Parrot Fire Kris Northern
InvestigationsIN NUMBER, DATA, AND SPACE®
“ Rather than zoom into the fractal you can zoom into the edge of it and continually fi nd the same pattern repeating itself much like the shoreline of a lake viewed from a plane.”– Kris Northern Student Activity Book
ANSWER KEY
UNITS 1–9
GRADE
5
Created by Pearson to supplementInvestigations in Number, Data, and Space®
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Unit 1 | Number Puzzles and Multiple Towers 1
Page 11. Answers will vary.
Sample answer: 8
2
4
8
Students should list multiples of 2.
2. Answers will vary.
Sample answer: 30
5
6
30
Students should list multiples of 5.
3. Answers will vary.
Sample answer: 7
177
Students should list prime numbers.
Page 24. Answers will vary.
Sample answer: 16
4
4
16
Students should list square numbers.
5. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
6. 4, 9, 16, 25, 36, 49, 64, 81, 100
Page 31. 1, 2, 3, 6, 7, 14, 21, 42
2. Answers will vary.
Sample answer: 42, 84, 126, 168, 210
3. Explanations will vary.
4. B5. B
Page 41.–3. Answers will vary.
Sample answers:
1. 5 x 6 = 30
2. 5 x 8 = 40
3. 8 x 8 = 64
Page 51. Answers will vary.
Sample answer: 12
2
6
124
3
12
Students should list multiples of 4.
Page 62. Answers will vary.
Sample answer: 24
3
8
24 4
6
24
Students should list multiples of 12.
3. Answers will vary.
Sample answer: 100
20
5
100
25
4
100
Students should list multiples of 100.
UNIT 1: NUMBER PUZZLES AND MULTIPLE TOWERS
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2 INVESTIGATIONS Answer Key
Page 7Review students’ work.
1,897
Page 8
✔ Puzzle Answer
✔ 1 16
✔ 2 24
✔ 3 20, 40
✔ 4 1, 3
✔ 5 150
✔ 6 120, 240
✔ 7 36
✔ 8 ★ 6, 14
✔ 9 ★ Impossible
✔ 10 ★ 350
✔ 11 ★ 99
✔ 12 ★ 154
✔ 13 2, 7
✔ 14 12
Page 9Table A: 14, 42, 56, 21, 70, 77, 49, 84, 28, 63, 35
Table B: 16, 72, 32, 88, 64, 80, 48, 40, 24, 96, 56
Table C: 60, 24, 12, 48, 18, 36, 54, 30, 72, 66, 42
Table D: 45, 18, 108, 36, 90, 63, 27, 54, 99, 72, 81
Page 10Answers will vary.
Page 111. 12
2. Answers will vary.
3. B
Page 121. Two factors:
18: 1 x 18; 2 x 9; 3 x 6
180: 1 x 180; 2 x 90; 3 x 60; 4 x 45; 5 x 36; 6 x 30; 9 x 20; 10 x 18; 12 x 15
Combinations with more than two factors will vary.
Prime factorizations:
18 = 2 x 3 x 3
180 = 2 x 2 x 3 x 3 x 5
2. Explanations will vary.
Page 131. 1, 2, 3, 4, 6, 9, 12, 18, 36
2. 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
3. All of the factors of 36 are also factors of 72.
4. B
Page 14Table A: 21, 42, 63, 14, 28, 70, 56, 84, 35, 49, 77
Table B: 16, 56, 24, 40, 48, 80, 64, 88, 96, 32, 72
Table C and Table D: Answers will vary.
Page 151. Two factors:
12: 1 x 12; 2 x 6; 3 x 4
120: 1 x 120; 2 x 60; 3 x 40; 4 x 30; 5 x 24; 6 x 20; 8 x 15; 10 x 12
Combinations with more than two factors will vary.
Prime factorizations:
12 = 2 x 2 x 3
120 = 2 x 2 x 2 x 3 x 5
2. Two factors:
21: 1 x 21; 3 x 7
210: 1 x 210; 2 x 105; 3 x 70; 5 x 42; 6 x 35;
7 x 30; 10 x 21; 14 x 15
Combinations with more than two factors:
21: none
210: 3 x 7 x 10; 2 x 3 x 5 x 7
Page 161. 1, 2, 4, 5, 10, 20, 25, 50, 100
2. 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
3. Answers will vary.
4. D
Page 17Table A: 54, 24, 42, 30, 48, 18, 72, 12, 66, 36, 60
Table B: 32, 40, 24, 16, 48, 80, 56, 96, 64, 32, 72
Table C and Table D: Answers will vary.
Page 191.–3. Review students’ work.
Explanations will vary.
Page 204. 120 = 2 x 2 x 2 x 3 x 5
180 = 2 x 2 x 3 x 3 x 5
210 = 2 x 3 x 5 x 7
5. No
Explanations will vary.
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Unit 1 | Number Puzzles and Multiple Towers 3
Page 211. 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
2. Answers will vary.
Sample answer: 150, 300, 450, 600, 750
3. C
Page 22Answers will vary.
Page 231.–2. Answers will vary.
Sample answers:
1. Two factors: 2 x 30; 3 x 20; 4 x 15
More than two factors: 2 x 5 x 6
2. Two factors: 2 x 45; 3 x 30; 5 x 18; 6 x 15
More than two factors: 3 x 3 x 10; 2 x 5 x 9; 2 x 3 x 3 x 5
3. C
Page 24Answers will vary.
Page 25Review students’ work.
1. 312
2. 612
3. C
Page 261.–2. Answers will vary.
Sample answers:
1. Two factors: 2 x 25; 5 x 10
More than two factors: 2 x 5 x 5
2. Two factors: 2 x 36; 3 x 24; 4 x 18; 6 x 12; 9 x 8
More than two factors: 3 x 3 x 8; 6 x 4 x 3; 2 x 2 x 2 x 3 x 3
Page 27Review students’ work.
27 x 19 = 513
42 x 32 = 1,344
76 x 8 = 608
82 x 56 = 4,592
65 x 14 = 910
Page 28Review students’ work.
1. 494
2. C
Page 291. 360
2. 441
3. 900
Page 31Students should fi ll in the recording sheet based on game play.
Page 32Review students’ work.
1. 936
Students should circle the following problems:
2. 5 x 50
3. 40 x 20 and 200 x 4
4. 300 x 20
Page 33Explanations will vary.
1. < 2. = 3. =4. > 5. =
Page 35Explanations will vary.
1. 120; 240
200; 80
56
336
2. 350; 250
700; 500
750
875
3. 210; 400
420; 140
105
567
4. 700; 105
280; 1,050
1,022
Page 36Review students’ work.
1. 1,036 students
2. 1,088 soccer players
3. 1,372 football players
4. 1,824 people
5. 1,540 people
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4 INVESTIGATIONS Answer Key
Page 37Review students’ work.
1. 1,632
2. 588
3. B
Page 381. Two factors: 1 x 144; 2 x 72; 3 x 48;
4 x 36; 6 x 24; 8 x 18; 9 x 16; 12 x 12
More than two factors: 2 x 2 x 36; 2 x 3 x 24; 2 x 4 x 18; 2 x 6 x 12; 2 x 8 x 9; 3 x 3 x 16; 3 x 4 x 12; 3 x 6 x 8; 4 x 4 x 9; 4 x 6 x 6; 2 x 2 x 4 x 9; 2 x 2 x 6 x 6; 2 x 2 x 2 x 18; 2 x 2 x 3 x 12; 2 x 3 x 4 x 6; 2 x 3 x 3 x 8; 3 x 3 x 4 x 4; 2 x 2 x 3 x 3 x 4; 2 x 2 x 2 x 3 x 6; 2 x 2 x 2 x 2 x 9
Prime factorization:
2 x 2 x 2 x 2 x 3 x 3
2. Two factors: 1 x 300; 2 x 150; 3 x 100; 4 x 75; 5 x 60; 6 x 50; 10 x 30; 12 x 25; 15 x 20
More than two factors: 2 x 2 x 75; 2 x 3 x 50; 2 x 5 x 30; 2 x 6 x 25; 2 x 10 x 15; 3 x 4 x 25; 3 x 5 x 20; 3 x 10 x 10; 4 x 5 x 15; 5 x 5 x 12; 5 x 6 x 10; 2 x 2 x 3 x 25; 2 x 2 x 5 x 15; 2 x 3 x 5 x 10; 2 x 5 x 5 x 6; 3 x 4 x 5 x 5
Prime factorization:
2 x 2 x 3 x 5 x 5
Page 39Explanations will vary.
1. 260; 60
520; 180
780
130
936
2. 490; 280
980; 2,400
540
3,283
3. 150; 1,250
300; 625
1,500
1,875
4. 4,800; 5,400
18; 180
160
5,518
Page 40Review students’ work.
1. $12.71
Page 41Review students’ work.
1. a. 600
b. 800
c. 390
1,014
2. a. 3,300
b. 1,500
c. 550
1,815
Page 42Review students’ work.
3. a. 470
b. 1,200
c. 360
1,692
4. a. 90
b. 1,500
c. 1,060
1,590
Page 43Review students’ work.
1. 783
2. 481
3. 1,014
4. 495
5. 760
6.–7. Answers will vary.
8. 525
Page 44Review students’ work.
1. 5,100
2. 3,528
Page 45Review students’ work.
3. 2,048
4. 9,522
Page 46Explanations will vary.
1. 248
2. 1,381
3. 1,655
4. 342
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Unit 1 | Number Puzzles and Multiple Towers 5
Page 47Review students’ work.
1. 13 R6
2.–3. Answers will vary.
4. B
Page 48Review students’ work.
1,702
Page 491. 210
2. 53. 15
4. 20
5. 105
6. 10
7. 315
Page 50 8. 30
9. 45
10. 21
11. Answers will vary.
Page 511. 885 pages
2. 503 pages
3. 184 pages
Page 521. Answers will vary.
2. 15
Page 53Review students’ work.
1. 12
2. 15 shelves fi lled; 10 books left
3. 25
4. 34 students
Page 541. a. $190.15
b. $9.85
2. a. $297.48
b. $2.52
Page 55Review students’ work.
1. 64
2. 72
3. 60 R15
4. 101
5. Answers will vary.
Page 561. a. 1,289 stamps
b. 211 stamps
2. a. 1,311 stamps
b. 189 stamps
3. 22 stamps
Page 571. 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255,
270, 285, 300, 315, 330, 345, 360, 375, 390, 405, 420, 435, 450, 465, 480
2. 30
Review students’ work.
3. 600, 750
Explanations will vary.
Page 58Review students’ work.
4. 18 fl owers
5. 43
Page 59Explanations will vary.
1. 2; 4; 10; 12 R10
2. 180; 90; 14
3. 150; 300; 450; 7
4. 10; 5; 20; 28 R2
Page 60Explanations will vary.
5. 210; 420; 630; 33 R7
6. 10; 20; 22
7. 250; 500; 750; 1,000; 39 R7
8. 4; 40; 80; 92
Page 61Review students’ work.
1. 18
2. 40
3. B
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6 INVESTIGATIONS Answer Key
Page 62Review students’ work.
