Math Work Sheet Library 6-8

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.

Square Roots
ANSWERS: (Page 80) 1. B, 2. E, 3. C, 4. G, 5. A, 6. H, 7. D, 8. F

Geometry: The Coordinate Plane
ANSWERS: (Page 80) 1. A, 2. G, 3. B, 4. F, 5. C, 6. H

Multiplication and Division of Fractions #1
ANSWERS: (Page 80) 1. C, 2. E, 3. D, 4. H, 5. A, 6. F, 7. B, 8. H

Converting Fractions to Decimals
ANSWERS: (Page 80) 1. C, 2. F , 3. A, 4. G, 5. A, 6. H, 7. D, 8. F

Home on the Range, Mean, Median, and Mode (number puzzles)

Converting Temperatures (number puzzles)

Daily Warm-up 31/32
Warm-Up 31: 1. B, 2. 26 baskets
Warm-Up 32: 1. 38, 2. D

Daily Warm-up 5/6
Warm-Up 5: 1. B, 2. D
Warm-Up 6: 1. 6 combinations; 2. vanilla, chocolate; vanilla, strawberry; vanilla, vanilla; chocolate, strawberry; chocolate, chocolate

Daily Warm-up 11/12
Warm-Up 11: 1. A. 450 cm2, B. 225 cm2, C. 675 cm2, 2. D
Warm-Up 12: 1. B, 2. Divide 2.4 by 4 to get the length. The length of each side will be 0.6 meters.

Daily Warm-up 43/44
Warm-Up 43: 1. A, 2. 25 x 3 x 5
Warm-Up 44: 1. D, 2. A. 4,366, B. 3,828, C. 5,850, D. 4,956

Daily Warm-up 7/8
Warm-Up 7: 1. D, 2. D
Warm-Up 8: 1. C, 2. C

Volume of a Rectangular Prism
ANSWERS: (Page 236) 1. 1,320 mm3, 2. 2,520 ft. 3, 3. 6,250 m3, 4. 30,000 cm3, 5. 36,960 in. 3, 6. 5,400 mm3, 7. 47.25 m3, 8. 32.55 cm3

Converting Fluid Ounces and Cups
ANSWERS: (Page 235) 1. 8 fl. oz., 2. 15 fl. oz., 3. 32 fl. oz., 4. 48 fl. oz., 5. 64 fl. oz., 6. 72 fl. oz., 7. 32 fl. oz., 8. 64 fl. oz., 9. 160 fl. oz., 10. 96 fl. oz., 11. 4 qt., 12. 16 qt., 13. 128 fl. oz., 14. 60 qt., 15. 1,920 fl. oz., 16. 16 fl. oz., 17. 48 fl. oz., 18. 112 fl. oz., 19. 40 pints, 20. 176 cups, 21. 120 pints, 22. 1,280 fl. oz., 23. 34 cups

ANSWERS: (Page 232) 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

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 and 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/review, 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)

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 (calendar, 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 sequence)
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: 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 (math review - 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 (probablity)

Algebraic Expressions (algebra, equations)

Improper Fractions (fractions, mixed fractions, number lines)
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 (area, geometry, word problems)
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%.

Algebra Word Problems (algebra, word problems, equations)