in the car, at home, or on vacation, these engaging activities are designed to boost confi dence and bridge the summer-learning gap. Summer Bridge Math features curriculum-based activities, an assessment test, and an incentive contract that will encourage learning all summer long!

Skills Include:

• Addition and Subtraction • Fractions and Decimals • Multiplication and Division • Problem Solving • Time and Money • And Much More!

www.summerbridgeactivities.com

Includes Assessment Test!

RB-904090 Gr 5-6 CVR.indd 1 1/30/07 3:45:52 PM

Summer Bridge Math RB-904090 © Rainbow Bridge Publishing

How to Use This Book

Table of Contents

How to Use This Book . . . . . . . . . . . . . . . . . .2Assessment . . . . . . . . . . . . . . . . . . . . . . . . . .3Assessment Analysis . . . . . . . . . . . . . . . . . . . .5Incentive Contract . . . . . . . . . . . . . . . . . . . . . .6Numeration . . . . . . . . . . . . . . . . . . . . . . . . . .7Addition and Subtraction . . . . . . . . . . . . . . . .13Multiplication and Division . . . . . . . . . . . . . .21Time and Money . . . . . . . . . . . . . . . . . . . . .30

Measurement . . . . . . . . . . . . . . . . . . . . . . . .34Fractions and Decimals . . . . . . . . . . . . . . . . .40Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . .70Ratio and Percent . . . . . . . . . . . . . . . . . . . . .77Probability and Statistics . . . . . . . . . . . . . . . .81Problem Solving . . . . . . . . . . . . . . . . . . . . . .87

Answer Key . . . . . . . . . . . . . . . . . . . . . . . . .93

The Summer Bridge Math series is designed to help children improve their

mathematical skills during the summer months and between grades. Summer Bridge Math includes several extra components to help make your child’s study of

mathematics easier and more inviting.

For example, an Assessment test has been included to help you determine your

child’s mathematical knowledge and what skills need improvement. Use this test, as

well as the Assessment Analysis, as a diagnostic tool for those areas in which your

child may need extra practice.

Furthermore, the Incentive Contract will motivate your child to complete the

work in Summer Bridge Math. Together, you and your child choose the reward for

completing specific sections of the book. Check off the pages that your child has

completed, and he or she will have a record of his or her accomplishment.

Examples are included for each new skill that your child will learn. The examples

are located in red boxes at the top of the pages. On each page, the directions refer

to the example your child needs to complete a specific type of activity.

RB-904090 pgs. 1-48.indd 2 10/10/07 2:26:46 PM

3© Rainbow Bridge Publishing Summer Bridge Math RB-904090

Write the value of each underlined digit. A. 8,234 26,384 288,403 1,643,522 ________________ _________________ ________________ _________________

Estimate each sum or difference. B. 32 789 8,286 4,015 + 17 + 212 – 1,323 + 2,675

Solve. C. (12 + 8) – (4 + 12) = 8 + (7 – 3) = (10 + 2) +

D. 1,214 5,004 x + 4 =16 n – 8 =12 2,003 – 324 x = n = 468 + 92

E. $6.25 832 3,736 y x 3 = 27 36 ÷ j = 9 x 329 y = j =

Fill in each blank. F. 1 mile = _______ ft. 4,000 lbs. = _____ tons

G. 1 mile = _______ yds. 1 gal. = _________ qts.

H. 1 m = _________ dm 1 km = ________ m

I. 1 kg = _________ g 12 c. = ________ p.

Solve. Reduce or simplify if needed. J.

K. 23.14 44 3.2 0.46 82.8 + 1.006 – 0.17 x 4.6

Assessment

1 + 2 35

15

= 5 − 2 39

69

= 3 x 5 23

34

= 4 ÷ 1 13

12

=

RB-904090 pgs. 1-48.indd 3 10/10/07 2:26:46 PM

Draw an example of each figure. L. Line AB Segment ST Ray CD

Classify each angle as acute, right, obtuse, or straight.M.

Draw an isosceles triangle. Draw a right triangle. N. O.

Find the perimeter and area of the figure. Write the ratio in 3 different ways. P. P = _____ in.