1. 36 shelves
2. 51 books
3. 34
4. 44 R11
Page 63Students should fi ll in the recording sheet based on game play.
Page 64Explanations will vary.
1. <
2. >3. <4. >
Page 65Review students’ work.
1. 29 students
2. 26 envelopes
3. 27 pages
Page 66Review students’ work.
4. 115 R2
5. 45
6. 14 R32
Page 67Review students’ work.
1. 654 apples
2. 937 oranges
3. a. 1,095 mangos
b. 905 mangos
Page 69Review students’ work.
1. 768 players
2. 14
3. 11 envelopes
Page 70Review students’ work.
4. 3,422 people
5. 30 pattern blocks
6. 546
Page 711.–2. Review students’ work.
Answers will vary.
Sample answers:
1. 2 quarters, 2 dimes, 6 nickels, 600 pennies;
4 quarters, 5 dimes, 10 nickels, 500 pennies
2. 10 quarters, 125 pennies;
37 dimes, 1 nickel
Page 72Explanations will vary.
1. 192 frames
2. 288 frames; 600 frames; 1,440 frames; 21 seconds
3. 720 pictures
4. Speeded up
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Unit 2 | Prisms and Pyramids 7
Page 1First answers will vary.
1. 24 cubes
2. 27 cubes
3. 40 cubes
Page 2First answers will vary.
4.
54 cubes
5.
48 cubes
6. 60 cubes
Page 3Explanations will vary.
Page 41. 20 sugar cubes
2. 3 layers
3. 60 sugar cubes
4. First pattern
5. C
Page 5Review students’ work.
1. 1,674
2. 2,592
Page 7First answers will vary.
1. 16 cubes
2. 30 cubes
Page 8First answers will vary.
3.
36 cubes
4.
48 cubes
5.
60 cubes
UNIT 2: PRISMS AND PYRAMIDS
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8 INVESTIGATIONS Answer Key
Page 9Review students’ work.
1. 500 ÷ 27 = 18 R14
18 oranges
2. 400 ÷ 24 = 16 R16
17 crates
3. 200 ÷ 16 = 12 R8
12 1_2 crackers
Page 101. 12 cubes
2. 24 cubes
3. 36 cubes
4. 48 cubes
Page 11Review students’ work.
Explanations will vary.
1. 30 cubes
2.–3. Answers will vary.
Challenge: 10 boxes
Answers will vary.
Sample answers: 1 x 1 x 60; 1 x 2 x 30; 1 x 3 x 20; 1 x 4 x 15; 1 x 5 x 12; 1 x 6 x 10; 2 x 2 x 15; 2 x 3 x 10; 2 x 5 x 6; 3 x 4 x 5
Page 12Review students’ work.
1. 3,696
2. 2,166
Page 13Review students’ work.
1. 495 fi fth graders
2. 33 rows
Page 14Review students’ work.
3. 770 fi fth graders
4. 22 rows
Page 15First answers will vary.
A: 6 packages
B: 24 packages
C: 18 packages
D: 6 packages
E: 12 packages
Page 161.–2. Review students’ work.
Explanations will vary.
Page 173.–4. Review students’ work.
Explanations will vary.
5. 84 x 19 = 1,596
49 x 28 = 1,372
16 x 128 = 2,048
207 x 46= 9,522
Page 181. Two factors: 1 x 160; 2 x 80; 4 x 40; 5 x 32; 8 x 20;
10 x 16
Combinations with more than two factors will vary.
Prime factorization: 2 x 2 x 2 x 2 x 2 x 5
2. Two factors: 1 x 240; 2 x 120; 3 x 80; 4 x 60; 5 x 48; 6 x 40; 8 x 30; 10 x 24; 12 x 20; 15 x 16
Combinations with more than two factors will vary.
Prime factorization: 2 x 2 x 2 x 2 x 3 x 5
Page 19Review students’ work.
1. 120 units
2. 90 units
3. 140 units
4. 240 units
5. 288 units
Page 201.–3. Dimensions will vary.
Sample dimensions are given.
Explanations will vary.
1. 48 cubes
96 cubes
4 x 6 x 4
2. 72 cubes
144 cubes
8 x 2 x 9
3. 120 cubes
240 cubes
8 x 5 x 6
Page 214.–6. Dimensions will vary.
Sample dimensions are given.
Explanations will vary.
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Unit 2 | Prisms and Pyramids 9
4. 160 cubes
80 cubes
2 x 8 x 5
5. 180 cubes
90 cubes
6 x 5 x 3
6. Review students’ work.
Page 22Review students’ work.
1. a. Answers will vary.
b. 18
2. a. Answers will vary.
b. 25
Page 23First answers will vary.
A: 12 packages
D: 10 packages
E: 24 packages
Page 24Review students’ work.
1. 1,152 2. 2,263
3. 986 4. C
Page 25Explanations will vary.
1. 24 cubes
2. 48 cubes
Dimensions will vary.
Sample answer: 4 x 3 x 4
Page 263. Review students’ work.
Challenge: 9 boxes
Answers will vary.
Sample answers: 1 x 1 x 48; 1 x 2 x 24; 1 x 3 x 16; 1 x 4 x 12; 1 x 6 x 8; 2 x 2 x 12; 2 x 3 x 8; 2 x 4 x 6; 3 x 4 x 4
Page 27Answers will vary.
Sample answer: Three packages of size A, eight packages of size B, six packages of size C, and two packages of size D will each fi ll a box with dimensions 2 x 2 x 6.
Challenge: Answers will vary.
Sample answer: 2 x 30 x 2
Page 28Review students’ work.
1. 1,225
2. 3,220
Page 29Review students’ work.
1. a. Answers will vary.
b. 22
Page 30Review students’ work.
2. a. Answers will vary.
b. 23
Page 311. Two factors: 1 x 120; 2 x 60; 3 x 40; 4 x 30;
5 x 24; 6 x 20; 8 x 15; 10 x 12
Combinations with more than two factors: 2 x 2 x 30; 2 x 3 x 20; 2 x 4 x 15; 2 x 5 x 12; 2 x 6 x 10; 3 x 4 x 10; 3 x 5 x 8; 4 x 5 x 6; 2 x 2 x 2 x 15; 2 x 2 x 3 x 10; 2 x 2 x 5 x 6; 2 x 3 x 4 x 5
Prime factorization: 2 x 2 x 2 x 3 x 5
2. Two factors: 1 x 210; 3 x 70; 5 x 42; 6 x 35; 7 x 30; 10 x 21; 14 x 15
Combinations with more than two factors: 3 x 7 x 10; 2 x 3 x 5 x 7
Page 321. 9; 8 x 9 = 72
2. 11; 6 x 11 = 66
3. 8; 7 x 8 = 56
4. 8; 12 x 8 = 96
5. 7; 11 x 7 = 77
6. 6; 9 x 6 = 54
7. 9; 12 x 9 = 108
8. 7; 7 x 7 = 49
Page 33Students should:
1. Circle 46 x 77; underline 39 x 86.
2. Circle 69 x 33; underline 36 x 58.
3. Circle 114 ÷ 6; underline 68 ÷ 34.
4. Circle 905 ÷ 5; underline 224 ÷ 16.
5. A
Page 34Answers will vary.
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U N I T 1
Number Puzzles and Multiple Towers 1–6
U N I T 2
Prisms and Pyramids 7–10
U N I T 3
Thousands of Miles, Thousands of Seats 11–15
U N I T 4
What’s That Portion? 16–20
U N I T 5
Measuring Polygons 21–26
U N I T 6
Decimals on Grids and Number Lines 27–32
U N I T 7
How Many People? How Many Teams? 33–37
U N I T 8
Growth Patterns 38–45
U N I T 9
How Long Can You Stand on One Foot? 45–47
Contents
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10 INVESTIGATIONS Answer Key
Page 35Review students’ work.
1. 322 players
2. 690 seats
3. $1,265
4. 644 players
Page 361. 72 centimeter cubes
Explanations will vary.
2. a. Answers will vary.
Sample answers: 6 x 4 x 6; 3 x 8 x 6
b. Explanations will vary.
3. Review students’ work.
Page 374. a. Answers will vary.
Sample answers:
3 x 2 x 6
3 x 4 x 3
b. Explanations will vary.
5. Review students’ work.
Challenge: Answers will vary.
Sample answer:
6 x 8 x 6
Explanations will vary.
Page 381. Victoria
Explanations will vary.
2. A
Page 40Review students’ work.
1. 111 quarters
2.–3. Answers will vary.
Sample answers:
2. 200 dimes, 155 nickels;
250 dimes, 55 nickels
3. 80 quarters, 70 dimes, 15 nickels;
100 quarters, 25 dimes, 5 nickels
Page 41Explanations will vary.
1. 120; 150; 180
2. 450; 900
3. 144; 324; 576; 900
Page 431. 4 cm wide; 5 cm long; 5 cm high
100 cubic centimeters
Explanations will vary.
2. C
Page 44 1. 6; 9 x 6 = 54
2. 11; 5 x 11 = 55
3. 7; 8 x 7 = 56
4. 7; 12 x 7 = 84
5. 7; 9 x 7 = 63
6. 12; 8 x 12 = 96
7. 8; 9 x 8 = 72
8. 8; 8 x 8 = 64
9. 9; 9 x 9 = 81
10. 9; 12 x 9 = 108
Page 45Answers will vary.
Page 47Review students’ work.
1. 24 magazines
2. a. 48 books
b. 24 books
c. 29 books, with 7 books left over
Page 48Review students’ work.
1. 1,755
2. 4,000
Page 491. 91,636,272 cubic feet
8,480,746 2 _ 3 cubic feet
83,155,525 1 _ 3 cubic feet
Page 502. 4,400 feet
3. With Great Pyramid dimensions:
274,908,816 cubic feet
With Pharaoh Menkaure’s pyramid dimensions: 25,442,240 cubic feet
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Unit 3 | Thousands of Miles, Thousands of Seats 11
Page 1 1. 3,277 2. 3,257
3. 3,317 4. 3,217
5. 3,367 6. 3,167
7. 3,767 8. 2,767
9. 9,692 10. 10,002
11. 9,682 12. 10,202
13. 9,502 14. 14,702
15. 7,702 16. 19,702
17. Explanations will vary.
18. C
Page 21. Review students’ work.
2. 850; 750 + 100 = 850
3. 1,250; 750 + 500 = 1,250
4. 1,950; 750 + 1,200 = 1,950
5. 350; 750 – 400 = 350
6. 4,750; 750 + 4,000 = 4,750
Page 3 7. 6,775; 5,275 + 1,500 = 6,775
8. 2,275; 5,275 – 3,000 = 2,275
9. 2,775; 5,275 – 2,500 = 2,775
10. 9,475; 5,275 + 4,200 = 9,475
11. 3,575; 5,275 – 1,700 = 3,575
12. 9,800; 10,000 – 200 = 9,800
13. 6,600; 10,000 – 3,400 = 6,600
14. 8,900; 10,000 – 1,100 = 8,900
15. 5,600; 10,000 – 4,400 = 5,600
16. 2,000; 10,000 – 8,000 = 2,000
Page 4Review students’ work.
