The math lessons below have been selected from the resources of Teacher Created Resources. (Click on the advertisement above for a complete catalog of Teacher Created Resources teacher-ready activities.) The lessons are arranged by grade; scroll down to find lessons for your level. Answer keys are provided below for lessons that require them.

Number Puzzles
ANSWERS: (Page 108) 

Add or Subtract (mathematical workouts)
ANSWERS: (Page 92) 
1. 2 + 4 + 2 + 2 - 3 = 7
2. 9 - 9 + 9 - 2 + 2 = 9 or 9 + 9 - 9 + 2 - 2 = 9
3. 5 + 5 + 5 - 4 - 3 = 8
4. 1 + 2 - 3 + 4 + 5 = 9
5. 7 + 6 - 2 - 3 + 8 = 16
6. 5 - 3 + 2 + 4 + 1 = 9
7. 5 + 1 + 1 + 3 + 4 = 14
8. 8 - 1 - 6 + 2 + 8 = 11
9. 2 + 1 + 8 + 9 - 3 = 17
10. 7 + 6 - 5 + 4 - 3 = 9
11. 6 + 5 - 2 + 1 - 2 = 8

Mathematics: Circles and Solids
ANSWERS: (Page 143) 1. C, 2. F, 3. A, 4. H, 5. C

Computation and Number Concepts
ANSWERS: (Page 140) 1. C, 2. H, 3. A, 4. F, 5. E, 6. G, 7. A, 8. F, 9. B, 10. H

Using a Pie Chart
ANSWERS: (Page 238) 1. Art Supplies: $2.00, Snacks: $3.00, Clothes: $4.00, Savings: $1.00, 2. $4.00, 3. $2.00 x 52 = $104.00, 4. 7 weeks

I've Been Framed!
ANSWERS: (Page 235) 1. (35 ÷ 5) x (27 ÷ 3) = 63, 2. (32 ÷ 4) x (49 ÷ 7) = 56, 3. (72 ÷ 9) x (24 ÷ 8) = 24, 4. (56 ÷ 7) x (64 ÷ 8) = 64, 5. (36 ÷ 6) x (35 ÷ 7) = 30

Multiplication Mystery Puzzle
ANSWERS: (Page 234) 1. 3,000, 2. 855, 3. 4,125, 4. 504, 5. 342, 6. 1,800, 7. 4,125, 8. 504, 9. 3,000, 10. 10,350, 11. 4,836, 12. 99, 13. 99, 14. 1,800, 15. 342,  16. 3,000,  17. 189,  18. 1,188,  19. 3,000,  20. 342,  21. 4,125,  22. 1,188,  23. 2,175,  24. 342,  25. 1,800,  26. 399,  27. 2,175,  28. 936, Answer: Sometimes rabbits just multiply.

More Work with Parallel and Intersecting Lines
ANSWERS: (Page 237) 

Dandy Division Squares
ANSWERS: (Page 236)
Square #1: Top Row: 16, Middle Row: 8, 2, Bottom Row: 4
Square #2: Top Row: 40, Middle Row: 60, 3, Bottom Row: 2
Square #3: Top Row: 50, Middle Row: 40, 4, Bottom Row: 5

Inching Along (measurement)
ANSWERS: (Page 233) 1. a, 2. b, 3. a, 4. c, 5. a, 6. b

Draw the Bars
ANSWERS: (Page 106)

Telling Time (telling time - hours)

Number Patterns (patterns, number sequence)
ANSWERS: (Page 10) Naming the Pattern. 1. 14, 16, 18, 20, 22; 2. 37, 39, 41, 43, 45; 3. 31, 33, 35, 37, 39; 4. Counting by 2's; 5. 30, 35, 40, 45, 50; 6. 86, 91, 96, 101, 106; 7. 62, 67, 72, 77, 82; 8. Counting by 5's; 9. 80, 90, 100, 110, 120; 10. 35, 45, 55, 65, 75; 11. 73, 83, 93, 103, 113; 12. Counting by 10's; 13. 200, 250, 300, 350, 400; 14. 280, 330, 380, 430, 480; 15. 760, 810, 860, 910, 960; 16. Counting by 50's; 17. 600, 700, 800, 900, 1000; 18. 410, 510, 610, 710, 810; 19. 575, 675, 775, 875, 975; 20. Counting by 100's; (Page 11) Identifying the Pattern. 1. already done; 2. balloon, cloud, A A B C D A A B; 3. snail, A B B C D D A B; 4. 2, 3, 4, A, AB, ABC, ABCD; 5. Patterns will vary. Labeling will vary.

Math Vocabulary (addition, subtraction, math vocabulary)
ANSWERS: (Page 10) 1. addends 123, 300, sum 423; 2. addends 160, 125, sum 285; 3. addends 407, 312, sum 719; 4. addends 525, 330, sum 855; 5. addends 222, 333, sum 555; 6. addends 709, 270, sum 979; 7. 227, 352; 8. 579. 9. 419, 560; 10. 979; 11. 255 + 400;= 655; 12. 158 + 511 = 669. (Page 11) 1. 321, 2. 311, 3. 600, 4. 241, 5. 311, 6. 321, 7. 749, 8. 210, 9. 539, 10. 428, 11. 310, 12. 118, 13. 567 - 246 = 321, 14. 821 - 301 = 520.

Estimation (estimating, measuring)

Using Graphs and Directions (graphing - coordinates, following directions)
ANSWERS: 1. pick and shovel--(4, 0). 2. palms form an X--(4, 2). 3. sand dollar--(2, 1). 4. pail and shovel--(1, 0). 5. beach umbrella and towel--(3, 3). 6. diver's mask and fins--(3, 4). 7. sandcastle--(5, 5); quicksand--(4, 4). 8. starfish--(5, 4); anchor--(5, 3). 9. rowboat--(1, 3). 10;treasure chest--(1, 2).

Math Concepts with Food (multiplication)

Writing Numbers-Expanded Form (division by 9, word problems)
ANSWERS: (Page 30) Answers will vary. (Page 31) 1. 300,000;+ 40,000;+ 2,000;+ 200;+ 10; 342,210. 2. 300,000;+ 40,000;+ 5,000;+ 10;+ 6; 345,016. 3. 500,000;+ 30,000;+ 200;+ 1; 530,201. 4. 700,000;+ 50,000;+ 900;+ 10;+ 1; 750,911. 5. 400,000;+ 70,000;+ 6,000;+ 800;+ 20; 476,820. 6. 100,000;+ 400;+ 30;+ 7; 100,437. 7. 800,000;+ 60,000;+ 1,000;+ 100;+ 90;+ 2; 861,192.

Measuring Weight (measuring, ounces/pounds, metric system)
ANSWERS: (Page 26) 1. 32; 2. 64; 3. 96; 4. 128; 5. 144; 6. 3; 7. 5; 8. 6; 9. 7; 10. 8; 11. 10; 12. lb.; 13. lb.; 14. oz.; 15. oz.; 16. lb.; 17. oz.; 18. oz.; 19. lb.; 20. oz.; 21. lb.; 22. oz.; 23. oz.; 24. oz.; 25. lb.; 26. oz. Challenge: Answers will vary. (Page 27) 1. 3,000; 2. 4,000; 3. 6,000; 4. 7,000; 5. 9,000; 6. 10,000; 7. 1; 8. 3; 9. 4; 10. 5; 11. 7; 12. 8; 13. 9; 14. kg; 15. g. 16. g; 17. g; 18. kg; 19. g; 20. g; 21. g; 22. kg; 23. g; 24. kg; 25. kg; 26. kg; 27. kg; 28. g. Challenge: Answers will vary. (Page 28) 1. .90; 2. 45; 3. 2.25; 4. 3.15; 5. 1.80; 6. 6.6; 7. 13.2; 8. 19.8; 9. 22.0; 10. 17.6.

Two-Digit Addition/No Regrouping (addition, following directions)

Shapes Activities (shapes, geometry, tangrams)

Nonstandard Measurement (measuring, comparing measurements)
ANSWERS:(Page 6) 1.-6. Answers will vary. 7. Yes, because I would need to use fewer fingers. (Page 7) 1.-10. Answers will vary. (Page 8) 1.-9. Answers will vary. 10. If my foot was longer than 12 inches, it would take fewer feet to measure items.