Q. A = _____ sq. in

Find the mean, median, and mode for each set of data. Round to the nearest tenth. S. 2, 8, 6, 4, 5, 3, 2, 4 T. 45, 45, 70, 40, 60, 42, 42, 60, 42 mean = mean = median = median =

mode = mode =

Solve. U. The sixth graders at Jackson Elementary School read 682 books.

The rest of the school read 5,972 books. The students missed

their goal by 96 books. The goal was to read how many books? books

Assessment (continued)

Summer Bridge Math RB-904090

4© Rainbow Bridge Publishing

7 in.

4 in. R. 4 cats to 6 dogs

RB-904090 pgs. 1-48.indd 4 10/10/07 2:26:46 PM

5

Assessment Analysis

After reviewing the Assessment test, match the problems answered incorrectly

to the corresponding activity pages. Your child should spend extra time on those

activities to strengthen math skills.

Assessment Answer Key

Summer Bridge Math RB-904090© Rainbow Bridge Publishing

A B S T C D, ,

A. 200; 80; 200,000;

1,000,000

B. 50; 1,000; 7,000; 7,000 C. 4, 0

D. 3,777; 4,680; 12; 20

E. $2,056.25; 4 r408; 9; 4

F. 5,280; 2 G. 1,760; 4

H. 10; 1,000

I. 1,000; 6 J. 3⅘ , 3⅓ , 21¼ , 3⅜

K. 24.146; 43.83; 14.72; 180 L. M. right, straight, acute, obtuse

N. should have 2 equal sides

O. should have 1 right

angle P. 22 Q. 28

R. 4 6 ; 4:6; 4 to 6 S. 4.3; 4; 2 and 4 T. 49.6; 45; 42 U. 6,750 books

Diagnostic Problem

Review Section

Review Pages

A. Numeration 7–12

B., C., D. Addition and Subtraction 13–20

E. Multiplication and Division 21–29

F., G., H., I. Measurement 34–39

J., K. Fractions and Decimals 40–69

L., M., N., O., P., Q. Geometry 70–76

R. Ratio and Percent 77–80

S., T. Probability and Statistics 81–86

U. Problem Solving 87–92

RB-904090 pgs. 1-48.indd 5 10/10/07 2:26:48 PM

Numeration √

7 Place Value

8 Writing Numbers in Standard Form

9 Reading Expanded Notation

10 Changing the Place Value

11 Rounding Numbers

12 Order of Operations

Addition and Subtraction √

13 Addition with and without Regrouping

14 Number Puzzle

15 Rounding and Estimating

16 Solving Addition Equations

17 Subtracting with and without Regrouping

18 Subtracting Across Zeroes

19 Rounding and Estimating

20 Solving Subtraction Equations

Multiplication and Division √

21 Multiplying by a 1-Digit Number



24 Multiplication Properties

25 Solving Multiplication Equations

26 Dividing by a 1-Digit Number



29 Solving Division Equations

Time and Money √

30 Elapsed Time

31 Estimating Time

32 Multiplying Money

33 Dividing Money

Measurement √

34 Length in the Standard System

35 Length in the Metric System

36 Weight in the Standard System

37 Weight in the Metric System

38 Capacity in the Standard System

39 Capacity in the Metric System

Fractions and Decimals √

40 Writing Fractions

41 Greatest Common Factors

42 Simplifying Fractions

43 Least Common Multiples

44 Least Common Denominators

45 Comparing and Ordering

46 Improper Fractions and Mixed Numbers

47 Adding and Subtracting: Like Denominators

48 Adding and Subtracting: Unlike Denominators

49 Adding and Subtracting Mixed Numbers

50 Multiplying Fractions

51 Multiplying Fractions by Whole Numbers

52 Multiplying Whole Numbers by Mixed Numbers

53 Multiplying Fractions by Mixed Numbers

54 Multiplying Two Mixed Numbers

55 Reciprocals

56 Dividing by Fractions

57 Diving Mixed Numbers

58 Solving Equations with Fractions

59 Comparing and Ordering

60 Place Value

61 Writing Decimals in Standard Form

62 Rounding Decimals

63 Adding Decimals

64 Subtracting Decimals

65 Multiplying Decimals

66 Dividing Decimals

67 Dividing by Decimals

68 Changing Fractions to Decimals

69 Changing Decimals to Fractions

Geometry √

70 Plane Figures

71 Classifying Lines

72 Classifying Angles

73 Classifying Triangles

74 Classifying Quadrilaterals