1. 1,794
2. 2,142
3. A
Page 5Review students’ work.
1. 4,978
2. 8,460
3. 10,827
Page 7Review students’ work.
1. 9,927
2. 6,502
Page 8Review students’ work.
3. 1,994
4. 9,550
5. Answers will vary.
Sample answer: 75; 9,925
Page 9Students should fi ll in the recording sheet based on game play.
Page 10Review students’ work.
1. 1,596
2. 3,105
3. A
Page 11Review students’ work.
1. 9
2. 1,009
3. 3,009
4. 5,009
5. 788
6. 3,788
7. 7,788
8. 8,788
9. 1,515
10. 2,515
11. 4,515
12. 6,515
Page 131. 5,500 2. 6,970
5,503 7,970
5,506 7,980
5,516 7,972
3. 10,150 4. 16,760
10,050 16,810
10,047 16,819
5. 25,830 6. 8,940
25,940 8,930
26,050 8,920
26,056 8,910
UNIT 3: THOUSANDS OF MILES, THOUSANDS OF SEATS
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12 INVESTIGATIONS Answer Key
Page 147. 7,974 8. 137,560
7,975 138,060
7,985 138,065
7,995 138,075
9. 3,265 10. 89,945
3,165 89,745
3,065 89,735
3,075 89,635
Page 15Review students’ work.
1. 9,148
2. 3,895
3. 2,999
4.–5. Answers will vary.
Sample answers:
4. 1,000; 9,000
5. 5,000; 5,000
Page 16 1. 9; 7 × 9 = 63
2. 8; 9 × 8 = 72
3. 7; 8 × 7 = 56
4. 7; 6 × 7 = 42
5. 11; 11 × 11 = 121
6. 12; 7 × 12 = 84
7. 6; 8 × 6 = 48
8. 4; 9 × 4 = 36
9. 6; 7 × 6= 42
10. 6; 9 × 6 = 54
Page 171. 4,830; 4,833; 4,843
2. 7,750; 7,740; 7,730
3. 13,398; 13,498; 13,548
4. 24,756; 24,766; 24,775
5. 11,532; 11,533; 11,543
6. 35,436; 36,436; 36,336
Page 191. 613
2. 815
3. 483
4. 416
5. 631
6. Explanations will vary.
7. C
Page 20Review students’ work.
1. 1,294
2. 45 students
Page 21Review students’ work.
3. $4.34
4. 580
Page 22 1. 8; 4 × 8 = 32
2. 9; 8 × 9 = 72
3. 4; 7 × 4 = 28
4. 6; 7 × 6 = 42
5. 8; 11 × 8 = 88
6. 7; 12 × 7 = 84
7. 9; 5 × 9 = 45
8. 9; 9 × 9 = 81
9. 6; 3 × 6 = 18
10. 12; 8 × 12 = 96
Page 23Review students’ work.
1. 168
2. 1,193
3. $7.80
4. 477 students
Page 26Review students’ work.
1. 937 miles
Page 27Review students’ work.
2. 1,085 miles
3. 1,557 miles
4. 219 miles
5. 1,980 miles
Page 28Review students’ work.
1. a. Answers will vary.
b. 32
2. a. Answers will vary.
b. 25
3. D
Page 29Review students’ work.
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Unit 3 | Thousands of Miles, Thousands of Seats 13
1. 426 miles
Page 30Review students’ work.
2. 931 miles
3. 1,354 miles
4. 539 miles
Page 31Review students’ work.
1. 1,713
a. 1,768
b. 500
c. 1,708
2. 911
a. 1,008
b. 300
c. 908
Page 32Review students’ work.
3. 5,145
a. 5,163
b. 1,500
c. 5,063
4. 5,886
a. 6,711
b. 3,900
c. 5,711
Page 33Review students’ work.
1. 473
2. 836
3. 2,483
4. D
Page 341. 800 + 50 + 13
– (200 + 40 + 7)
600 + 10 + 6
616
2. 200 + 120 + 5
– (100 + 60 + 4)
100 + 60 + 1
161
Page 353. 400 + 80 + 18
– (200 + 70 + 9)
200 + 10 + 9
219
4. 400 + 120 + 3
– (200 + 90 + 2)
200 + 30 + 1
231
Page 365. 600 + 110 + 10
– (400 + 90 + 9)
200 + 20 + 1
221
Page 37Review students’ work.
1. 1,784
a. 2,402
b. 1,700
c. 1,784
2. 4,575
a. 4,647
b. 2,300
c. 4,547
Page 38Review students’ work.
3. 3,236
a. 3,303
b. 900
c. 3,203
4. 7,472
a. 7,697
b. 4,300
c. 7,475
Page 39Review students’ work.
1. 1,248 miles
Page 40Review students’ work.
2. 474 miles
3. 619 miles
4. 1,057 miles
5. 426 miles
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14 INVESTIGATIONS Answer Key
Page 41 1. 12; 12 × 12 = 144
2. 4; 8 × 4 = 32
3. 7; 4 × 7 = 28
4. 8; 7 × 8 = 56
5. 10; 11 × 10 = 110
6. 8; 8 × 8 = 64
7. 7; 9 × 7 = 63
8. 9; 3 × 9 = 27
9. 7; 7 × 7 = 49
10. 9; 9 × 9 = 81
11. D
Page 42Review students’ work.
1. 2,295
2. 442 baseball cards
3. 4,590
4. 416
Page 43Review students’ work.
1. 988 students
2. 896 soccer players
3. 1,876 football players
4. 1,888 people
5. A
Page 45Review students’ work.
1. 489 miles
Page 46Review students’ work.
2. 497 miles
3. 1,633 miles
4. 423 miles
Page 47Students should fi ll in the recording sheet based on game play.
Page 48Review students’ work.
1. 19 shelves fi lled, 18 books left
2. 33 shelves
3. 42 books
4. 17 magazines
5. C
Page 49Review students’ work.
1. 7,715; 215
2. 7,052; 448
3. 7,512; 12
4. 7,529; 29
Page 521. 11,000 people
20,000 – 9,000 = 11,000
2. a. 14,000 people
9,000 + 5,000 = 14,000
b. 6,000 people
20,000 – 14,000 = 6,000
3. 18,500 people
20,000 – 1,500 = 18,500
Page 534. 54,035 people
64,035 – 10,000 = 54,035
5. 34,035 people
54,035 – 20,000 = 34,035
6. 9,035 people
34,035 – 25,000 = 9,035
Page 547. 67,203 people
69,703 – 2,500 = 67,203
8. 57,203 people
67,203 – 10,000 = 57,203
9. a. 47,800 people
10,000 + 37,800 = 47,800
b. 19,403 people
67,203 – 47,800 = 19,403
10. 42,203 people
67,203 – 25,000 = 42,203
Page 5511.–13. Answers will vary.
Sample answers using Badger Arena:
11. 5,000 people
20,000 – 15,000 = 5,000
12. 18,700 people
20,000 – 1,300 = 18,700
13. 16,800 people
20,000 – 3,200 = 16,800
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Unit 3 | Thousands of Miles, Thousands of Seats 15
Page 56Review students’ work.
1. 35,464
2. 33,245
3. 18,688
4. A
Page 57Review students’ work.
1. 2,417
2. 8,095
3. 12,469
Page 59Review students’ work.
1. 286 seats
2. 39,812 tickets
3. 5,220 tickets
4. 115,600 tickets
Page 60Review students’ work.
5. 16,650 people
6. a. 53,367 people
b. 4,178 people
7. 8,462 people
8. 19,533 people
Page 61Review students’ work.
9. 53,016 tickets
10. 723 people
11. a. 1,299 people
b. 15,381 people
Page 62Review students’ work.
12. a. 11,415 people
b. 72,606 people
c. 915 people
13. 9,435 people
Page 631.–4. Answers will vary.
Page 64Review students’ work.
1. 18 rows
2. 9 rows
3. 2,592 raffl e tickets
4. $5,184
5. B
Page 65Review students’ work.
1. 13,403
2. 5,674
3. 1,976
4. 13,422
Page 67Explanations will vary.
1. 27
2. 22
3. 22 × 27 = 594
4. 270
5. a. 540
b. 675
Page 68Review students’ work.
1. 11,825 people
2. a. 37,765 people
b. 2,235 people
3. 38,358 people
Page 691. 17 feet
2. 980 feet
3. 29,796 feet
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16 INVESTIGATIONS Answer Key
Page 11. a. 2
_ 5
b. 3 _ 5
2. a. 6 pieces
b. 4 pieces
3. 5 _ 6
4. a. 14 words
b. 50%
Page 25. a. Students should circle 4 marbles.
b. 8 marbles
6. a. 6 children
b. 2_8
7. Explanations will vary.
a. True
b. False
c. True
Page 31. 5,410
2. 2,998
3. 9,352
4. 4,849
5. 9,907
Page 4Answers will vary.
Page 5Fractions will vary.
Sample fractions are given.
Grid 1: 25%; 25 ___ 100 , 1 _ 4
Grid 2: 75%; 75 ___ 100 , 3 _ 4
Grid 3: 20%; 20 ___ 100 , 1 _ 5
Grid 4: 60%; 60 ___ 100 , 3 _ 5
Page 6Review students’ work.
1. 9,098
2. $210.22
Page 7Answers will vary.
Page 9Review students’ work.
Answers will vary.
Page 1050%
33 1 _ 3 %; 66 2 _ 3 %
25%; 50%; 75%
20%; 40%; 60%; 80%
16 2 _ 3 %; 33 1 _ 3 %; 50%; 66 2 _ 3 ; 83 1 _ 3 %
12 1 _ 2 %; 25%; 37 1 _ 2 %; 50%; 62 1 _ 2 %; 75%; 87 1 _ 2 %
10%; 20%; 30%; 40%; 50%; 60%; 70%; 80%; 90%
Page 111. 3_
5 ; 60%
2. 1_8 ; 12 1_2 %
3. 6_6 ; 100%
4. B
Page 12Review students’ work.
Answers will vary.
Page 131. A 2. B
3. B 4. C
5. C 6. A
7. A 8. A
9. D
Page 14Review students’ work.
Answers will vary.
Page 151. a. 15 students
b. 1_3 ; 33 1_3 %
c. 1_6 ; 16 2_3 %
d. 20 students
2. a. 50%
b. 15 words
Page 16Review students’ work.
3. 40 students
4. a. 24 fi fth graders
b. 37 1 _ 2 %
UNIT 4: WHAT’S THAT PORTION?
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Unit 4 | What’s That Portion? 17
Page 17Review students’ work.
1. 5,845
2. 8,830
Page 181.–5. Answers will vary.
Sample answers:
1. 1 _ 3 , 2 _ 6 , 3 _ 9
2. 1 _ 4 , 2 _ 8 , 3 __ 12
3. 2 _ 5 , 4 __ 10 , 40
___ 100
4. 3 _ 4 , 6 _ 8 , 9 __ 12
5. 4 _ 5 , 8 __ 10 , 80
___ 100
Page 191. 1_
8 ; 1_6 ; 1_4 ; 1_3 ; 2_5 ; 1_2 ; 3_5 ; 5_8 ; 2_3 ; 3_4 ; 4_52. B
Page 20Answers will vary.