Counting Coins and Bills (money, graphing)
ANSWERS: (Page 30) 1. 3 quarters, 2 dimes, and 1 nickel (or) 2 quarters, 4 dimes, and 2 nickels; 2. 1 quarter, 7 dimes, and 1 nickel; 3. 1 half dollar, 1 quarter, and 5 nickels; 4. 2 half dollars; 5. 1 half dollar, 1 quarter, 2 dimes, and 5 pennies; 6. 10;dimes; 7. George Washington; 8. Andrew Jackson; 9. Abraham Lincoln; 10;Alexander Hamilton. (Page 31)

The graph would be completed as follows: Monday = $4.00; Tuesday = $7.00; Wednesday = $1.00; Thursday = $5.00; Friday = $2.00. 1. $1.56; 2. $5.25; 3. $3.35; 4. $4.30; 5. $2.80. 6. $2.99; 7. $5.75; 8. $2.35. (Page 32) 1. $4.00; 2. $7.00; 3. $1.00; 4. 5, $5.00; 5. 2, $2.00; 6. 19 magazines; 7. $19.00; 8. Tuesday.

Fact Familes (number facts, addition/subtraction)
ANSWERS: 1. 3 + 7 = 10; 7 + 3 = 10; 10;- 7 = 3; 10;- 3 = 7. 2. 4 + 9 = 13; 9 + 4 = 13; 13 - 9 = 4; 13 - 4 = 9. 3. 2 + 15 = 17; 15 + 2 = 17; 17 - 2 = 15; 17 - 15 = 2. 4. 6 + 11 = 17; 11 + 6 = 17; 17 - 6 = 11; 17 - 11 = 6. 5. 1 + 16 = 17; 16 + 1 = 17; 17 - 1 = 16; 17 - 16 = 1. 6. 5 + 13 = 18; 13 + 5 = 18; 18 - 5 = 13; 18 - 13 = 5. 7. +, -. 8. -, +. 9. +, + or -. 10. +, -. 11. -, +. 12. +, -. 13. 16 - 6 = 10;- 3 = 7 horses. 14. 6 - 3 = 3 more sheep. 15. 7 - 3 = 4 more horses. 16. 7 - 6 = 1 fewer sheep. 17. sheep + horses (6 + 7 = 13). 18. horses - sheep (7 - 6 = 1).

Graphs (estimating, graphing)

Identifying Fractions (simple fractions)
ANSWERS: 1. 1, 2, 3, 4, 5, 6; 2. one whole, one half, one third, one fourth, one fifth, one sixth; 3. 1/1, 1/2, 1/3, 1/4, 1/5, 1/6.

Drawing Word Problems (word problems)

Congrugent Parts (geometry, fractions)
ANSWERS:

Rounding Numbers (rounding numbers, place value, word problems)
ANSWERS: (Page 18) 1. 40; 2. 30; 3. 40; 4. 60; 5. 70; 6. 90; 7. 300; 8. 600; 9. 500; 10;600; 12. 800; 13. 900; 14. 8,000; 15. 8,000; 16. 4,000; 17. 6,000; 18. 9,000; 19. 2,000. (Page 19) 1. 40;+ 20;= 60; 60;children were invited to the party. 2. 150;+ 130;+ 210;= 490; Mariah bought 490;items in all. 3. 190;- 90;= 100; 100;people said "no." 4. 210;+ 320;+ 60;= 590; Lucy set out 590;jellybeans. 5. 570;- 240;= 330;- 200;= 130; The third cupcake had 130;sprinkles. 6. 220;+ 300;+ 370;= 890; 890;points were scored in all. 7. 60, 100, 130, 490, 590, 890. (Page 20) 1. H 300; 2. T 30; 3. Th 1,000;or H 1,100;or T 1,090; 4. T 10; 5. H 800;or T 820; 6. Th 2,000;or H 2,400;or T 2,370; 7. T 50; 8. Th 4,000;or H 4,000;or T 4,030; 9. Th 1,000;or H 700; 10. Th 6,000;or H 6,000;or T 5,960; 11. 100;+ 400;= 500. 12. 600;- 300;= 300; 13. 500;+ 300;= 800; 14. 900;- 800;= 100; 15. 500;+ 200;= 700; 16. 700;- 600;= 100; 17. 800;+ 100;= 900; 18. 500;- 400;= 100.

Adding and Subtracting with Charts (reading a chart)

Multiplication (simple multiplication)

Word Problems (word problems - addition, subtraction, multiplication, division)
ANSWERS: 1. multiplication, 1,224 Tooth Yankers; 2. division, 195 days; 3. subtraction, 926 Hard Rock Candies; 4. addition, 4,340;candies; 5. division, 400;munchies; 6. multiplication, 1,425 Super Sour Suckers.

Measuring With Rulers/Yardsticks (measurement - inches, feet, yards, meters)
ANSWERS: (Page 6) 1. 2 inches; 2. 1 1/2inches; 3. 2 inches; 4. 2 1/2 inches; 5. Answers will vary. 6. Answers will vary. 7. Answers will vary. 8. Answers will vary. (Page 7) Answers will vary. (Page 8) Answers will vary.

Probability (probability)
ANSWERS: Check students' answers. 1. yes; 2. no; 3. yes; 4. Answers will vary. 5. No. Each event is equally likely. 6. Answers will vary.

Long Division Rules (long division)
Note: This activity might require preteaching this lesson.
ANSWERS: (Page 32) 1. 88-Since the last digit of the dividend is an even number, 176 is divisible by the divisor 2. 2. 72-The last digit of the dividend is 0;so 360;is divisible by 5. 3. 42-The sum of the digits in the dividend adds up to 9, which is divisible by 3. 4. 44-The number formed by the last two digits of the dividend (76) is divisible by 4. 5. 129-The last digit of the dividend is 5 so 645 is divisible by 5. 6. 271-The sum of the digits in the dividend adds up to 12, which is divisible by 3. 7. 81-The number formed by the last two digits in the dividend (24) is divisible by 4. 8. 109-The last digit is an even number so 218 is divisible by 2. 9. 130-The number formed by the last two digits in the dividend (20) is divisible by 4. 10. 254-The sum of the digits of the dividend adds up to 15, which is divisible by 3. (Page 33) 1. 55-The last digit of the dividend is 0;so 550;is divisible by 10. 2. 54-The dividend is divisible by both 2 and 3. 3. 109-The sum of the digits in the dividend adds up to 18, which is divisible by 9. 4. 56-The dividend is divisible by both 2 and 3. 5. 17-The last digit of the dividend is 0;so 170;is divisible by 10. 6. 85-The sum of the digits in the dividend adds up to 18, which is divisible by 9. 7. 69-The dividend is divisible by both 2 and 3. 8. 86-The last digit of the dividend is 0;so 860;is divisible by 10. 9. 62-The sum of the digits in the dividend adds up to 18, which is divisible by 9. 10. 23-The last digit of the dividend is 0;so 230;is divisible by 10.

Multiplication Factors (multiplication, factors)
ANSWERS: (Page 38) Working with Common Factors. 1. 1, 2, 4. 2. 1 ,2. 3. 1, 5. 4. 1, 2, 4, 8. 5. 1, 2, 5, 10. 6. 1, 2, 3, 4, 6, 12. 7. 1, 2. 8. 1, 2, 4. 9. 6: 1, 2, 3, 6 10: 1, 2, 5, 10; CF: 1, 2. 10. 9: 1, 3, 9 18: 1, 2, 3, 6, 9, 18; CF: 1, 3, 9. 11. 12: 1, 2, 3, 4, 6, 12 16: 1, 2, 4, 8, 16; CF: 1, 2, 4. 12. 7: 1, 7 14: 1, 2, 7, 14; CF: 1, 7. 13. 10: 1, 2, 5, 10;30: 1, 2, 3, 5, 6, 15, 30; CF: 1, 2, 5. 14. 24: 1, 2, 3, 4, 6, 12, 24 30: 1, 2, 3, 5, 6, 15, 30; CF: 1, 2, 3, 6. 15. 32: 1, 2, 4, 8, 16, 32 16: 1, 2, 4, 8, 16; CF: 1, 2, 4, 8, 16. 16. 48: 1, 2, 3, 4, 6, 8, 12, 18, 24, 48 36: 1, 2, 3, 4, 6, 9, 12, 18, 36; CF: 1, 2, 3, 4, 6, 12, 18. 17. 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. 18: 1, 2, 3, 6, 9, 18 CF: 1, 2, 3, 6, 9, 18. 18. 18: 1, 2, 3, 6, 9, 18 12: 1, 2, 3, 4, 6, 12, 18; CF: 1, 2, 3, 6. 19. 6: 1, 2, 3, 6 12: 1, 2, 3, 4, 6, 12. 18: 1, 2, 3, 6, 9, 18; CF: 1, 2, 3, 6. 20. 9: 1, 3, 9 12: 1, 2, 3, 4, 6, 12; 24: 1, 2, 3, 4, 6, 8, 12, 24 1, 3. 21. 10: 1, 2, 5, 10;15: 1, 3, 5, 15, 25: 1, 5, 25; C.F. 1, 5. 22. 16: 1, 2, 4, 8, 16 24: 1, 2, 3, 4, 6, 8, 12, 24, 36: 1, 2, 3, 4, 6, 9, 12, 18, 36; C.F. 1, 2, 4. (Page 39) Working with Common Multiples. 1. 3: 3, 6, 9, 12, 15, 18/2: 2, 34, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24 CM: 6, 12, 18. 2. 4: 4, 8, 12,16, 20, 24/2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24 CM: 4, 8, 12, 16, 20, 24. 3. 6: 6, 12, 18, 24/8: 8, 16, 24; CM: 24. 4. 9: 9, 18, 27, 36 6: 6, 12, 18, 24, 36; CM: 18, 36. 5. 9: 9, 18, 27, 36/4: 4, 8, 12,16, 20, 24; CM: 36. 6. 12: 12, 24, 36/9: 9, 18, 27, 36; CM: 36. 7. 9:9, 18, 27, 36, 45, 54, 3: 3, 6, 9, 12, 15, 18; CM: 9. 8. 12: 12, 24, 36, 48, 60, 72, 10: 10, 20, 30, 40, 50, 60; CM: 60. 9. 10: 10, 20, 30, 40, 50, 60, 5: 5, 10, 15, 20, 25, 30; CM: 30. 10. 3: 3, 6, 9, 12, 15, 18/12: 12, 24, 36, 48, 60, 72; CM: 12.