75 Congruent and Similar Figures

76 Perimeter and Area

Ratio and Percent √

77 Writing Ratios

78 Equal Ratios

79 Understanding Percent

80 Finding the Percent of a Number

Probability and Statistics √

81 Chance and Probability

82 Finding Averages

83 Mean, Median, and Mode

84 Using Graphs

85 Circle Graphs

86 Tree Diagrams

Problem Solving √

87 Addition and Subtraction

88 Multiplication and Division

89 Time

90 Fractions

91 Decimals

92 Probability and Statistics

My

Incentive

Is:

My

Incentive

Is:

My

Incentive

Is:

My

Incentive

Is:

My

Incentive

Is:

My

Incentive

Is:

My

Incentive

Is:

My

Incentive

Is:

My

Incentive

Is:

My

Incentive

Is:

© Rainbow Bridge Publishing

Incentive Contract

RB-904090 pgs. 1-48.indd 6 10/10/07 2:26:49 PM


Study the chart below. The underlined digit 6 is in the hundred thousands place. So, it

has a value of 600,000.

F. Write two 12-digit numbers so that one is exactly 10 billion more than the other.

_____________________________________________________________________________

Place Value

Billions Millions Thousands Ones

Hu

nd

red

Billion

s

Ten

Billion

s

Billion

s

Hu

nd

red

Million

s

Ten

Million

s

Million

s

Hu

nd

red

Thou

sand

s

Ten

Thou

sand

s

Thou

sand

s

Hu

nd

red

s

Ten

s

Ones

5, 5 0 3, 6 7 3, 9 8 2

Study the example above. Then, write the value of each underlined digit.

A. 2,843 5,701 62,483____________________ ____________________ ____________________

B. 13,905 3,873,452 473,206,311____________________ ____________________ ____________________

C. 79,337 638,317 7,741,412____________________ ____________________ ____________________

D. 878,304 748,244,862 98,423,648____________________ ____________________ ____________________

E. 458,231 981,324,109 1,346,225______________________ ______________________ ____________________

numeration

RB-904090 pgs. 1-48.indd 7 10/10/07 2:26:49 PM


A. eight thousand five hundred sixty

B. fifty-three thousand twenty-four

C. nine million sixty-four thousand seven hundred one

D. sixteen million eight hundred ninety-four

E. thirty-six thousand two hundred seventy-five

F. five hundred six million three thousand two hundred

G. seventeen billion fifty-six million three hundred forty-one

thousand eighteen

H. twenty-eight million five hundred sixty-one thousand

one hundred twenty-two

I. seventy billion eight hundred sixteen million four

hundred twenty-one thousand six

J. four hundred thirteen billion seven hundred thirty-seven

million sixteen

K. nine hundred fifteen billion three hundred sixty-one million

eight hundred twenty-four thousand one hundred ninety-seven

L. five million eight thousand sixty-seven

M. twenty-eight million six hundred two thousand one hundred

forty-three

N. forty-one billion three hundred sixty-two million one

thousand sixty-six

O. one hundred million five hundred eighty-nine thousand

seven hundred thirty-four

_____________________

_____________________

_____________________

_____________________

_____________________

_____________________

_____________________

_____________________

_____________________

_____________________

_____________________

_____________________

_____________________

_____________________

_____________________

Writing Numbers in Standard Form numeration

sixteen thousand two hundred forty-three = 16,243Don’t forget to use a comma to separate each group of three digits.

Study the example above. Then, write each number in standard form.

RB-904090 pgs. 1-48.indd 8 10/10/07 2:26:51 PM


Study the example above. Then, circle the correct standard form of each number written in expanded notation. Use the space to the right of the problem to find the answer.