Sample answer:
Page 21Review students’ work.
Explanations will vary.
1. 7 __ 10
2. 9 __ 10
3. 4 _ 3
4. 3 _ 8
Page 22Review students’ work.
Explanations will vary.
5. 3_5
6. Martin
7. Charles
8. Answers will vary.Sample answer: Mercedes’ frozen yogurt was twice as large a Nora’s.
Page 231. 3,300; 3,303; 3,403
2. 6,580; 7,580; 7,590
3. 6,532; 6,533; 6,543
4. 13,020; 14,020; 14,057
5. 34,940; 35,040; 35,070; 35,073
6. 14,930; 14,910; 14,890; 14,885
Page 241.–3. Answers will vary.
Sample answers:
1. 2 _ 3 = 4 _ 6
2 _ 3 = 66 2 _ 3 %
2 _ 3 < 1
2. 3 _ 4 = 6 _ 8
3 _ 4 = 75%
3 _ 4 > 1 _ 2
3. 9 __ 12 > 8 __ 12
75% > 66 2 _ 3 %
Page 25Students should connect the following balls and goals:
1. Less than 1 _ 2 and 50%: 30%, 3 _ 8 , 4%, 1 _ 6 , 43%
Between 1 _ 2 and 1 and 50% and 100%: 3 _ 4 , 80%, 7 _ 8 , 69%, 95%
2. 70% > 1 _ 2
Explanations will vary.
3. C
Page 261–3. Review students’ work.
Answers will vary.
Page 27Explanations will vary.
1. a. 2 _ 3
b. 5 _ 8
c. 3 _ 6
d. Renaldo; Hana
2. 6 runners
3. Nora
Page 28Explanations will vary.
4. Shandra
5. a. 16 students
b. 8 students
c. 4 students
d. 1 _ 8
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18 INVESTIGATIONS Answer Key
Page 29Review students’ work.
1. 8, 018
2. 10,708
3. 14,188
4. 79,392
Page 301 _ 4 ; 3 __ 10 ; 1 _ 3 ; 2 _ 5 ; 1 _ 2 ; 7 __ 10 ; 3 _ 4 ; 4 _ 5 ; 5 _ 6 ; 9 __ 10
Page 311. 1_
4 ; 1_3 ; 1_2 ; 3_5 ; 7_8 ; 9__10
Page 322. 0; 1 _ 6 ; 1 _ 4 ; 3 __ 10 ; 1 _ 3 ; 5 _ 8 ; 2 __ 3 ; 3 _ 4 ; 7 _ 8 ; 1
Page 331. False
2. True
3. True
Page 34Review students’ work.
1. 796
2. 13,161
3. 37,415
4. 6,329
Page 351_5 ; 1_4 ; 3__
10 ; 1_3 ; 3_8 ; 2_3 ; 7__10 ; 4_5 ; 5_6 ; 7_8
Page 371. 1
__ 12
2. 2 __ 12 ; 1 _ 6
3. 3 __ 12 ; 1 _ 4
4. 4 __ 12 ; 2 _ 6 ; 1 _ 3
5. 5 __ 12
6. 6 __ 12 ; 3 _ 6 ; 2 _ 4 ; 1 _ 2
7. 7 __ 12
8. 8 __ 12 ; 4 _ 6 ; 2 _ 3
9. 9 __ 12 ; 3 _ 4
10. 10 __ 12 ; 5 _ 6
11. 11 __ 12
12. 12 __ 12 ; 6 _ 6 ; 4 _ 4 ; 3 _ 3 ; 2 _ 2
Page 38Review students’ work.
1. 3 _ 4
2. 7 __ 12
3. 1 1__12
Page 39Review students’ work.
Answers will vary.
Page 401. True
2. False
3. False
Page 41Pair 1 and Pair 2: Review students’ work.
Answers will vary and should show the following:1 _ 3 > 1 _ 4
1 _ 2 < 3 _ 5
5 _ 8 < 7 __ 10
3 _ 2 > 4 _ 3
9 _ 5 > 7 _ 4
2 _ 3 < 5 _ 6
1 _ 8 < 2 __ 10
3 _ 4 < 4 _ 5
Page 43Review students’ work.
1. a. 37,507 tickets
b. 52,272 tickets
2. a. 37,017 tickets
b. 20,607 tickets
Page 44Round 1: 1 1 __ 12 ; 1; Alexander
Round 2: 11 __ 12 ; 11
__ 12 ; tie
Round 3: 7 __ 12 ; 7 __ 12 ; tie
Round 4: 1 1 __ 12 ; 1 1 _ 4 ; Nora
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Unit 4 | What’s That Portion? 19
Page 453 _ 4
Review students’ work.
Answers will vary.
Sample answer:
1_3
5__12
3_4
Page 46Explanations will vary.
1. 11 __ 12
2. 11 __ 12
3. 1 _ 3
4. 2 1 _ 2 feet; 1 _ 4
5. 1 5 __ 12
Page 47Students should fi ll in the page based on game play.
Page 48Review students’ work.
1. 1 1 __ 12 ; 5 _ 6
Circled: 1 1 __ 12
2. 7 __ 12 ; 2 _ 3
Circled: 2 _ 3
3. B
Page 49Explanations will vary.
1. 7__12
2. 3_8
3. 2_3
4. 1_2
5. 1 1_2
Page 51
0 __ 1 1 __ 2 1
0 __ 3 1 __ 3 2 __ 3 1
0 __ 4 1 __ 4 2 __ 4 3 __ 4 1
0 __ 5 1 __ 5 2 __ 5 3 __ 5 4 __ 5 1
0 __ 6 1 __ 6 2 __ 6 3 __ 6 4 __ 6 5 __ 6 1
0 __ 8 1 __ 8 2 __ 8 3 __ 8 4 __ 8 5 __ 8 6 __ 8 7 __ 8 1
0 __ 10 1 __ 10 2 __ 10 3 __ 10 4 __ 10 5 __ 10 6 __ 10 7 __ 10 8 __ 10 9 __ 10 1
Page 53Review students’ work.
1. 13,163 books
2. 5,712 books
3. 2,319 books
4. 5,092 books
Page 54Review students’ work.
1. 9__10 ; 5_6
Circled: 9__10
2. 1; 3_4 Circled: 1
3. C
Page 55Round 1: 5 _ 6 ; 11
__ 12 ; Hana
Round 2: 11 __ 12 ; 1 1 __ 12 ; tie
Round 3: 1; 1 1 __ 12 ; Renaldo
Round 4: 1 1 _ 6 ; 1; Hana
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20 INVESTIGATIONS Answer Key
Page 57Review students’ work.
1. 6,204 feet
2. 13,010 feet
3. 3,497 feet
4. Mount McKinley
Page 581.–4. Answers will vary.
Sample answers:
1. 2 _ 4 , 3 __ 6 , 4 _ 8 , 5 __ 10 , 6 __ 12
2. 2 _ 6 , 3 __ 9 , 4 __ 12 , 5 __ 15 , 6 __ 18
3. 6 _ 8 , 9 __ 12 , 12
__ 16 , 15 __ 20 , 18
__ 24
4. 4 __ 10 , 6 __ 15 , 8 __ 20 , 10
__ 25 , 40 ___ 100
Page 59Students should fi ll in the page based on game play.
Page 60Review students’ work.
1. 1 1 _ 6 loaves of bread
2. 1 5 _ 8
3. 1 1 _ 3
Page 61Review students’ work.
4. 1_2 brownie
5. 2 1_46. 2_
3
Page 62Review students’ work.
Explanations will vary.
7. True
8. False
9. Yes
Page 63Explanations will vary.
1. =2. >3. >
Page 64Review students’ work.
1. 12,000
– 6,944
5,056
2. 335
517
+ 448
1,300
3.–4. It is impossible.
Explanations will vary.
Page 65Review students’ work.
Answers will vary.
Sample answers:
1. 4 _ 5 + 2 __ 10
1 _ 2 + 1 _ 5 + 3 __ 10
1 __ 12 + 1 _ 6 + 1 _ 4 + 5 __ 10
2. 5 _ 4 + 2 _ 8
1 _ 2 + 3 _ 4 + 2 _ 8
1 _ 3 + 1 _ 4 + 1 _ 6 + 6 _ 8
Page 67Explanations will vary.
1. <2. >3. =
Page 68Review students’ work.
Answers will vary.
Page 701. 1 1_2 miles
2. a. 9__10 mile
b. 7_8 mile
c. Millweed Pond
3. 2 1_8 miles
4. 5_8 mile
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Unit 5 | Measuring Polygons 21
Page 11.–2. Review students’ work.
Answers will vary.
Explanations will vary.
Page 23.–4. Review students’ work.
Answers will vary.
Explanations will vary.
Page 3Students should circle the following triangles:
1. Third triangle (no right angle)
2. First triangle (no right angle)
3. A
Page 4Explanations will vary.
1. 10 students
2. 1_2 ; 50%
3. 1_5 ; 20%
4. 1__20 ; 5%
Page 51.–2. Review students’ work.
Answers will vary.
Explanations will vary.
Page 63.–4. Review students’ work.
Answers will vary.
Explanations will vary.
Page 7Students should circle the following quadrilaterals:
1. Second quadrilateral (only 1 pair of parallel sides)
2. First quadrilateral (all sides are not equal in length)
3. C
Page 81. Review students’ work.
Yes. A square is a rhombus.
Yes. A square is a rectangle.
Page 92. Review students’ work.
Not necessarily.
Not all rectangles are squares.
Yes. All rectangles are parallelograms.
Page 103. Review students’ work.
4. a. All
b. Some
c. Some
d. All
e. Some
5. Explanations will vary.
Page 111.–4. Answers will vary.
Sample answers:
1. 2 _ 4 , 3 _ 6 , 4 _ 8 , 5 __ 10 , 6 __ 12
2. 4 _ 6 , 6 _ 9 , 8 __ 12 , 10
__ 15 , 12 __ 18
3. 75 ___ 100 , 3 _ 4 , 6 _ 8 , 9 __ 12 , 12
__ 16
4. 60 ___ 100 , 30
__ 50 , 15 __ 25 , 6 __ 10 , 3 _ 5
Page 121.–2. Answers will vary.
3.–4. Explanations will vary.
Page 13Explanations will vary.
1. Yes
2. No
3. No
Page 14Explanations will vary.
1. a. 3_4
b. 5_8
c. 5_6
d. Deon; Olivia
2. Zachary
3. Answers will vary.
Sample answer: Mitch’s sandwich was half the size of Lourdes’ sandwich.
Page 15Students should circle the following fi gures:
1. First and third fi gures
2. First, third, and fourth fi gures
3. Review students’ work.
4. Explanations will vary.
UNIT 5: MEASURING POLYGONS
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22 INVESTIGATIONS Answer Key
Page 17Explanations will vary.
60˚
N
60˚ 60˚
45˚
F
90˚ 45˚
30˚
L
90˚ 60˚
30˚
J
120˚ 30˚
90˚ 90˚
C
90˚ 90˚
60˚ 120˚
M
120˚ 60˚
Page 18Explanations will vary.