Factors (multiplication, factors, equations)
ANSWERS: 1. 7; 2. 6; 3. 12; 4. 9; 5. 8; 6. 12; 7. 6; 8. 8; 9. 10; 10. 5; 11. 12; 12. 5; 13. 8; 14. 8; 15. 11; 16. 7; 17. 6; 18. 5; 19. 8; 20. 1; 21. 9; 22. 11; 23. 9; 24. 9; 25. 8; 26. 9; 27. 8; 28. 11; 29. 4; 30. 12; 31. 9; 32. 4; 33. 12; 34. 8; 35. 7; 36. 4; 37. 3 x 3; 38. 6 x 6; 39. 10;x 10; 40. 12 x 12; 41. 5 x 5; 42. 4 x 4; 43. 11 x 11; 44. 2 x 2; 45. 7 x 7.

Multiplication Properties (multiplication, commutative/associative properties)
ANSWERS: (Page 30) 1. 40; 2. 40; 3. 54; 4. 54; 5. 56; 6. 56; 7. 84; 8. 84; 9. 120; 10. 120; 11. 126; 12. 126; 13. 180; 14. 180; 15. 114; 16. 114; 17. 119; 18. 119; 19. 7,200; 20. 7,200; 21. 4,200; 22. 4,200; 23. 3,600; 24. 3,600; 25. 5,600; 26. 5,600; 27. 750; 28. 750; 29. 2,600; 30. 2,600; (Page 31) 1. 224; 2. 224; 3. 224 4. 72 5. 72 6. 72 7. 135 8. 135 9. 135 10. 450; 11. 450; 12. 450; 13. 1,680; 14. 1,680; 15. 1,680; 16. 1,680; 17. 630; 18. 630; 19. 630; 20. 630; 21. 7,920; 22. 7,920; 23. 7,920; 24. 7,920; (Page 32) 1. 120; 2. 120; 3. 504; 4. 504; 5. 48; 6. 48; 7. 252; 8. 252; 9. 135; 10. 135; 11. 24,000; 12. 24,000; 13. 189,000; 14. 189,000; 15. 120,000; 16. 120,000; 17. 60,000; 18. 60,000; 19. 8,750; 20. 8,750.

Multiplication Sequences (multiplication, number sequence, equations, exponents)
ANSWERS: Click here for the answer key.

Working Backwards to Solve Problems (word problems)
ANSWERS: (Page 14) 1. d. 2. g. 3. (given). 4. l; 9:00;a.m. - (15 minutes + 20;minutes + 35 minutes); 9:00;a.m. - 70;minutes, or 1 hour 10;minutes = 7:50;a.m. 5. c. 6. h. 7. (given). 8. l. Answer to question at top of page: 85 2 = 42.5, but page numbers go in order; pages 42 and 43. (Page 15) 9. d. 10. h. 11. k. 12. n. 13. b. 14. (given). 15. h. 16. k. Answers to questions at top of page: 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64 strawberries; 64 + 8 (taken out earlier) = 72 strawberries at the start. (Page 16) 17. d. 18. e. 19. i. 20. o. Answer to question at top of page: 3 trips with 10;cars + 2 trips with 6 trucks; 30;cars + 12 trucks = 42 vehicles.

Family Profile (math in real life)
You might want to use this lesson along with this activity.

Multiplying by 10 (multiplication, place value)
ANSWERS: (Page 18) 1. 140; 2. 160; 3. 450; 4. 650; 5. 190; 6. 170; 7. 220; 8. 370; 9. 380; 10;980; 11. 760; 12. 650; 13. 680; 14. 770; 15. 730; 16. 330; 18 350; 19. 530; 20;9,860; 21. 8,720; 22. 6,210; 23. 7,650; 24. 5,430; 25. 97,670; 26. 75,020; 27. 10,430; 28. 89,760; 29. 60,040; (Page 19) 1. 700; 2. 800; 3. 400; 4. 4,300; 5. 3,200; 6. 5,100; 7. 5,400; 8. 2,600; 9. 6,200; 10. 9,800; 11. 98,900; 12. 44,700; 13. 82,600; 14. 7,300; 15. 65,900; 16. 74,900; 17. 897,400; 18. 543,900; 19. 563,800; 20. 654,900; 21. 873,200; 22. 2,220,200; 23. 6,580,400; 24. 9,752,700; 25. 76,590,500; (Page 20) 1. 5,000; 2. 7,000; 3. 3,000; 4. 65,000; 5. 23,000; 6. 14,000; 7. 67,00; 8. 21,000; 9. 99,000; 10. 76,000; 11. 654,000; 12. 785,000; 13. 806,000; 14. 117,000; 15. 3,943,000; 16. 4,607,000; 17. 1,840,000; 18. 5,006,000; 19. 9,478,000; 20. 2,001,000; 21. 7,958,000; 22. 2,980,000; 23. 43,767,000; 24. 99,759,000; 25. 876,423,000; 26. 756,000,000.

Linking Addition/Multiplication (addition, multiplication)
ANSWERS: 1. 2 + 2 + 2 + 2 + 2 + 2 = 12; 2 x 6 = 12 or 6 x 2 = 12. 2. 3 + 3 + 3 + 3 + 3 + 3 + 3 = 21; 3 x 7 = 21 or 7 x 3 = 21. 3. 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 +1 + 1 + 1 + 1 + 1 + 1 = 14 or 8 + 6 = 14; 1 x 14 = 14. 4. 2 + 2 + 2 + 2 + 2 + 3 + 3 + 3 +1 + 1 + 1 + 1 + 1 + 1 = 25; (2 x 5) + (3 x 3) + (1 x 6) = 25. 5. 3 + 3 + 3 + 3 + 1 + 1 + 1 + 1 + 1 + 2 + 2 + 2 + 2 = 25; (3 x 4) + (1 x 5) + (2 x 4) = 25.

Collecting Data Internet Activity (statistics, graphing, integrating technology)

Word Problems With Patterns (word problems, patterns)
ANSWERS:

Calculating Measurements (measuring - temperature)
ANSWERS: 1. 32F; 2. 212F; 3. 42F; 4. 102F; 5. 10F; 6. 12F; 7. 4F; 8. 67F; 9. 42F; 10. 52F; 11. 72F; 12. 112F.

Two-Digit Multiplication (multiplication with regrouping)
ANSWERS: (Page 10) 1. 1,023; 2. 504; 3. 1,696; 4. 168; 5. 1,219; 6. 1,953; 7. 966; 8. 943; 9. 3,300; 10. 1,305; 11. 2,805; 12. 2,673; 13. 2,516; 14. 1,755; 15. 4,816; 16. 2,072; 17. 2,444; 18. 3,219; 19. 5,742; 20. 2,548. (Page 11) 1. 4,410; 2. 1,296; 3. 4,012; 4. 3,724; 5. 6,536; 6. 5,586; 7. 1,885; 8. 4,158; 9. 4,425; 10. 2,310; 11. 840; 12. 7,227; 13. 4,312; 14. 6,417; 15. 6,048; 16. 6,528. (Page 12) 1. 18,759; 2. 35,322; 3. 53,656; 4. 2,700; 5. 27,315; 6. 11,856; 7. 10,486; 8. 38,684; 9. 53,504; 10. 69,894; 11. 22,275; 12. 26,862; 13. 18,018; 14. 18,785; 15. 53,754; 16. 25,806.