A. 7,000,000 + 100,000 + 8,000 + 300 + 20 718,032 7,108,320 7,018,032 71,832

B. 900,000 + 40,000 + 5,000 + 200 + 10 9,405,210 904,510 945,210 945,201

C. 1,000,000,000 + 200,000,000 + 10,000,000 + 5,000,000 + 70,000 + 700 + 8 1,215,070,708 1,201,537,708 1,215,070,780 1,210,537,708

D. 5,000,000 + 70,000 + 3,000 + 200 + 4 57,324 5,073,204 5,073,024 5,703,024

E. 600,000 + 50,000 + 1,000 + 800 + 20 65,182 605,182 651,820 650,182

F. 7,000,000,000 + 500,000,000 + 60,000,000 + 3,000,000 + 1,000 + 200 + 50 7,500,631,250 7,056,312,050 7,563,001,250 7,005,631,250

G. 3,000,000 + 900 + 80 + 6 3,986 3,000,986 3,009,806 39,086

9,000,000 + 800,000 + 3,000 + 100 + 90 + 2 = 9,000,000800,000

3,00010090

+ 29,803,192

Always align the place values to find the number.

Reading Expanded Notation numeration

RB-904090 pgs. 1-48.indd 9 10/10/07 2:26:51 PM


Study the example above. Then, change the digit indicated for each problem. Circle the amount that the entire number changed.

A. Change the 5 in 25,136 to 7.

How much more is the new number?

7 2 2,000 7,000

C. Change the 3 in 173,286 to 5.


200 2,000 20 2

E. Change the 6 in 4,358,617 to 2.

How much less is the new number?

40 4 400 2

G. Change the 2 in 207,314 to 8.


8,000 800,000 6,000 600,000

I. Change the 4 in 6,040,328 to 9.


5,000,000 500 90 50,000

K. Change the 7 in 37,951,086 to 8.


100,000 1,000,000 1 8,000,000

B. Change the 8 in 28,496 to 3.


5 8 5,000 3,000

D. Change the 2 in 6,200,436 to 5.


3 200,000 300,000 5,00,000

F. Change the 8 in 87,362 to 3.


5,000,000 5 3 50,000

H. Change the 6 in 860,429 to 1.


5 50,000 60,000 1

J. Change the 5 in 873,295 to 3.


2 20,000 30,000 5

L. Change the 7 in 47,625 to 8.


8,000 1,000 1 70,000

Changing the Place Value numeration

Change the 8 in 48,233 to 6. The new number is 46,233.

The number was decreased by 2,000.

RB-904090 pgs. 1-48.indd 10 10/10/07 2:26:51 PM


Study the example above. Then, round each number to the underlined place value.

A. 93 518 683 294

_________ _________ _________ _________

B. 3,642 4,560 5,970 36,751

__________ __________ __________ __________

C. 74,659 62,241 55,210 24,940

__________ __________ __________ __________

D. 67,005 51,998 592,034 301,650

__________ __________ __________ __________

E. 682,504 29,549 189,055 703,295

__________ __________ ___________ __________

Rounding Numbers numeration

137

140

Look to the right of 3. If that number is 5 or greater, round up. If not, keep

the number the same and change all of the numbers to the right to 0.

F. Would it make sense to round a friend’s phone number? Would it make sense to round the

age of an ancient piece of pottery? Explain. _________________________________________

______________________________________________________________________________

132

130

RB-904090 pgs. 1-48.indd 11 10/10/07 2:26:52 PM


A. 5 + 4 × 2 = ________

B. 8 – 2 × 3 = ________

C. 6 × 4 – 3 = ________

D. 6 + 10 ÷ 2 = _______

E. 5 × (3 + 4) = _______

F. 15 ÷ 3 + 2 = _______

G. (18 – 8) × 2 = ______

(5 + 4) × 2 = _______

4 + 8 ÷ 2 = ________

12 ÷ (3 + 1) = ______

(6 + 10) ÷ 2 = ______

4 + 5 × 2 = ________

15 ÷ (3 + 2) = ______

3 + (4 x 5) = ______

(8 – 2) × 3 = ______

6 × (4 – 3) = ______

12 ÷ 3 + 1 = _______

5 × 3 + 4 = ________

(6 + 3) × 1 = _______

18 – 8 × 2 = _______

(3 + 6) × 4 = _______

Order of Operations numeration

Study the example above. Then, solve each problem.