120˚ 120˚
K
60˚ 60˚
30˚ 150˚
O
150˚ 30˚
60˚ 120˚
G
120˚ 60˚
120˚ 120˚
120˚ H 120˚
120˚ 120˚
Page 19Explanations will vary.
1. 180º
2. Yes
3. The sums are 360º
4. Answers will vary.
Page 201. Students should circle the following shapes:
A, B, D, F, G, H
2. Parallelograms: B, D, F, G
Rectangles: F, G
Rhombuses: B, F
3. A, B, D, H
4. B
Page 21Review students’ work.
1. 4 _ 5 2. 5
__ 10
3. 1 3 _ 4 4. 1 1 _ 4
Page 231.–3. Answers will vary.
4. C
Page 24Review students’ work.
1. 5 _ 6
2. 4 __ 10
3. 1 2 _ 3
4. 1 3 _ 8
Page 25Students should circle the following shapes:
1. None
2. Second shape
3. None
4. Third shape
5. Second shape
6. D
Page 271. Dimensions of Square Perimeter Area
1 inch by 1 inch 4 inches 1 square inch
2 inches by 2 inches 8 inches 4 square inches
3 inches by 3 inches 12 inches 9 square inches
4 inches by 4 inches 16 inches 16 square inches
5 inches by 5 inches 20 inches 25 square inches
6 inches by 6 inches 24 inches 36 square inches
7 inches by 7 inches 28 inches 49 square inches
2. Answers will vary.
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Unit 5 | Measuring Polygons 23
Page 281. Review students’ work.
a. 24 inches
b. 16 inches
c. 32 square inches
d. 8 square inches
2. All the rectangles have the same area.
Rectangle C has the longest perimeter.
Page 29Explanations will vary.
1. False
2. True
3. True
Page 311. 4 square inches
16 square inches
2. 9 square inches
36 square inches
3. The area of the larger square is 4 times larger than the area of the smaller square.
4. Explanations will vary.
Page 325. 8 inches
16 inches
6. 12 inches
24 inches
7. The perimeter of the larger square is double that of the smaller square.
8. Explanations will vary.
Page 33Review students’ work.
1. 1_2 + 1_6
2. Neither. They are equal.
3. 5_8 + 1_2 + 1_4
4. 1_8 + 3_4
Page 341. H, J
2. D, F
3. G, L
4. B, E, F
5. H, L
6. E, F
7. I, J
8. C, E, F
9. I, J
Page 35Review students’ work.
Dimensions of Rectangle
Perimeter Area
1. Original3 inches × 4 inches
14 inches12 square
inches
2. All sides x 26 inches × 8 inches
28 inches48 square
inches
3. All sides x 39 inches × 12 inches
42 inches108 square
inches
4. All sides x 412 inches × 16 inches
56 inches192 square
inches
5. All sides x 515 inches × 20 inches
70 inches300 square
inches
6. All sides x 618 inches × 24 inches
84 inches432 square
inches
7. 30 inches × 40 inches
140 inches
1,200 square inches
Explanations will vary.
Page 36 8. When each dimension is doubled the perimeter is
doubled.
9. When each dimension is doubled the area is quadrupled.
10. Yes
Explanations will vary.
Page 371 _ 8 ; 1 _ 5 ; 3 __ 10 ; 3 _ 8 ; 1 _ 2 ; 3 _ 5 ; 7 __ 10 ; 3 _ 4 ; 7 _ 8 ; 9 __ 10
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24 INVESTIGATIONS Answer Key
Page 38Review students’ work.
Dimensions of Rectangle
Perimeter Area
1. Original1 inch ×
4 inches10 inches
4 square inches
2. All sides x 22 inches ×
8 inches20 inches
16 square inches
3. All sides x 33 inches × 12 inches
30 inches36 square
inches
4. All sides x 44 inches × 16 inches
40 inches64 square
inches
5. All sides x 55 inches × 20 inches
50 inches100 square
inches
Page 39Review students’ work.
Explanations will vary.
Dimensions Perimeter Area
1. 8 inches by 3 inches 22 inches 24 square inches
2. 4 inches by 6 inches 20 inches 24 square inches
3. 2 inches by 12 inches 28 inches 24 square inches
4. 1 inch by 24 inches 50 inches 24 square inches
5. The area stays the same.
6. The perimeter changes.
7. Answers will vary.
Page 40Review students’ work.
1. a. 24 inches
b. 36 inches
c. 35 square inches
d. 42 square inches
2. The perimeter is the same for all the rectangles.
The 6 × 6 rectangle has the largest area.
Page 41Explanations will vary.
1. 90 feet
2. 19 feet
3. 36 feet
Page 43Review students’ work.
Dimensions Perimeter Area
1. 1 foot × 14 feet 30 feet 14 square feet
2. 2 feet × 13 feet 30 feet 26 square feet
3. 3 feet × 12 feet 30 feet 36 square feet
4. 4 feet × 11 feet 30 feet 44 square feet
5. 5 feet × 10 feet 30 feet 50 square feet
6. 6 feet × 9 feet 30 feet 54 square feet
7. 7 feet × 8 feet 30 feet 56 square feet
8. 7 feet × 8 feet
9. 1 foot × 14 feet
10. Answers will vary.
Page 44Review students’ work.
Explanations will vary.
Dimensions Perimeter Area
1. 16 inches by 12 inches 56 inches 192 square inches
2. 8 inches by 24 inches 64 inches 192 square inches
3. 4 inches by 48 inches 104 inches 192 square inches
4. 2 inches by 96 inches 196 inches 192 square inches
5. 1 inch by 192 inches 386 inches 192 square inches
6. The area remains the same.
7. The perimeter gets longer.
8. Answers will vary.
Page 45Review students’ work.
1. 9 feet × 9 feet
2. 3 feet × 15 feet
3. 6 feet × 12 feet
4. B
Page 461. 40%; 40
___ 100 , 2 _ 5
2. 30%; 30 ___ 100 , 3 __ 10
3. 50%; 50 ___ 100 , 1 _ 2
4. 20%; 20 ___ 100 , 1 _ 5
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Unit 5 | Measuring Polygons 25
Page 47Review students’ work.
Dimensions of Rectangle
Perimeter Area
1. Original2 inches ×
4 inches12 inches
8 square inches
2. All sides x 24 inches ×
8 inches24 inches
32 square inches
3. All sides x 36 inches × 12 inches
36 inches72 square
inches
4. All sides x 48 inches × 16 inches
48 inches128 square
inches
5. All sides x 510 inches × 20 inches
60 inches200 square
inches
Page 49Review students’ work.
Explanations will vary.
Polygon Original
Number of Pieces in Similar (Larger) Shapes
2nd 3rd 4th 5th
1. square B 1 4 9 16 25
2. rectangle C 1 4 9 16 25
3. triangle N 1 4 9 16 25
4. triangle J 1 4 9 16 25
5. rhombus M 1 4 9 16 25
6. parallelogram O 1 4 9 16 25
7. 100
8. 100
Page 50Students should shade the following number of squares:
1. 25 squares25___
100 , 1_42. 30 squares
30___100 , 3__
10
3. 80 squares
80%
4. 66 2_3 squares
66 2_3 %
Page 51Students should circle the following sets of fractions:1 _ 6 + 2_3 + 2__
121 __ 12 + 1 _ 4 + 2 _ 3
Page 531. Review students’ work.
Page 542. Explanations will vary.
Answers will vary.
Sample answers:
Second hexagon fi gure: Third hexagon fi gure:
Piece Number Used
triangle N 0
rhombus M 3
trapezoid K 0
hexagon H 3
Piece Number Used
triangle N 12
rhombus M 0
trapezoid K 2
hexagon H 6
3. The area is 4 of hexagon H.
4. The area is 9 of hexagon H.
Page 551.
8 square units
32 square units
2.
7 triangle units
63 triangle units
3. C
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26 INVESTIGATIONS Answer Key
Page 561.
6 square units
24 square units
2.
5 square units
45 square units
Page 57Review students’ work.
Explanations will vary.
1. Answers will vary.
2. 4 times larger
9 times larger
3. 2 times as long
3 times as long
Page 58Explanations will vary.
1. a. 12 students
b. 33 1 _ 3 %
c. 1 _ 6 ; 16 2 _ 3 %
2. a. 50%
b. 10%
c. 20%
d. 6 students; 20%
Page 591. 7 square units; 28 square units
2. 8 triangle units; 32 triangle units
3. 24 square units; 6 square units
4. 20 triangle units; 5 triangle units
5. 4 times as large
6. B
Page 61Explanations will vary.
1. Similar
2. Similar
3. Not similar
4. B
Page 62Review students’ work.
1. 7 __ 12 of a pan
2. 1 7 _ 8
3. 3 1 _ 6
Page 631. Side A Side B Side C Side D
Austin’s Pool 8 ft 16 ft 8 ft 16 ft
Brochure Pool 4 ft 8 ft 4 ft 8 ft
2. Review students’ work.
3. Explanations will vary.
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Unit 6 | Decimals on Grids and Number Lines 27
Page 21. 25
___ 100 , 1 _ 4 ; 0.25; 25%
2. 10 ___ 100 , 1 __ 10 ; 0.10, 0.1; 10%
3. 20 ___ 100 , 1 _ 5 ; 0.20, 0.2; 20%
4. 70 ___ 100 , 7 __ 10 ; 0.70, 0.7; 70%
Page 35. 75___
100 , 3_4 ; 0.75; 75%
6. 65___100 , 13__
20 ; 0.65; 65%
7. 42___100 , 21__
50 ; 0.42; 42%
8. 80___100 , 4_5 ; 0.80, 0.8; 80%
Page 49. 5
___ 100 , 1 __ 20 ; 0.05; 5%
10. 1 ___ 100 ; 0.01; 1%
11. Students should shade 40 squares.
Answers will vary.
Sample answers: 40 ___ 100 , 2 _ 5 , 0.4, 40%
12. Students should shade 98 squares.
Answers will vary.
Sample answers: 98 ___ 100 , 49
___ 100 , 0.98, 98%
Page 51. 25___
100 , 1_4 ; 0.25; 25%
2. 3___100 ; 0.03; 3%
3. Students should shade 80 squares.
Answers will vary.
Sample answers: 80___100 , 4_5 , 0.8, 80%
4. Students should shade 43 squares.
Answers will vary.
Sample answers: 43___100 , 43%
5. B
Page 6Review students’ work.
1. 3,831
2. 1,403
3. 18,592
4. 39,774
5. 11,007
Page 91. Students should shade 75 squares.
Answers will vary.
Sample answers: 0.750, 75___100 , 750____
1,000 , 3_4 , 75%
Page 102. Students should shade 12 1 _ 2 squares.
Answers will vary.
Sample answers: 125 ____ 1,000 ,
12 1 _ 2 ___ 100 , 1 _ 8 , 12 1 _ 2 %
Page 113. Students should shade 30 squares.
Answers will vary.
Sample answers: 0.30, 3 __ 10 , 30 ___ 100 , 30%
Page 124. Students should shade 15 squares.
Answers will vary.