Units of Time (telling time - hours/minutes, word problems)
ANSWERS: (Pages 6-8) 1. 6:10; 2. 10:15; 3. 12:05; 4. 1:20; 5. 6:50; 6. 7:20; 7. 8:30; 8. 11:25; 9. 6:20; 10. 6 days 1 hr; 11. 17 yrs 2 wks; 12. 1 day 4 hrs; 13. 2 wks; 14. 6 hrs; 15. 5:00; 16. 1:30; 17. 2 1/2 hrs; 18. 12:10; 19. 12:15 p.m.; 20. 2:20; 21. 50 mins; 22. 1:27; 23. 12 hrs; 24. 6 hrs 15 mins; 25. 5 hrs 45 mins; 26. 8 hrs; 27. 7 hrs 15 mins; 28. 1 hr 35 mins; 29. 60 mins; 30. 13 hrs 20 mins; 31. 4 hrs; 32. 24 days; 33. 60 beats per minute; 34. 7 hrs; 35. 12 mins; 36. 48 days; 37. 5 days; 38. 36 trips; 39. 7 hrs; 40. 15 hrs.

Coin Combinations (money, word problems)
ANSWERS:(Page 92) 1. 2 pennies, 1 nickel, 2 quarters; 2. 16 pennies, 1 nickel; 3. 1 penny, 2 dimes, 3 quarters; 4. 2 pennies, 2 nickels, 1 dime; 5. 4 pennies, 2 nickels, 1 quarter; 6. 3 pennies, 1 quarter, 1 half dollar. (Page 93) 1.1 penny, 2 nickels, 8 quarters or 1 penny, 1 half dollar, 5 quarters, 3 dimes, 1 nickel; 2. 3 pennies, 8 quarters, 2 half dollars; 3. 2 pennies, 10 dimes, 7 quarters, 1 half dollar; 4. 1 penny, 18 quarters; 5. 2 pennies, 4 nickels, 1 quarter, 7 half dollars; 6. 4 pennies, 1 dime, 2 half dollars, 12 quarters; 7. 10 dimes, 17 pennies; 8. 28 quarters, 1 dime, 3 nickels, 5 pennies.

Division (division by 9)
ANSWERS: (Page 8) 1. 31 R0 ; 2. 711 R0 ; 3. 509 R0 ; 4. 1,005 R0 ; 5. 402 R0 ; 6. 9,021 R0 ; 7. 801 R8 ; 8. 891 R0 ; 9. 606 R1 ; 10 491 R0 ; 11. 708 R2 ; 12. 507 R3 ; 13. 1,031 R0 ; 14. 306 R5 ; 15. 209 R0, 16. 1,016 R0; 17. 381 R0; 18 1,481 R0. (Page 9) 1. 137 pennies, 0 left over ; 2. 38 sq. ft. ; 3. 2,460 jelly beans, 3 left over ; 4. 3,706 sq. ft. ; 5. 3,819 kernels, 1 kernel ; 6. 7 cards, 5 cards ; 7. 8,481 marbles ; 24,646 cm ; 8. $12,345,679.

Estimating (estimating, multiplication, division)
ANSWERS: (Page 26) Actual Estimate 1. 19 R9 20; 2. 21 R22 20; 3. 22 R9 20 4. 34 R21 30; 5. 20 R21 20; 6. 222 R21 200. (Page 27) 1. 19 R9; 2. 22 R29; 3. 36 R9; 4. 31 R14; 5. 23 R25 6. 155 R11. (Page 28) 1. 304 R11; 2. 210 R4; 3. 310 R5; 4. 103 R60; 5.84; 6. 176 R24; 7. 110 R54; 8. 229 R40; 9. 217 R2; 10. 1141 R18; 11. 201 R55; 12. 997 R4.

Baseball Math (math practice, word problems, integrating technology)
ANSWERS: (Page 18) 1. 180 feet; 2. 180 feet; 3. 4 times longer; 4. 180 feet/360 feet = ; 5. 720 feet. (Pages 19-21) For Questions 1-4: Answers will vary depending on how many home runs each player hit in the previous year. 5. 5,280 feet in one mile. 6.16,285 home runs.

Time Zones (telling time, geography, word problems)
ANSWERS: (Page 17) 1. 8:00 a.m.; 2. 1:00 p.m.; 3. 1:00 p.m.; 4. 7:30 a.m.; 5. 6:00 p.m.; 6. EST; 7. 4 hrs ; 8. 6 1/2 hrs; 9. 12:00 p.m.; 10. 9:00 p.m.; 11. 10:00 p.m.; 12. 5:00 p.m.; 13. 5:00 p.m.; 14. 3:00 p.m.; (Page 18) 1. Wed. 10:00 a.m.; 2. Sat. 9:00 a.m.; 3. Sat. 7:00 a.m.; 4. Tues. 1:00 a.m.; 5. Fri. 1:00 a.m.; 6. Wed. 8:00 p.m.; 7. Thurs. 11:00 a.m.; 8. Fri. 6:00 p.m.; 9. Thurs. 5:00 p.m.; 19. Mon. 3:00 p.m.; 11. Fri. 11:00 p.m.; 12. Mon. 12:00 a.m.

Automobile Costs (math in real life)

Checking Accounts (math in real life)

Addition: Four-Digit Numbers (addition, math puzzles)

Extra Information in Word Problems (word problems)
Note: This activity can be used without page 21.
ANSWERS: (Pages 22-24) 1. d; 2. h; 3. i; 4. m; 5. c; 6. g; 7. (1,000 x 3/4) - 200 = 550; 8. j -- 3/4 of 1000 is 750 cars in on Tuesday. 750 cars - 200 compact cars = 550 standard-size cars ; 9. d; 10. f ; 11. (given); 12. j -- t (time) = 1.0 miles ,(distance) divided by 1/5 mile per min (rate) = 5 min; 13. b; 14. h; 15. i; 16. m; 17. b; 18. e; 19. i; 20. o -- If it costs 77 cents to produce 35 cars, then each car costs: 77/35 = 2.2 cents. It costs 2.2 cents to make each car. So 385 cars x 2.2 cents for each car = 847 cents, or $8.47 to produce 385 cars.

Computing Time (calendars - B.C./A.D.)
ANSWERS: (Page 35) 1. Feb./Mar.; 2. Ending in 29, the first month must be February.; 3. Feb. 19th; 4. Apr. 4th; 5. Mar. 18th; 6. 5; 7. 31 days; 8. 275 days; 9. Mar. 1; 10. December 26th; 11. April 23rd; 12. Monday. (Page 36) (dates as of year 2000) 1. 378 yr.; 2. 3,800 yr.; 3. 369 yr.; 4. 187 yr.; 5. 3,000 yr.; 6. 2,100 yr.; 7. 383 yr.; 8. 334 yr.

Decimals and Place Value (decimals, place value)
ANSWERS: 1. 0.345; 2. 0.2111; 3. 0.4563; 4. 0.08; 5. 0.6512; 6. 0.098; 7. 0.111; 8. 0.7612; 9. 0.005; 10. 0.3018; 11. 0.454; 12. 0.2107; 13. 0.078 ; 14. 0.1386; 15. 0.2; 16. 0.28292; 17. 21.532, 3.9854, 1.6453, 0.6521, 0.0076; 18. 18. 54.942, 1.23, 0.96435, 0.02, 0.0023; 19. 32.1, 4.8632, 4.86314, 0.7812, 0.77982; 20. 0.0932, 0.02632, 0.021001, 0.013751, 0.006321; 21. 11211.3, 1121.13, 112.113, 1.12113; 22. 89.654, 3.87439, 1.2397, 0.063418.

Order of Operations (equations, exponents, calculator)
ANSWERS: Check students' answers. 1. yes; 2. no; 3. yes; 4. Answers will vary. 5. No. Each event is equally likely. 6. Answers will vary.