Order of operations:

1. Work inside the parentheses first.

2. Multiply left to right.

3. Next, divide left to right.

4. Add left to right.

5. Last, subtract left to right.

(13 – 3) × 4 13 – 3 × 4 10 × 4 13 – 12 40 1

RB-904090 pgs. 1-48.indd 12 10/10/07 2:26:52 PM


Page 7: A. 40; 700; 2,000;B. 5; 800,000; 70,000,000; C. 9,000; 600,000; 7,000,000 D. 300; 40,000,000; 20,000; E. 30; 900,000,000; 1,000,000; F. Answers

will vary.

Page 8: A. 8,560; B. 53,024; C. 9,064,701; D. 16,000,894; E. 36,275; F. 506,003,200; G. 17,056,341,018; H. 28,561,122; I. 70,816,421,006; J. 413,737,000,016; K. 915,361,824,197; L. 5,008,067; M. 28,602,143; N. 41,362,001,066;

O. 100,589,734

Page 9: A. 7,108,320; B. 945,210; C. 1,215,070,708; D. 5,073,204; E. 651,820; F. 7,563,001,250;

G. 3,000,986

Page 10: A. 2,000; B. 5,000; C. 2,000; D. 300,000; E. 400; F. 50,000; G. 600,000; H. 50,000; I. 50,000; J. 2; K. 1,000,000; L. 1,000

Page 11: A. 90; 500; 70; 290; B. 3,600; 5,000; 6,000; 37,000; C. 70,000; 62,000; 60,000; 24,900; D. 70,000; 52,000; 600,000; 300,000; E. 683,000; 30,000; 189,100; 700,000; F. No. Answers will vary.

Page 12: A. 13, 18, 18; B. 2, 8, 6; C. 21, 3, 5; D. 11, 8, 19; E. 35, 14, 9; F. 7, 3, 2; G. 20, 23, 36

: A. 67; 776; 1,164; 553; 1,446; 550; B. 794; 982; 1,262; 1,516; 535; 8,967; C. 2,119; 4,643; 4,339; 16,519; 5,691; 13,903; D. 11,601; 10,062; 10,756; 7,959; 10,322; 7,983; E. 66,344; 109,018; 42,402; 82,780; 96,057; 522,229; F. 117,142; 59,429; 33,171; 74,171;

71,391; 807,121

Page 14: Across: A. 675,339; B. 67,813; C. 68,128; D. 17,763; E. 29,993; F. 320,235; G. 91,728; H. 66,187; I. 870,513; Down: F. 39,827; J. 9,631; K. 12,863;

L. 86,994; M. 770,598; N. 593,615

Page 15: A. 50; 90; 80; 50; B. 400; 900; 7,000; 30,000; C. 900,000; 300,000; 700,000; 6,000,000; D. 160; 90; 160; 100; E. 300; 1,300; 1,000; 6,000; F. 130,000; 150,000;

4,000,000; 12,000,000

Page 16: A. 8, 4; 7, 11; 6, 8; B. 7, 8; 5, 15; 7, 9; C. y = 3, x = 16, v = 10, m = 6; D. c = 6, n = 12, h = 18, s =

16; E. a = 13, w = 9, g = 16, p = 18

Page 17: A. 123; 222; 314; 65; 614; 349; B. 401; 81; 188; 387; 397; 132; C. 7,273; 4,121; 1,900; 1,058; 437; 6,989; D. 8,530; 4,629; 7,801; 1,289;

1,491; 3,095

Page 18: A. 158; 2,032; 164; 2,709; 3,551; 1,624; B. 5,283; 1,749; 5,001; 3,923; 4,406; 3,500; C. 77,841; 56,154; 32,418; 87,568; 74,168; 28,452; D. 372,236; 771,172; 90,001;

192,853; 671,718; 533,334

Page 19: A. 100; 700; 400; 400; B. 400; 1,000; 3,000; 7,000; C. 7,000; 9,000; 7,000; 8,000; D. 0; 100; 200; 0; E. 300; 400; 200; 300; F. 4,000; 2,000; 1,000; 6,000;