Sample answers: 0.150, 15___100 , 3__
20 , 15%
Page 135. Students should shade 78 squares.
Answers will vary.
Sample answers: 0.780, 78 ___ 100 , 39
__ 50 , 78%
Page 146. Students should shade 62 1_2 squares.
Answers will vary.
Sample answers: 625____1,000 ,
62 1 _ 2 ___100 , 5_8 , 62 1_2 %
Page15Students should connect the following:
1. Grid 1: 0.2, 200 ____ 1,000
Grid 2: 0.33, 33 ___ 100
Grid 3: 1 _ 8 , 0.125, 125 ____ 1,000
2. B
Page 171.–4. Review students’ work.
Answers will vary.
Page 18Review students’ work.
1. 2,204
2. 2,668
3. B
UNIT 6: DECIMALS ON GRIDS AND NUMBER LINES
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28 INVESTIGATIONS Answer Key
Page 191. Month Precipitation
February 0.31
January 0.32
March 0.78
April 0.88
May 1.25
2. Month Precipitation
February 3.01
January 3.24
March 3.46
April 3.75
May 3.96
Page 21Review students’ work.
1. 3,510
80 × 45 = 3,600
70 × 40 = 2,800
2. 4,096
32 × 100 = 3,200
10 × 128 = 1,280
3. B
Page 221. Month Precipitation
April 4.48
January 4.76
February 5.46
May 5.74
March 6.41
2. Month Precipitation
June 1.12
October 1.35
July 2.17
September 2.43
August 2.71
Page 231.–2. Equivalents will vary.
Sample answers are given.
Students should shade the following number of squares:
1. 50 square.
0.50, 50___100 , 5__
10 , 1_2 , 50%
2. 29 1_2 squares295____
1,000 , 29 1 _ 2 ___100 , 29.5%
Page 243.–4. Equivalents will vary.
Sample answers are given.
Students should shade the following number of squares:
3. 83 squares
0.830, 83 ___ 100 , 83%
4. 15 squares
0.15, 150 ____ 1,000 , 15
___ 100 , 3 __ 20 , 15%
Page 25Explanations will vary.
5. Hana
6. Mitch
7. Corn
Page 261. 0.123; 0.165; 0.245; 0.333; 0.400; 0.5; 0.601; 0.625;
0.661; 0.75; 0.79
2. A
Page 27Women: 55.96; 56.63; 56.65; 56.75; 57.02
Men: 49.91; 50.14; 50.50; 50.54; 50.54
Page 291. Answers will vary.
Sample answer:
0.075, 0.1, 0.275
0.3, 0.35, 0.55
0.6, 0.75, 0.875
2. C
Page 30Women: 2:11.08; 2:11.73; 2:13.95; 2:16.20; 2:16.76
Men: 2:00.03; 2:00.66; 2:00.67; 2:01.26; 2:02.61
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Unit 6 | Decimals on Grids and Number Lines 29
Page 311.
Team Wins LossesRecord*
(decimal)Rank Winning
Percentage
Bluebirds 20 5 0.800 1 80%
Cardinals 12 12 0.500 4 50%
Orioles 16 9 0.640 3 64%
Penguins 10 15 0.400 5 40%
Robins 19 6 0.760 2 76%
2.
Team Wins LossesRecord*
(decimal)Rank Winning
Percentage
Cheetahs 20 20 0.500 3 50%
Leopards 10 30 0.250 5 25%
Jaguars 18 23 0.439 4 43.9%
Tigers 35 5 0.875 1 87.5%
Lions 34 5 0.872 2 87.2%
Page 35
Page 32360
Two factors: 1 × 360; 2 × 180; 3 × 120; 4 × 90; 5 × 72; 6 × 60; 8 × 45; 9 × 40; 10 × 36; 12 × 30; 15 × 24; 18 × 20
Combinations with more than two factors will vary.
Prime factorization: 2 × 2 × 2 × 3 × 3 × 5
600
Two factors: 1 × 600; 2 × 300; 3 × 200; 4 × 150; 5 × 120; 6 × 100; 8 × 75; 10 × 60; 12 × 50; 15 × 40; 20 × 30; 24 × 25
Combinations with more than two factors will vary.
Prime factorization: 2 × 2 × 2 × 3 × 5 × 5
Page 33Women: 26.10; 26.11; 26.16; 26.19; 26.19
Men: 22.75; 22.86; 23.03; 23.04; 23.08
Page 35See below
Page 36Review students’ work.
1. a. Answers will vary.
b. 15
2. a. Answers will vary.
b. 35
3. A
N
__ D 1 2 3 4 5 6 7 8 9 10 11 12
1 1 2 3 4 5 6 7 8 9 10 11 12
2 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
3 0.3 0.6 1 1.3 1.6 2 2.3 2.6 3 3.3 3.6 4
4 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
5 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
6 0.16 0.3 0.5 0.6 0.83 1 1.16 1.3 1.5 1.6 1.83 2
7 0.142857 0.285714 0.428571 0.571428 0.714285 0.857142 1 1.142857 1.285714 1.428571 1.571428 1.714285
8 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1 1.125 1.25 1.375 1.5
9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1 1.1 1.2 1.3
10 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2
11 0.09 0.18 0.27 0.36 0.45 0.54 0.63 0.72 0.81 0.90 1 1.09
12 0.083 0.16 0.25 0.3 0.416 0.5 0.583 0.6 0.75 0.83 0.916 1
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30 INVESTIGATIONS Answer Key
Page 371.
Team Wins LossesRecord*
(decimal)Rank Winning
Percentage
Dolphins 15 34 0.306 5 30.6%
Guppies 38 11 0.776 2 77.6%
Marlins 25 25 0.500 3 50%
Sharks 24 25 0.490 4 49%
Swordfi sh 40 10 0.800 1 80%
2.
Team Wins LossesRecord*
(decimal)Rank Winning
Percentage
Wolves 98 27 0.784 1 78.4%
Coyotes 63 61 0.508 3 50.8%
Bobcats 96 28 0.774 2 77.4%
Wildcats 62 62 0.500 4 50%
Tigers 60 64 0.484 5 48.4%
Page 38 1. 6; 7 × 6 = 42
2. 12; 6 × 12 = 72
3. 6; 8 × 6 = 48
4. 12; 9 × 12 = 108
5. 5; 12 × 5 = 60
6. 6; 6 × 6 = 36
7. 8; 12 × 8 = 96
8. 9; 7 × 9 = 63
9. 8; 9 × 8 = 72
10. 6; 9 × 6 = 54
Page 390.3
5.25; 525%
0.6; 66 2_3 %
2 1_20.16;16 2_3 %3_4 ; 0.75
0.8; 80%3_8 ; 37.5%
Page 41Review students’ work.
1. 1,232 football players
2. 29 or 30 teams
3. 16 students
4. 2,033 people
Page 42Review students’ work.
1. 1 _ 5
2. 0.95
3. Yes
4. Tavon
Page 43Review students’ work.
1. 3,492 stickers
2. a. 31 bags
b. $434
3. a. 18 pages
b. $870
Page 441.
Month Precipitation
May 0.12
June 0.13
April 0.22
January 0.67
February 0.68
2. Month Precipitation
October 0.21
September 0.28
December 0.38
November 0.43
August 0.49
Page 451. 1.525 grams
2. Review students’ work.
Explanations will vary.
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Unit 6 | Decimals on Grids and Number Lines 31
Page 46Explanations will vary.
Students should circle the following estimates:
1. 2,400
2. 2,600
3. 5,500
4. 9,000
5. 83 × 29 = 2,407
69 × 38 = 2,622
26 × 211 = 5,486
496 × 18 = 8,928
Page 470.05; 0.25; 0.3; 0.325; 0.475; 0.55; 0.65; 0.75; 0.8; 0.95
Page 491.–3. Review students’ work.
Answers will vary.
Page 504.–6. Review students’ work.
Answers will vary.
Page 51Explanations will vary.
1. 26
2. 22
3. 26 × 22 = 572
4. 260
5. a. 780
b. 832
Page 52Review students’ work.
1. 6.4 miles
2. 1.03 grams
3. 4.944
4. 3.35 miles
5. 2.09
Page 53Review students’ work.
6. 6.87 inches
7. 2.23 inches
8. 3.35 inches
9. 9.05 inches
10. 9.06 inches
Page 541. Nan: 18.925
Kwang: 17.425
Elena: 18.612
Carly: 19.087
Daniela: 18.949
Katy: 18.187
2. Carly, Nan, Daniela, Elena, Katy, Kwang
3. A
Page 55Review students’ work.
1. 0.85
2. 0.85
3. 0.8
4. 0.95
5. Charles
Page 57Students should fi ll in the recording sheet based on game play.
Page 581.–4. Students should fi ll in the recording sheet based
on game play.
5. Explanations will vary.
Page 59Review students’ work.
1. 3.24 grams
2. 7.13 miles
3. 5.88 miles
4. 2.305 grams
Page 60Review students’ work.
5. 6.434
6. John Abercrombie: 54.64
Daniel Rohleder: 54.17
Matthew Scanlan: 54.81
Jonathan Schmidt: 54.19
William Stovall: 54.24
7. Daniel Rohleder: 54.17
Jonathan Schmidt: 54.19
William Stovall: 54.24
John Abercrombie: 54.64
Matthew Scanlan: 54.81
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32 INVESTIGATIONS Answer Key
Page 61Review students’ work.
8. Kimberly Vandenberg: 60.25
Misty Hyman: 60.35
Morgan Scroggy: 60.16
Shelly Ripple Johnston: 61.16
Tanica Jamison: 59.23
9. Tanica Jamison: 59.23
Morgan Scroggy: 60.16
Kimberly Vandenberg: 60.25
Misty Hyman: 60.35
Shelly Ripple Johnston: 61.16
Page 621. Rafael Martinez: 19.200
Dae Eun Kim: 19.425
Fabian Hambuechen: 18.862
Paul Hamm: 19.562
Marian Dragulescu: 19.049
Wei Yang: 19.400
2. Paul Hamm: 19.562
Dae Eun Kim: 19.425
Wei Yang: 19.400
Rafael Martinez: 19.200
Marian Dragulescu: 19.049
Fabian Hambuechen: 18.862
3. C
Page 631. 1.083; 0.832
2. 1.058; 0.999
3. 0.267; 0.935
4. 1.001; 0.54
5. 0.977; 0.900
Page 64Review students’ work.
1. 8.29 inches
2. 6.05 inches
3. 6.57 inches
4. 9.48 inches
5. 30.39 inches
Page 65Explanations will vary.
Students should circle:
1. 420 × 4; 7 × 240; 84 × 20
2. 100 × 80; 10 × 800; 10 × 10 × 10 × 8
3. 720 ÷ 12; 240 ÷ 4; 360 ÷ 6
4. B
Page 6610 Charles Hamelin
6 Peter Darazs
8 Ho-Suk Lee
2 Fabio Carta
3 Apolo Anton Ohno
9 JiaJun Li
7 Hyun-Soo Ahn
1 Mathieu Turcotte
5 Niels Kerstholt
11 Viktor Knoch
4 Satoru Terao
Explanations will vary.