Calculating Discounts and Sales (money, percents, discounts, math in real life)
ANSWERS: (Page 33) Sweetwater Train Fares 1. $1.75. 2. $2.60. 3. 57%. 4. $2.48; yes. 5. No, he needs 40 one-way tickets for 20 days, which will cost $70 versus a monthly pass for $47.25 6. No, four 10-ride passes cost $59.60 while a monthly pass costs $47.25. (Pages 34-35) Big Bill's Warehouse of Sales 1. He would pay $2.05 more on sale. 2. He charged $9.98. $1.99 more. 3. $419.90 extra. 4. $7,080.00 more. 5. $1,615.16 profit. 6. She will save $.04. 7. Big Bill cheated him out of $10.00. 8. $14,000.00. 9. $6,265.00. 10. $6,275.60. 11. 25% off $20 is $5. The drill costs $15. 30% off $22 is $6.60. The drill costs $15.40. Rick's offers the better savings. 12. $14,850.

Multiplication: Commutative Property (multiplication, commutative/associative properties)
ANSWERS: (Page 19) Commutative Property Activity Sheet. 1 and 2. 72; 3 and 4. 42; 5 and 6. 80; 7 and 8. 170; 9 and 10. 190; 11 and 12. 600; 13 and 14. 2,000; 15 and 16. 4,800; 17 and 18. 2, 800; 19 and 20. 2, 700; 21 and 22. 4, 200; 23 and 24. 4,125; 25 and 26. 1,125; 27 and 28. 1,541; 29 and 30. 714. (Page 20) Associative Property Activity Sheet. 1 and 2. 504; 3 and 4. 300; 5 and 6. 600; 7 and 8. 6,000; 9 and 10. 80,000; 11 and 12. 180,000; 13 and 14. 3,750; 15 and 16. 12,300; 17 and 18. 379,500; 19 and 20. 264,264.

Multiplication Exponents (number sequence, multiplication, exponents)
ANSWERS: (Page 34) Multiplication Sequences. 1. 64, 128, 256, 512; 2. 81, 243, 729, 2,187; 3. 108, 324, 972, 2,916; 4. 625, 3,125, 15,625, 78,125; 5. 256, 1,024, 4,096, 16,384; 6. 343, 2,401, 16,807, 117,649; 7. 47, 95, 191, 383, (a x 2) + 1; 8. 65, 129, 257, 513, (a x 2) - 1; 9. 284, 851, 2,552, 7,655, (a x 3) - 1; 10. 125, 253, 509, 1,021, (a x 2) + 3. (Page 35) Multiplying with Exponents. 1. 3 x 3 = 9; 2. 7 x 7 = 49; 3. 4 x 4 = 16; 4. 9 x 9 = 81; 5. 2 x 2 = 4; 6. 8 x 8 = 64; 7. 10 x 10 = 100; 8. 6 x 6 = 36; 9. 11 x 11 = 121; 10. 12 x 12 = 144; 11. 2 x 2 = 4, 4 x 2 = 8, 23 = 8; 12. 3 x 3 = 9, 9 x 3 = 27, 33 = 27; 13. 5 x 5 = 25, 25 x 5 = 125, 53 = 125; 14. 7 x 7 = 49, 49 x 7 = 343, 73 = 343; 15. 4 x 4 = 16, 16 x 4 = 64, 43 = 64; 16. 6 x 6 = 36, 36 x 6 = 216, 63 = 216; 17. 10 x 10 = 100, 100 x 10 = 1,000, 103 = 1,000; 18. 9 x 9 = 81, 81 x 9 = 729, 93 = 729. 19. 11 x 11 = 121, 121 x 11 = 1,331, 113 = 1,331; 20. 12 x 12 = 144, 144 x 12 = 1,728, 123 = 1,728.

Unusual Number Patterns (multiplication, patterns, palindromes, puzzles)
ANSWERS: (Page 132) 1. 1331; 2. 1661; 3. 2662; 4. 1881; 5. 1991; 6. 6. 2552; 7. 5995; 8. 3883; 9. 26862; 10. 268862; 11. 1356531; 12. 13688631; 13. 1551; 14. 15651; 15. 1368631; 16. 18981; 17. 135787531; 18. 48884; 19. 24442; 20. 1357997531. Extension: Answers will vary. (Page 133) Chart: 1; 121; 12321; 1234321; 123454321; 12345654321; 1234567654321; 123456787654321; 12345678987654321. Numbered examples: 1. Answers may vary. 2. Answers may vary. 3. Answers may vary. 4. 111,111,111; 5. 222,222,222; 6. 333,333,333; 7. 444,444,444; 8. 555,555,555; 9. 666,666,666; 10. 777,777,777; 11. 888,888,888; 12. 999,999,999; 13. A zero is added before the last digit. (Page 134) 1. 1600; 2. 1599; 3. 1596; 4. 1591; 5. 1584; 6. 1575; 7. 1564; 8. 1551; 9. 3600; 10. 3599; 11. 3596; 12. 3591; 13. 3584; 14. 3575; 15. 3564; 16. 3551; 17. given; 18. 31459, 126872, 278621, 405493; 19. 42176, 109300, 003901, 113201; 20. 54321, 66666, 66666, 133332. 21. - 24. Answers will vary.

Telling Time: Computing Elapsed Time (telling time - hours, minutes, seconds)
ANSWERS: (Page 40) 1. 3 hr. 15 min. 2. 3 hr. 45 min. 3. 2 hr. 30 min. 4. 4 hr. 45 min. 5. 3 hr. 35 min, 6. 6 hr. 25 min. 7. 2 hr. 30 min, 8. 6 hr. 30 min. 9. 2 hr. 15 min. 10. 1 hr. 5 min. 11. 2 hr. 30 min. 12. 5 hr. 30 min. 13. 2 hr. 15 min. 14. 4 hr. 10 min. 15. 3 hr. 16. 8 hr. 17. 7 hr. 18. 7 hr. 30 min. 19. 13 hr. 20. 10 hr. 45 min. Challenge: 18 hr. 16 min.

Prime Factors (multiplication, prime numbers)
ANSWERS: 1. 5, 2, 3; 2. 7, 2, 2; 3. 7, 2, 3; 4. 11, 2, 2; 5. 5, 2, 5; 6. 11. 2, 3; 7. 11, 7; 8. 7, 3, 3; 9. 3, 5; 10. 2, 3, 3; 11. 11, 2; 12. 2, 2, 3, 3; 13. 2, 2, 2; 14. 2, 2, 2, 2, 2; 15. 5, 5; 16. 5, 5, 5.

Calendar Computations (calendars, word problems)
ANSWERS: (Page 88) 1. 31 2. January, March, May, July, August, October, December; 3. February, April, June, September, November; 4. 5; 5. 4; 6. 5; 7. Mondays, Tuesdays, Wednesdays; 8. 3; 9. 19th, Friday; 10. 25th, Thursday; 11. 14th, Wednesday; 12. 5th, Monday. (Page 89) 1. April, June, September, November; 2. 28th, Friday; 3. 20; 4. 10; 5. Monday the 3rd; 6. Friday the 28th; 7. April; 8. 10th, Wednesday; 9. Thursday; 10. 23rd, Tuesday; 11. Answer will vary. 12. No, because February never has 30 days. (Page 90) 1. February; 2. No, they are not leap years and not evenly divisible by 400. 3. March, 21st; 4. January, 4th; 5. March, 25th; 6. 60th; 7. 306; 8. 2 or 3; 9. 15 or 16; 10. 2400, It is the only century evenly divisible by 400. Dates: Wed.-1, Thur.-2, Fri.-3, Sat.-4.

Roman Numerals (Roman numerals)
ANSWERS: (Page 88) 1. 1; 2. 4; 3. 6; 4. 10; 5. 3; 6. 5; 7. 8; 8. 12; 9. 7; 10. 9; 11. 15; 12. 13; 13. XXI; 14. XXII; 15. XXIII; 16. XXIV; 17. XXV; 18. XXVI; 19. XXVII; 20. XXVIII; 21. XXIX; 22. 30; 23. 26; 24. 33; 25. 35; 26. 29; 27. 38; 28. 39; 29. 34; 30. 37; 31. XLV; 32. XLIX; 33. XLVIII; 34. XLVII; 35. XVI; 36. XLVI; 37. XXVII; 38. XXXVII; 39. XXIX; 40. Answers will vary. 41. Answers will vary. 42. Answers will vary. (Page 89) 1. DI; 2. CIII; 3. CCCV; 4. LV; 5. LXXX; 6. LXXXIII; 7. CD; 8. IC; 9. LXVIII; 10. CC; 11. CI; 12. LXXV; 13. CIX; 14. CX; 15. CXI; 16. CXV; 17. CXXV; 18. CCX; 19. XL; 20. DC; 21. DCCC; 22. CCCXXXIII; 23. DLIII; 24. CMI; 25. 500; 26. 300; 27. 105; 28. 58; 29. 290; 30. 80; 31. 40; 32. 45; 33. 195; 34. 59; 35. 88; 36. 90; 37. 48; 38. 49; 39. 490. (Page 90) 1. 2000l 2. 2001; 3. 2005; 4. 1900; 5. 1800; 6. 1803; 7. 1912; 8. 1950; 9. 1983; 10. 1600; 11. 1718; 12. 1998; 13. MM; 14. MMI; 15. MMX; 16. MCM; 17. MCMLX; 18. MDCCC; 19. MCMX; 20. MCMXL; 21. MDCCCLXXXI; 22. MDCLIV; 23. MCDXCII; 24. MDLXXXVIII; 25. 5; 26. 10; 27. 50; 28. 100; 29. 500; 30. 1000; 31. 2000; 32. 300; 33. 1500; 34. 1700; 35. 3650; 36. 1666; 37. LXIII; 38. XCVII; 39. CC; 40. L.