G. 10,000; 10,000; 10,000; 10,000

Page 20: A. 6, 11; 8, 15; 8, 21; B. 25, 42; 62, 187; 20, 120; C. g = 56, x = 36, j = 26, m = 28; D. q = 115, r = 56, w = 64, z = 41; E. y = 167,

h = 25, a = 36, c = 107

Page 21: A. 425; 360; 116; 147; 434; B. 4,581; 844; 1,680; 5,598; 2,505; C. 2,896; 4,205; 1,611; 4,314; 5,679; D. 76,344; 40,502; 28,935; 39,132; 22,050

Page 22: A. 1,850; 1,888; 2,304; 3,416; 1,092; B. 2,112; 4,902; 5,952; 2,808; 3,325; C. 23,825; 16,872; 16,568; 39,704; 16,974; D. 205,179;

289,902; 157,534; 617,768; 391,902

Page 23: A. 290,322; 372,723; 572,286; 856,304; 260,766; B. 82,369; 332,762; 136,125; 236,572; 171,720; C. 39,449; 157,320; 380,328; 315,864; 750,339; D. 1,101,790; 1,210,808; 480,075;

385,985; 547,328

Page 24: A. 0, zero; B. 6, 3, 4, associative; C. 7, 8, commutative; D. 6, commutative; E. 7, 4, associative; F. 0, zero; G. 1, identity; H. 5, 9, associative; I. 241, identity; J. 9, 4, 9, 3, distributive; K. 3, 12, 3, 10, distributive

Page 25: A. 8, 9; 9, 9; 6, 7; B. 7, 5; 5, 10; 7, 8; C. x = 4, v = 4, h = 8, g = 3; D. n = 8, j = 2, t = 5, d = 10;

E. b = 4, f = 17, c = 12, r = 13

Page 26: A. 867, 422, 112 r2, 113 r4, 201 r2; B. 211 r4, 270 r4, 913 r1,512 r2, 708 r2; C. 311 r7, 712 r1,

650 r1, 214 r1, 214 r1

Page 27: A. 18 r29, 22 r19, 260 r9, 31 r23; B. 222 r8, 252 r3, 42 r3, 122 r61; C. 96 r7, 50 r47, 2,333 r1,

2,025 r43

Page 28: A. 6, 8, 7, 4 r441; B. 70 r101, 7 r6, 34 r72, 273 r89; C. 309 r10, 501 r18, 274 r160,

400 r78

Page 29: A. 9, 36; 8, 56; 4, 64; B. 18, 450; 16, 384; 12, 180; C. b = 49, p = 24, t = 63, j = 42; D. c = 50, g = 36, y = 1,875, s = 242; E. w = 918, k = 540, d = 492,

z = 464

Page 30: A. 3:35, 7:50, 11:10; B. 4:45, 10:25, 3:00; C. 7:40 P.M., 8:30 A.M.; D. 12:40 P.M., 9:55 A.M.; E. 4:00 P.M., 5:20 A.M.; F. 4:30 P.M.,

12:00 P.M.

Page 31: A. 10:00 A.M., 8:00 A.M., 9:00 A.M.; B. 3:00 P.M., 1:00 P.M., 10:00 A.M.; C. 1:00 P.M., 7:00 A.M.,

8:00 A.M.

Page 32: A. $34.65, $38.10, $66.78, $79.36; B. $123.84, $231.48, $278.18, $273.84; C. $527.52, $516.78, $394.20, $680.45; D. $1,094.16, $1,970.46, $1,529.88, $2,921.92; E. $3,027.22, $2,821.50,

$6,073.74, $9,704.32

Page 33: A. $2.03, $2.52, $3.81, $3.26; B. $5.28, $4.95, $5.28, $8.11; C. $5.56, $10.08, $8.23, $8.65; D. $24.55, $17.01, $12.41, $17.65;

E. $32.37, $59.88, $93.23, $165.79

Answer Key

RB-904090 pgs. 49-96.indd 93 10/10/07 2:31:02 PM

school stops for summer—learning never...

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