37662_01-47.indd 3237662_01-47.indd 32 8/17/07 8:16:57 AM8/17/07 8:16:57 AM
Unit 7 | How Many People? How Many Teams? 33
Page 11. Yes
2. Review students’ work.
Page 21. 5 x 8
2. Review students’ work.
3. C
Page 31. 3; 12; 21
2.–3. Answers will vary.
Page 41.–2. Answers will vary.
3. C
Page 5 1. True
2. False
3. False
4. False
5. False
6. 4
7. 48
8. 2
9. 30
10. 15 or 1 × 15
Page 71.–2. Answers will vary.
Sample answers:
1. 20 × 64; 80 × 16
2. They are multiples or factors of 40 and 32.
Page 81. 11
2. 36
3. 84. 32
5. 26.–7. Answers will vary.
8. D
Page 9Answers will vary.
Sample answers:
12 × 36; 8 × 54
Page 111. 20
2. Answers will vary.
3. Review students’ work.
4. Answers will vary.
Sample answer: 180 ÷ 30
Page 12Students should circle:
1. Ted Williams: 0.344
2. Joe DiMaggio: 0.325
3. Babe Ruth: 0.342
4. Ty Cobb: 0.366
5. Stan Musial: 0.331
6. Yogi Berra: 0.285
7. Mickey Mantle: 0.298
8. Roberto Clemente: 0.317
Page 1375 × 42 = 3,150; 275 × 8 = 2,200; 186 × 34 = 6,32463 × 24 = 1,512; 134 × 26 = 3,484
1. Review students’ work.
Answers will vary.
Page 142.–3. Review students’ work.
Answers will vary.
Page 15Students should place the decimals on the number line in the following order:
0, 0.16, 0.235, 0.284, 0.492, 0.5, 0.773, 0.821, 1, 1.5, 1.899, 1.9, 2, 2.045, 2.16, 2.492, 2.5
Page 1695 × 64 = 6,080; 225 × 25 = 5,625
187 × 42 = 7,854; 72 × 45 = 3,240
1.–2. Review students’ work.
Answers will vary.
Page 1778 × 27 = 2,106; 54 × 41 = 2,214; 743 × 6 = 4,458
218 × 15 = 3,270; 145 × 35 = 5,075; 264 × 24 = 6,336
1.–3. Review students’ work.
Answers will vary.
Page 18Review students’ work.
1. 3,220
2. 4,248
3. C
UNIT 7: HOW MANY PEOPLE? HOW MANY TEAMS?
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34 INVESTIGATIONS Answer Key
Page 191. 1,620
2. Answers will vary.
Page 21Solution 1 Solution 2
138
× 24
2,000
600
160
400
120
+ 32
3,312
1 13
138
× 24
552
+ 2,760
3,312
Page 221.–2. Answers will vary.
3. Solution 1 Solution 2
184
× 61
6,000
4,800
240
100
80
+ 4
11,224
5 2
184
× 61
184
+ 11,040
11,224
Page 23Review students’ work.
1. 7,200
2. 6,111
3. B
Page 241. 896 players
2. 4,320 players
3. 2,040 players
Page 25Review students’ work.
1. 3,738
2. 3,492
3. 7,560
4. 9,920
5. 26,082
Page 26Review students’ work.
1. 12.565 miles
2. 9.22 miles
3. 18 miles
4. 2.761
Page 27 1. 0.65
2. 0.2
3. 0.45
4. 0.1
5. 0.525
6. 0.7
7. 0.25
8. 0.05
9. 0.725 or 0.775
10. 0.325
11. D
Page 281. 1,008 pencils
2. 15 bags
3. 18 boxes
4. 1,476 books
Page 291. 13 R28
2. 32 teams and 6 students left over
3. 54 R22
4. 47 envelopes
Page 30 1. 3 stickers
2. 6 stickers
3. 16 stickers
4. 3 cubes
5. 7 cubes
6. 18 cubes
7. 10 pens
8. 21 pens
9. 54 pens
10. D
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Unit 7 | How Many People? How Many Teams? 35
Page 31Review students’ work.
1. 6 2. 3
3. 10 4. 8
5. 70 6. 50
7. 40 8. 15
9. 240 10. 70
Page 33Review students’ work.
1. 67 students
2. 26
3. 54
4. 40
Page 341. 31 R4
2. 32 bags
3. 31 pounds
4. 31 boxes
5. 27 boxes with 16 cows
4 boxes with 17 cows
6. B
Page 35Review students’ work.
1. 1,305
2. 28 students
3. 29
4. 1,820
Page 371. 47 R26
a. 20
b. 1,680
c. Answers will vary.
2. 23 full bags
a. 20
b. 280
c. Answers will vary.
Page 383. 85 R4
a. 2,400
b. 40
c. Answers will vary.
4. 37 boxes with 11 cookies left over
a. 660
b. 20
c. Answers will vary.
Page 395. 249 R1
a. 400
b. 250
c. Answers will vary.
6. 27 students
a. 20
b. 1,000
c. Answers will vary.
Page 40Review students’ work.
1. 20 packages
$19.80
2. 5 packages
$17.45
3. 20 packages
$25.80
4. 17 packages of pencils
6 packages of glue sticks
$16.83 + $20.94 = $37.77
Page 41Review students’ work.
5. 25 packages of pencils
25 packages of pens
$24.75 + $49.50 = $74.25
6. Answers will vary.
Sample answers:
2 pencils and 1 eraser
The total cost is $44.10, so they would return $5.90.
Page 42Review students’ work.
1. 5,213
2. 1,702
3. 5,144
4. 68 R2
5. 54 R7
6. C
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36 INVESTIGATIONS Answer Key
Page 43Review students’ work.
1. 40
2. 27 students
3. 29 students
Page 45Review students’ work.
First steps will vary.
1. 2,117
2. 5 R12
3. 144 R2
4. 3,374
5. 12 R6
6. A
Page 461. $119.88
2. $39.90
3. $89.82
4. $179.94
5. $104.97
Page 47498 ÷ 9 = 55 R3
376 ÷ 6 = 62 R4
685 ÷ 34 = 20 R5
2,837 ÷ 52 = 54 R29
3,989 ÷ 49 = 81 R20
1. Review students’ work.
Answers will vary.
Page 482.–3. Review students’ work.
Answers will vary.
Page 49 1. 1,860 2. 105
3. 4,880 4. 400
5. 1,800 6. 36
7. 12,800 8. 6
9. 56,000 10. 50
11. D
Page 50Review students’ work.
1. 64 R2 2. 19 R27
3. 41 R13 4. 20 R31
Page 51Review students’ work.
1. 24
2. 20 R8
3. A
Page 531. Nutrition bars and fruit juice or bottled water; 15
boxes of nutrition bars and 29 boxes of fruit juice or 10 cases of bottled water
2. $155.26 for nutrition bars and fruit juice; $109.75 for nutrition bars and bottled water
Page 541. Largest: 46 × 77 = 3,542
Smallest 39 × 86 = 3,354
2. Largest: 3,400 ÷ 34 = 100
Smallest: 1,680 ÷ 24 = 70
3. C
Page 55Review students’ work.
1. 4,000 2. 420
3. 3,750 4. 195
5. 600 6. 60
7. 30 8. 70
9. 50 10. 140
Page 57Review students’ work.
Grade Number of Teams
Students Not on a Team
Third 10 3
Fourth 14 3
Fifth 18 6
Page 58Review students’ work.
Grade Number of Students on a Team
Third5 teams of 7 students
and 6 teams of 8 students
Fourth5 teams of 11 students
and 6 teams of 10 students
Fifth7 teams of 14 students
and 4 teams of 13 students
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Unit 7 | How Many People? How Many Teams? 37
Page 59Review students’ work.
1. 59 third graders
2. 24 third graders
3. 174 students
Page 60Review students’ work.
1. 11 full classrooms
18 students in the classroom that is not full
2. 12 teams with 13 students and 16 teams with 12 students
Page 611. 480 balloons
12 balloons
2. 450 cards
18 boxes
3. $684
$76
4. D5. B
Page 62Review students’ work.
1. 2,300 2. 17,500
3. 1,200 4. 1,200
5. 8,000 6. 2
7. 200 8. 50
9. 36 10. 500
Page 63Review students’ work.
1. 1,400 balloons
$19.92
2. 9 packages
$44.91
3. 18 packages
$52.02
Page 64Review students’ work.
1. 47,872
2. 61,101
3. 64,827
4. Answers will vary.
Page 65Review students’ work.
5. 94 R3
6. 64 R56
7. 147 R4
8. Answers will vary.
Page 661. 31,962
2. 337
3. 95,690
4. A
Page 67Review students’ work.
1. 1,800 cans of juice
2. 3,000 cans of juice
3. 1,440 oranges
4. 2,700 oranges
Page 69Review students’ work.
1. 12,816
2. 143 R9
3. C
Page 70Review students’ work.
1. 20 cases
2. 40 cases
3. 60 cases
Page 71Review students’ work.
1. 2,040 mph
2,720 mph
3,400 mph
2. 56 2 _ 3 miles per minute
3. a. 6,800 mph
b. 113 1 _ 3 miles per minute
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38 INVESTIGATIONS Answer Key
Page 1Answers will vary.
Page 2Review students’ work.
Page 3Explanations will vary.
1. 4,275
2. 9,981
3. 1,893
4. 9,709
5. B
Page 4Review students’ work.
1. 8,923
2. 8,865
3. 7,848
4. 2,766
Page 6Answers will vary.
Sample answers:
Age (years)
Tony’s Height (cm)
Maya’s Height (cm)
Susie’s Height (cm)
2 85 90 80
3 91 99 85
4 97 108 90
5 103 117 95
6 110 126 100
7 116 135 107
8 122 139 115
9 128 142 118
10 135 145 120
Page 7Answers will vary.
Sample answer:
Tony, Maya and Susie
Hei
ght (
cent
imet
ers)
150145140135130125120115110105100
9590858075
2 3 4 5 6 7 8 9 10Age (years)
SusieTonyMaya
Page 8Review students’ work.
1. 16,118
2. 12,003
3. B
Page 9Height (cm): 13; 16; 19; 22; 25; 28; 31; 34; 49; 304
Page 101.–2. Explanations will vary.
Page 11
Hei
ght (
cent
imet
ers)
40Graph of Flickerbill’s Growth
35
30
25
20
15
10
5
00
(birth) 1 2 3 4 5 6 7 8 9 10
Age (years)
UNIT 8: GROWTH PATTERNS
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Unit 8 | Growth Patterns 39
Page 12Review students’ work.
1. 674
2. 6,283
3. C
Page 14Answers will vary.