Number Sequences (number sequence, Fibonacci)
ANSWERS: (Page 68) 1. (2, 4, 6, 8, 10, 12, 14, 16, 18); n + 2. 2. (1, 2, 3, 4, 5, 6, 7, 8, 9); n + 1. 3. (9, 13, 17, 21, 25, 29, 33, 37, 41); n + 4. 4. (6, 14, 22, 30, 38, 46, 54, 62, 70, 78); n + 8. 5. (5, 10, 15, 20, 25, 30, 35, 40, 45), n + 5. 6. (7, 10, 13, 16, 19, 22, 25, 28, 31); n + 3. 7. (40, 38, 36, 34, 32, 30, 28, 26); n - 2. 8. (132, 121, 110, 99, 88, 77, 66, 55); n - 11. 9. (98, 93, 88, 83, 78, 73, 68, 63, 58); n - 5. 10. (4, 10, 16, 22, 28, 34, 40, 46, 52); n + 6. 11. (1, 2, 4, 8, 16, 32, 64, 128, 256); n x 2. 12. (1, 3, 9, 27, 81, 243, 729, 2187); n x 3. 13. (3, 6, 12, 24, 48, 96, 192, 384); n x 2. 14. (1, 4, 16, 64, 256, 1024, 4096, 16384); n x 4. 15. (5, 15, 45, 135, 405, 1215, 3645); n x 3. 16. (1, 5, 25, 125, 625, 3125, 15625, 78125); n x 5. 17. (2048, 1024, 512, 256, 128, 64, 32, 16); n 2. (Page 69) 1. (2, 5, 11, 23, 47, 95, 191, 383); (n x 2) + 1. 2. (3, 10, 31, 94, 283, 850, 2551, 7654); (n x 3) + 1. 3. (1, 6, 26, 106, 426, 1706, 6826, 27306); (n x 4) + 2. 4. (1, 2, 7, 32, 157, 782, 3907, 19532, 97657);(n x 5) - 3. 5. (1, 4, 9, 16, 25, 36, 49, 64, 81); (counting numbers squared). 6. (1, 8, 36, 148, 596, 2388, 9556, 38228); (n x 4) + 4. 7. (4, 11, 32, 95, 284, 851, 2552, 7655); k (n x 3) - 1. 8. (1, 5, 33, 229, 1601, 11205, 78433, 549029); (n x 7) - 2. 9. (5, 13, 29, 61, 125, 253, 509, 1021); (n x 2) + 3. 10. (7, 15, 31, 63, 127, 255, 511, 1023, 2047); (n x 2) + 1. 11. (-10, -8, -5, -1, +4, +10, +17, +25, +34, +44); (add +2, +3, +4, etc.). 12. (27, 26, 24, 21, 17, 12, 6, -1, -9, -18, -28); (subtract 1, 2, 3, etc.). 13. (100, 90, 81, 73, 66, 60, 55, 51); (subtract 10, 9, 8, etc.). 14. (2, 3, 5, 7, 11, 13, 17, 19, 23, 29); (prime numbers). 15. (1, 8, 27, 64, 125, 216, 343, 512); (counting numbers cubed). 16. (-10, -5, +1, +8, +16, +25, +35, +46, +58); (add +5, +6, +7, etc.). 17. (-30, -20, -11, -3, +4, +10, +15, +19, +22, +24); (add +10, +9, +8, etc.). 18. (2, 5, 10, 17, 26, 37, 50, 65, 82, 101); (counting numbers squared +1). (Page 70) 1. (89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765); 2. 143; 3. 143; 4. (24, 39, 63, 102, 165), Sum: 429, Product: 11 x 39 = 429; 5. (56, 91, 147, 238, 385), Sum: 1001, Product: 11 x 91 = 1001; 6. (80, 130, 210, 340, 550), Sum: 1430, Product: 11 x 130 = 1430; 7. (45, 73, 118, 191, 309), Sum: 803, Product: 11 x 73 = 803; 8. (40, 65, 105, 170, 275), Sum: 715, Product: 11 x 65 = 715; 9. Answers will vary.

Common Multiples (lowest common multiples, lowest common denominators)
ANSWERS: Answer key on page 140 (see work sheet).

Mental Multiplication (thinking about math)
ANSWERS: 1. 832; 2. 1,080; 3. 700; 4. 960; 5. 922; 6. 1,150; 7. 2,300; 8. 1,755; 9. 4,200; 10. 2,900; 11. 1,900; 12. 3,350; 13. 3,400; 14. 3,900; 15. 2,200; 16. 1,550; 17. 1,200; 18. 2,300; 19. 600; 20. 2,050; 21. 189; 22. 288; 23. 558; 24. 387; 25. 504.

Word Problems (word problems - all operations, skills, concepts)
ANSWERS: (Pages 37-39) 1. 4 pieces. 2. 2 1/2 quarts; no. 3. $ 2.00. 4. a. $ .40, b. $ .50. 5. $609.44. 6. $417.30. 7. $90.62. 8. $19.33. 9. $56.55. 10. $1.26. 11. $0.04. 12. 16. 13. no; less (1/5). 14. Paul: $6.00, Todd: $7.25, Eli $5.00; total: $18.25. 15. $16.00; $32.00. 16. 12, 15, 3. 17. $31,250. 18. 35.95 inches. 19. 6 tries. 20. 489 divided by 6 equals 81 with a remainder of 3. He can sell 81 bunches, which would leave him 3 to sell at the regular price. 21. $6 per hour. 22. 35 lbs. per box. 23. 38 hours; $266. 24. b; $58. 25. d. 360 lbs. 26. 10 p.m. is 9 hours later. If the clock loses 3 minutes every hour, it will be 27 minutes behind or 9:33 p.m. when it is supposed to read 10 p.m. 27. Number of houses = $4,608/$256 per house = 18 houses. 28. $0.23 is spent on the peel. $1.80 - $0.23 = $1.57 on banana. 29. James spent $37.42; he saved $12.48. 30. Laurel paid $13.50 for the gift. Joey paid $9.00 for the gift.

Probabilities (probability)
ANSWERS: Answers will vary.

Algebraic Expressions (algebra, equations)

Improper Fractions (fractions, number lines, mixed fractions)
ANSWERS: (Page 64) 1. 4/3; 2. 12/11; 3. 6/5; 4. 9/4; 5. 7/7; 6. 7/3; 7. 6/2; 8. 8/2; 9.10/4; 10. 1; 11. 3; 12. 2; 13. 7; 14. 6; 15. 4; 16. 3; 17. 5; 18. 2; 19. 10/5; 20. 9/3; 21. 8/2; 22. 5/1; 23. 12/3; 24. 8/2.
(Page 65) 1. 5/2; 2. =; 3. 6/2; 4. 5/2; 5. 6/2; 6. 11/4; 7. 6/2; 8. =; 9. 12/4; 10. =; 11. =; 12. 11/4; 13. 1 1/4; 14. 1 1/2; 15. 2 1/3; 16. 2 2/3; 17. 2 1/4; 18. 1 2/5; 19. 1 3/4; 20. 2 1/2; 21. 1 1/2. (Page 66) 1. 2 1/4; 2. 4 1/2; 3. 3 1/3; 4. 1 1/7; 5. 2 2/5; 6. 3 1/4; 7. 1 1/9; 8. 1 1/3; 9. 1 1/6; 10. 2 4/5; 11. 3 1/2; 12. 3 3/4; 13. 3 4/5; 14. 1 2/7; 15. 2 1/7; 16. 1 1/3; 17. 1 1/2; 18. 2 1/2; 19. 1 1/2; 20. 3 1/2 21. 1 1/4; 22. 1 2/5; 23. 1 1/3; 24. 1 2/3; 25. 1 1/2.

Factorials (factorials, problem solving)
ANSWERS: (Page 32) Discuss and review students' responses. (Page 33) (Answers on the chart may be in different order.) RYBOG; RYBGO; RYOGB; RYOBG; ROYGB; ROYBG; ROGYB; ROGBY; ROBYG; ROBGY; 1. 120 possible arrangements; 2. 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720; 3. 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040. (Page 34) 1. 720; 2. 7 x 6 x 5 x 4 x 3 x 2 x 1, 5,040; 3. 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1, 40,320 4. 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1, 362,880; 5. 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1, 3,628,800; 6. 12 7. 3 x 2 x 1 x 4 x 3 x 2 x 1, 144; 8. 2 x 1 x 5 x 4 x 3 x 2 x 1, 240; 9. 6 x 5 x 4 x 3 x 2 x 1 x 3 x 2 x 1, 4,320; 10. 12; 11. 20; 12. 72; 13. 10; 14. 151,200; 15. 11,880.

Problem Solving Strategies (estimating, problem solving)
ANSWERS: (Page 30) 1. 6 tops/4 skorts; 2. 3 pennies, 3 nickels, 0 dimes, 3 quarters; 3. A. 1 penny, 0 nickels,4 dimes, 4 quarters, 0 half dollars, B. 1 penny, 4 nickels, 2 dimes, 0 quarters, 2 half dollars; 4. 6, 9, 12, 15, 18; 5. 300, 350, 400, 450, 500; 6. 3 footballs, 6 tennis balls, 3 baseballs, 2 basketballs; 7. Jack is 26 years old; Dad is 52 years old; 8. Marie is 22 years old; Mother is 44 years old. (Page 31) 1. $360.00; 2. 2,700; 3. 240 total-- 16 skirts, 32 jeans, 64 shorts, 128 blouses; 4. $372.00 total -- Elaine $12.00, Christina $24.00, Alyse $48.00, Doreen $96.00, Melissa $192.00; 5. James 2 years old, Raymond 3 years old, Brett 4 1/2 years old, John 6 years old, Robert 11 years old. (Page 32) 1. 3 hr. 2 min.; 2. 31 games; 3. 81 times; 4. 30 names; 5. 20 points on 8th game, 35 points on 14th game; 6. 35 players are 13 years old.

Perimeter and Circumference (perimeter, circumference, geometry)
ANSWERS: (Page 10) 1. 18.2 cm; 2. 26.2 cm; 3. 131/2 cm; 4. 161/2 ft.; 5. 151/4 in.; 6. 183/8 cm.; 7.-10. Answers will vary. (Page 11) 1. 15.6 cm; 2. 111/4 in.; 3. 24.4 m; 4. 183/4 ft.; 5. 74.4 m; 6. 64 yd.; 7. 137.4 cm; 8. 105.3 m; (Page 12) 1. 19.1 m; 2. 22.6 m; 3. 26 in.; 4. 201/2 ft.; 5. 25.12 m; 6. 37.68 in.; 7. 31.4 cm.

Perfect Numbers (factoring)
ANSWERS: (Page 72) 1. 1, 3, 7, 21, 1, 3, 7; 2. 1, 5, 25, 1, 5; 3. 1, 2, 3, 6, 9, 18, 1, 2, 3, 6, 9; 4. 1, 2, 4, 5, 10, 20, 1, 2, 4, 5, 10; 5. 1, 2, 4, 7, 14, 28, 1, 2, 4, 7, 14; 6. 1, 2, 4, 8, 16, 1, 2, 4, 8; 7. 1, 2, 3, 4, 6, 9, 12, 18, 36, 1, 2, 3, 4, 6, 9, 12, 18; 8. 1, 2, 4, 11, 22, 44, 1, 2, 4, 11, 22; 9. 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 123; 10. 1, 3, 9, 27, 81, 1, 3, 9, 27, 40; 11. 1, 2, 4, 5, 10, 20, 25, 50, 100, 1, 2, 4, 5, 10, 20, 25, 50, 117; 12. 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 259; 13. 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200, 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 265; 14. 1, 2, 7, 14, 49, 98, 1, 2, 7, 14, 49, 73. (Page 73) 1. 1, 2, 4, 5, 10, 22, abundant; 2. 1, 2, 4, 8, 15, defective; 3. 1, 2, 19, 22, defective; 4. 1, 2, 5, 10, 25, 43, defective; 5. 1, 2, 4, 8, 16, 32, 63, defective; 6. 1, 2, 3, 6, 9, 21, abundant; 7. 1, 2, 4, 5, 10, 20, 25, 50, 117, abundant; 8. 1, 2, 3, 4, 6, 9, 12, 18, 55, abundant; 9. 1, 2, 3, 4, 6, 8, 12, 16, 24, 76, abundant; 10. 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 259, abundant; 11. 1, 5, 25, 31, defective; 12. 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 222, abundant; 13. 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 108, abundant; 14. 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 144, abundant. (Page 74) 1. 1, 2, 4, 29, 58, 94, defective; 2. 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 568, abundant; 3. 1, 5, 19, 25, defective; 4. 1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 460, abundant; 5. 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 240, abundant; 6. 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 531, abundant; 7. 1, 2, 4, 8, 16, 31, 62, 124, 248, 496, perfect; 8. 1, 2, 4, 6, 8, 12, 24, 37, 74, 111, 148, 222, 444, 1093, abundant; 9. 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 2088, abundant; 10. 1, 2, 4, 5, 10, 20, 25, 50, 100, 217, abundant; 11. 1, 2, 3, 6, 83, 166, 249, 510, abundant; 12. 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 1921, abundant; 13. 1, 2, 4, 5, 10, 20, 25, 40, 50, 100, 200, 250, 500, 1207, abundant; 14. 1, 3, 9, 27, 37, 111, 333, 521, defective.

Prime Factors (factoring, prime numbers)
ANSWERS: (Page 52) 1. 1, 2, 3, 4, 6, 12, composite; 2. 1, 2, 7, 14, composite; 3. 1, 2, 4, 7, 14, 28, composite; 4. 1, 19, prime; 5. 1, 5, 7, 35, composite; 6. 1, 23:prime; 7. 1, 2, 11, 22, composite; 8. 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, composite; 9. 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, composite; 10. 1, 71, prime; 11. 1, 2, 4, 6, 7, 12, 14, 21, 42, 84, composite; 12. 1, 7, 13, 91, composite; 13. 1, 3, 9, 27, 81, composite; 14. 1, 13, prime; 15. 1, 2, 4, 5, 10, 20, 25, 50, 100, composite; 16. 1, 101, prime; 17. 1, 2, 3, 4, 6, 8, 12, 18, 24, 36, 48, 72, 144, composite; 18. 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300, composite; 19. 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360, composite; 20. 1, 2, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 144, 288, composite. (Page 53) 1. 2 x 32; 2. 23 x 3; 3. 22 x 32; 4. 22 x 7; 5. 22 x 3 x 5; 6. 23 x 32; 7. 24 x 32; 8. 22 x 33; 9. 24 x 33; 10. 33 x 37. (Page 54) 1. 4, x, y, z; 2. 5, 3, a, b; 3. 5, 4, a, b, c; 4. 9, x, y, z; 5. 3, 4, a, d, b, c; 6. 17, 12, n, p; 7. 12, 13, y, z; 8. 3, 2, 4, 5,a, b, x, y, z; 9. 3, 4, x, y, z; 10. 4, 5, 3, a, b; 11. 4, abc; 12. 9, xyz; 13. 19,xyz; 14. 23, abx; 15. 26,ab; 16. 15, adn; 17. 1, xy; 18. 4, abc.

Integers (integers, number lines, negative numbers)
ANSWERS: (Page 56) 1. -10; 2. -8; 3. +7; 4. -16; 5. -21; 6. -24; 7. -13; 8. +10; 9. +2; 10. -13; 11. -6; 12. -2; 13. +7; 14. -24; 15. -4; 16. -23; 17. +25; 18. -3; 19. -25; 20. -15; 21. -21. (Page 57) 1. +6; 2. -4; 3. +16; 4. -59; 5. +11; 6. -13; 7. -22; 8. +31; 9. -23; 10. -22; 11. -21; 12. -34; 13. -110; 14. -32; 15. -56; 16. -40; 17. +450; 18. -579; 19. +176; 20. -1; 21. -198. (Page 58) 1. -15; 2. +25; 3. -20; 4. -18; 5. -18; 6. -21; 7. -72; 8. +90; 9. +200; 10. -144; 11. +144; 12. -100; 13. +150; 14. +150; 15. -150; 16. +400; 17. -400; 18. -400; 19. +1,000; 20. +1,000; 21. -1,000.

Multiplying Decimals (multiplication, decimals, place value)
ANSWERS: (Page 27) 1. 2.7; 2. .14; 3. 4.338; 4. 1825.2; 5. 4121; 6. 6; 7. 150.9; 8. 10.625; 9. 1.628; 10. 31.88; 11. .056; 12. .00702; 13. .084; 14. 599.104; 15. 161.505; 16. 2.16408; 17. 56.088; 18. 48.708; 19. 7.616; 20. .18446; 21. 1.8; 22. 53; 23. 145; 24. .091; 25. 112.34; 26. .922; 27. 524.75; 28. 893,155; 29. 0.23; 30. 1679.45. (Page 28) 1. $93.96; 2. $4.47; 3. $105.30; 4. $69.93; 5. $53.38; 6. $420.52; 7. $585.39; 8. $256.50; 9. 2.646; 10. 1.872; 11. 2.6628; 12. 0.00228; 13. $6.30; 14. 4.78; 15. 137.74; 16. $1.38; 17. $8.37; 18. .1218.

Famous Mathematicians (math history)

Timelines (timelines)
ANSWERS: (Page 85) The age of the monuments will vary. c. 2750 B.C. -- Stonehenge c. 2600 B.C. -- Ziggurat at Ur; c. 2580 B.C. -- Pyramids at Giza; c. 2550 B.C. -- The Great Sphinx; c. 1333 B.C. -- Tutankhamun's Tomb; c. 960 B.C. -- Solomon's Temple; c. 600 B.C. -- Hanging Gardens of Babylon; c. 550 B.C. -- Temple of Artemis/Ephesus; c. 456 B.C. -- Statue of Zeus; c. 447 B.C. -- Parthenon at Athens; c. 353 B.C. -- Mausoleum at Halicarnassus; c. 292 B.C. -- Colossus of Rhodes; c. 283 B.C. -- Lighthouse at Alexandria; c. 214 B.C. -- Great Wall of China; 150 B.C. -- The Great Stupa at Sanchi, India; 7 B.C. -- The Roman Pantheon; B.C. ; A.D. ; 50 A.D. -- Aztec Pyramid of the Sun; 80 A.D. -- Colosseum in Rome; c. 730 A.D. -- Jaguar Temple at Tikal; 1067 A.D. -- Tower of London; 1150 A.D. -- Angkor Wat Temples; 1163 A.D. -- Cathedral of Notre Dame; 1339 A.D. -- The Kremlin in Moscow; 1599 A.D. -- Globe Theater in London; 1629 A.D. -- Taj Majal; 1662 A.D. -- Palace at Versailles; 1675 A.D. -- New St. Paul's Cathedral; 1703 A.D. -- Buckingham Palace; 1884 A.D. -- Statue of Liberty; 1889 A.D. -- Eiffel Tower; 1931 A.D. -- Empire State Building. (Page 86) The "Years Ago" calculation will depend on the current year. c. 8000 B.C. -- Agriculture was invented in Mesopotamia. c. 5000 B.C. -- Crop irrigation was invented in Mesopotamia. c. 3500 B.C. -- The potter's wheel was developed in Mesopotamia. c. 3500 B.C. -- The plow was invented in Mesopotamia. c. 3200 B.C. -- The Egyptians invented a form of ink. c. 3100 B.C. -- The Egyptians invented an early form of writing. c. 3000 B.C. -- The abacus was developed in China or Babylonia. c. 1800 B.C. -- The Babylonians developed multiplication tables. c. 1000 B.C. -- Scissors were invented in Europe and Asia. c. 1000 B.C. -- Kites were developed in China. c. 800 B.C. -- Coins were created in Near East. c. 700 B.C. -- The Chinese began keeping records of comets. c. 236 B.C -- Archimedes invented the Archimedean screw for lifting water from lower levels. B.C. A.D. c. 300 A.D -- Stirrups for riding horses were developed in China. c. 600 A.D. -- Chess was invented in India. c. 644 A.D. -- The windmill was developed in Iran. 868 A.D. -- The first printed book was made in China. c. 1000 A.D. -- Gunpowder was invented in China. c. 1040 A.D. -- Movable type for printing books was invented in China. c. 1280 A.D. -- Spectacles were developed in Italy. 1514 A.D. -- Plus (+) and minus (-) signs were first used. 1565 A.D. -- Pencils were designed by Gesner in Switzerland. c. 1608 A.D. -- Hans Lippershey of Holland built the first telescope. c. 1665 A.D. -- Isaac Newton discovered the universal law of gravitation. 1865 A.D. -- Louis Pasteur developed the germ theory of disease. 1879 A.D. -- Thomas Edison invented the first practical light bulb. 1903 A.D. -- The Wright brothers built and flew the first heavier-than-air plane. 1925 A.D. -- Television was invented by J. Baird of Scotland. Internet Links

Geometry Word Problems (geometry, word problems, area)
ANSWERS: (Page 22) 1. A. 314.5 sq. ft., B. 34.9 or 35 sq. yd., C. $698.00 or $700.00; 2. A. 185 sq. ft., B. 5 rolls, C. $125. 3. A. 244 3/8 sq. ft., 230 sq. ft., 244 3/8 sq. ft., 230 sq. ft., 425 sq. ft., B. 1,373 3/4 sq. ft. or 1,374 sq. ft., C. 4 gallons, $71.96. (Page 23) 1. A. 2,356 sq. ft., B. $23.56; 2. A. 200 ft., B. $6.00; 3. A. 1,116 sq. ft.. B. $11.16; 4. A. 34.54 ft., B. $1.04, C. 94.99 sq. ft., D. $0.95; 5. A. 643.75 sq. ft., B. $96.56; 6. A. 221 sq. ft., B. $39.78; 7. A. 37.68 ft., B.113.04 sq. ft.; Extension: Answers will vary. (Page 24) 1. 240 cartons; 2. 4,070 cu. ft.; 3. 25,688.34 cu. in.; 4. 1,417.95 cu. cm; 5. 370 cu. ft.; 6. 14,820 cu. ft.; 7. 162,887.5 cu. ft.; 8. 10,160,922 lb.; 9. 1,218,398.5 gallons; 10. 471 cu. in.; 11. 84,780 cu.ft.

Real World Math (math in real life, all operations)
ANSWERS: (Pages 29-31) Part I: 1. $8,400, no; 2. $4,080, yes; 3. $7,506.60, yes; 4. #2 and #3, $554.40; 5. $650.00; 6. $7,800/12 =, $650 x 12 =. Part II: 1. $360.00, Yes; 2. $288.00, Yes; Part III: 15% of her income is $675; 1. $3,150; 2. $5,400; 3. $25.00; 4. ($60.00 x 12) + 200 = $920.00; 5. $60.00. Part IV: (Yearly amount paid per bill) Electricity -- $144; Water -- $216; Gas -- $360; Master 1 Credit Card -- $180; Apex Credit Card -- $240. (Price per day) Sunday -- $6.82; Monday -- $5.22; Tuesday -- $2.52; Wednesday -- $2.40; Thursday -- $1.53; Friday -- $2.85; Saturday -- $2.40.

Geometry: Triangles (geometry, triangles, solving puzzles)
ANSWERS: (Page 29) 1. isosceles, acute; 2. obtuse, scalene; 3. right, scalene; 4. isosceles, acute; 5. acute, scalene; 6. isosceles, obtuse; 7. right, scalene; 8. obtuse, scalene; 9. obtuse, scalene. (Page 30) AGC (obtuse, scalene); BAG (acute, scalene); BAQ (scalene, right); QCB (scalene, obtuse).

Calculating Interest (money, interest, math in real life)
ANSWERS: (Page 39) 1. $45.00; 2. $45.42; 3. $10.00; 4. $30.00; 5. $135.00; 6. $73.75; 7. $19.90; 8. $9.12; 9. $298; 10. $54.08. (Page 40); 1. $42.29; 2. $196; 3. $16.20; 4. $0.25; 5. $1372.70. Chart: 1. 1/10, .10, 10%; 2. 1/4, .25, 25%; 3. 9/20, .45, 45%; 4. 3/20, .15, 15%; 5. 4/5, .80, 80%; 6. 5/6, .833, 83.3%; 7. 77//100, .77, 77%; 8. 1/20,.20, 20%; 9. 1/50,.222, 22%; 10. 2/5, .40, 40%.

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