Page 15
Age (years)
Height (cm)
Krink Trifoot Water Weasel
0 (birth) 1 15 15
1 6 17 20
2 11 19 25
3 16 21 30
4 21 23 35
5 26 25 40
6 31 27 45
7 36 29 50
8 41 31 55
9 46 33 60
10 51 35 65
15 76 45 90
100 501 215 515
Page 16Animals of Rhoma
Hei
ght (
cent
imet
ers)
70
65
60
55
50
45
40
35
30
25
20
15
10
5
00
(birth) 1 2 3 4 5 6 7 8 9 10
Age (years)
Page 171. 9,074; 8,974; 8,924
2. 5,595; 5,605; 5,615
3. 17,698; 17,898; 17,900
4. 22,038; 26,038; 26,043
5. 4,980; 4,880; 4,890
6. 22,536; 24,536; 24,336
Page 18Height (cm): 22; 29; 37; 46; 56
Krink
Krink
TrifootTrifoot
Water W
easel
Water W
easel
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40 INVESTIGATIONS Answer Key
Page 19Fastwalker
70
65
60
55
50
45
40
35
30
25
20
15
10
5
00
(birth)1 2 3 4 5 6 7 8 9 10 11 12
Age (years)
Page 201.–3. Answers will vary.
Page 21Review students’ work.
1. $60.13
2. 15,862
3. 30,416
4. 59,052
5. B
Page 22
Age
(years)
Height (cm)
Spiraltail Inksnake
0 (birth) 2.5 15
1 5 16.5
2 7.5 18
3 10 19.5
4 12.5 21
5 15 22.5
6 17.5 24
7 20 25.5
8 22.5 27
9 25 28.5
10 27.5 30
Page 231. 9; 12; 15; 18; 30; 45; 60; 300; 3 × n
Page 242.–3. Answers will vary.
Page 251. Arithmetic expressions will vary.
Sample expressions are given.
Number of Rows
Perimeter (cm)
Arithmetic Expression
1 8 2 × (1 + 3)
2 10 2 × (2 + 3)
3 12 2 × (3 + 3)
4 14 2 × (4 + 3)
5 16 2 × (5 + 3)
6 18 2 × (6 + 3)
10 26 2 × (10 + 3)
15 36 2 × (15 + 3)
20 46 2 × (20 + 3)
100 206 2 × (100 + 3)
n 2n +6 2 × (n + 3)
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Unit 8 | Growth Patterns 41
Page 262. Increases by 2 cm
3.–4. Answers will vary.
Page 27Review students’ work.
1. 98,673
2. 22,641
3. 8,858
4. $762.83
5. A
Page 28Review students’ work.
1. 52,752
2. 62,002
3. 45,103
4. 60,991
Page 29Review students’ work.
1. 15,275 people
2. a. 34,315 people
b. 5,685 people
3. 1,362 people
Page 301. Answers will vary.
Arithmetic expressions will vary.
Total Number of tiles for
4 tiles: 4; 8; 12; 16; 20; 24; 40; 60; 80; 400; 4 × n
5 tiles: 5; 10; 15; 20; 25; 30; 50; 75; 100; 500; 5 × n
6 tiles: 6; 12; 18; 24; 30; 36; 60; 90; 120; 600; 6 × n
Page 312. Increases by 4 (or 5 or 6)
3.–4. Answers will vary.
Page 325. 60
Tota
l Num
ber o
f Tile
s
58565452504846444240383634323028262422201816141210
864200 1 2 3 4 5 6 7 8 9 10
Number of Rows
6 Tiles
5 Tiles
4 Tiles
6 Tiles
5 Tiles
4 Tiles
6. Answers will vary.
Page 331. Answers will vary.
Arithmetic expressions will vary.
Perimeter (cm) for
4 tiles across: 10; 12; 14; 16; 18; 20; 28; 38; 48; 208; 2 × (n + 4)
5 tiles across: 12; 14; 16; 18; 20; 22; 30; 40; 50; 210; 2 × (n + 5)
6 tiles across: 14; 16; 18; 20; 22; 24; 32; 42; 52; 212; 2 × (n + 6)
Page 342. Increases by 2 cm
3.–4. Answers will vary.
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42 INVESTIGATIONS Answer Key
Page 355.
60
Perim
eter
(cen
timet
ers)
58565452504846444240383634323028262422201816141210
864200 1 2 3 4 5 6 7 8 9 10
Number of Rows
6 Tiles5 Tiles4 Tiles
6 Tiles5 Tiles4 Tiles
6. Answers will vary.
Page 36Review students’ work.
1. 395 people
2. 1,566 marchers
3. 8,568 people
4. 8,606 people
5. C
Page 37Review students’ work.
1. 33,185
2. 50,750
3. 1,865
4. 32,807
Page 391. Arithmetic expressions will vary.
Total Number of Tiles: 10; 20; 30; 40; 50; 60; 100; 150; 200; 1;000; 10 × n
Page 402. Increases by 10
3.–4. Answers will vary.
Page 415.
60
Tota
l Num
ber o
f Tile
s
58565452504846444240383634323028262422201816141210
864200 1 2 3 4 5 6 7 8 9 10
Number of Rows
6. Answers will vary.
Page 421. Arithmetic expressions will vary.
Perimeter (cm) for 10 tiles across: 22; 24; 26; 28; 30; 32; 40; 50; 60; 220; 2 × (n + 10)
Page 432. Increases by 2 cm
3.–4. Answers will vary.
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Unit 8 | Growth Patterns 43
Page 445.
60
Perim
eter
(cen
timet
ers)
58565452504846444240383634323028262422201816141210
864200 1 2 3 4 5 6 7 8 9 10
Number of Rows
6. Answers will vary.
Page 45Review students’ work.
1. $51.74
2. $3.65
3. $26.66
4. $71.60
5. C
Page 461. 72,994
2. 46,969
3. 28,392
4.–5. Answers will vary.
Page 471. Arithmetic expressions will vary.
Total Number of Pennies: 4; 6; 8; 10; 12; 14; 22; 32; 42; 202; (n × 2) + 2
Page 482. Increases by 2
3.–4. Answers will vary.
Page 495.
Tota
l Num
ber o
f Pen
nies
130125120115110105100
959085807570656055504540353025201510
500 1 2 3 4 5 6 7 8 9 10 11 12
Number of Rounds
6. Answers will vary.
Page 501. Arithmetic expressions will vary.
Total Number of Pennies: 16; 32; 64; 128; 256
2. Answers will vary.
Page 513.
Tota
l Num
ber o
f Pen
nies
130125120115110105100
959085807570656055504540353025201510
50
0 1 2 3 4 5 6
Number of Rounds
4. Answers will vary.
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44 INVESTIGATIONS Answer Key
Page 52Estimates will vary.
Explanations will vary.
1. 74,672 2. 75,036
3. 75,700 4. D
Page 531. Arithmetic expressions will vary.
Number of Tiles: 1; 4; 9; 16;25; 36; 100; 225; 400
2. Answers will vary.
Page 543.
Tota
l Num
ber o
f Tile
s
110105100
959085807570656055504540353025201510
50
0 1 2 3 4 5 6 7 8 9 10
Length of One Side (centimeters)
4. Answers will vary.
Page 55Review students’ work.
1. 85,630 2. 57,511
3. 24,207 4. 58,291
5. A
Page 56Review students’ work.
1. $152.85 2. $201.50
3. $242.95 4. $309.60
5. No
Page 571. Arithmetic expressions will vary.
Number of Tiles: 10; 15; 21; 28; 36; 45; 55
Page 582.–3. Answers will vary.
Page 594.
Tota
l Num
ber o
f Tile
s
110105100
959085807570656055504540353025201510
50
0 1 2 3 4 5 6 7 8 9 10
Length of One Side (centimeters)
5. Answers will vary.
Page 601. Arithmetic expressions will vary.
Numbers of Tiles: 16; 25; 36; 49; 64; 81; 100
Page 612.–3. Answers will vary.
Page 624.
Tota
l Num
ber o
f Tile
s
110105100
959085807570656055504540353025201510
50
0 1 2 3 4 5 6 7 8 9 10
Length of One Side (centimeters)
5. Answers will vary.
Page 63Review students’ work.
1. 99,850 people
2. 22,373 people
3. 24,544 people
4. B
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Unit 9 | How Long Can You Stand On One Foot? 45
Page 641.
Week Vince’s Total Donation ($)
Marta’s Total Donation ($)
Paula’s Total Donation ($)
Start 6 10 0
1 8 11 3
2 10 12 6
3 12 13 9
4 14 14 12
5 16 15 15
10 26 20 30
15 36 25 45
20 46 30 60
Page 652. Charity Donations
75
Tota
l Don
atio
n (d
olla
rs)
70656055504540353025201510
50
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Number of Weeks
VinceVincePaula
Paula
MartaMarta
a. Paula
b. Vince: 12 weeks
Marta: 20 weeks
Paula: 10 weeks
c. Vince: $110
Marta: $62
Paula: $156
Page 1Answers will vary.
Page 21. Answers will vary.
2. 27
3. D
Page 41.–2. Answers will vary.
Page 6Explanations will vary.
Answers will vary.
Sample answers:
Set A: Gymnasts, ages 9–20
Set B: First and second graders, ages 6–8
Set C: Karate students, ages 16–49
Set D: People over 50
Page 7Review students’ work.
1. 5,180
2. 11,524
Page 81,554 ÷ 75 = 20 R54
3,164 ÷ 79 = 40 R4
8,904 ÷ 21 = 424
6,478 ÷ 42 = 154 R10
1.–2. Review students’ work.
Page 9Answers will vary.
Page 10Answers will vary.
Page 111. 8; 36; 9
2. Answers will vary.
Sample answers:
24 × 24; 96 × 6
3. 8; 72
4. Answers will vary.
Sample answers:
1,000 ÷ 100; 250 ÷ 25
UNIT 9: HOW LONG CAN YOU STAND ON ONE FOOT?
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46 INVESTIGATIONS Answer Key
Page 121.–3. Answers will vary.
Page 131. 39 seconds
2. 39 seconds
3. Explanations will vary.
4. D
Page 161.–2. Answers will vary.
Page 171.–4. Answers will vary.
Page 181.–3. Answers will vary.
Page 19Review students’ work.
1. 47 R26
840 ÷ 42 = 20
40 × 42 = 1,680
2. 85 R4
80 × 30 = 2,400
1,200 ÷ 30 = 40
Page 20Review students’ work.
1. 1,568 players
2. 2,720 players
3. 28 teams and 8 students left over
4. 25 teams
Page 21Review students’ work.
1. 3,000 2. 720
3. 4,200 4. 1,440
5. 7,000 6. 70
7. 150 8. 4
9. 30 10. 140
Page 24Answers will vary.
Explanations will vary.
Page 25
What are you comparing? Girls Boys Who is better?
1. Median 34 28 Girls
2. Highest value 67 70 Boys
3. Top 1 _ 2 above ___ seconds 34 28 Girls
4. Top 1 _ 4 above ___ seconds 46 62 Boys
5. Explanations will vary.
6. B
Page 26237 × 76 = 18,012
55 × 168 = 9,240
901 × 49 = 44,149
813 × 28 = 22,764
1.–2. Review students’ work.
Page 27Review students’ work.
1. 19 R3
2. 14 R12
3. 13 R40
4. 46 R8
Page 281.–3. Answers will vary.
Page 294.–6. Answers will vary.
Page 321. Explanations will vary.
Answers will vary.
Sample answers:
a. B
b. C
c. A
2. C
Page 341.–2. Answers will vary.
Page 351.–4. Answers will vary.
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Unit 9 | How Long Can You Stand On One Foot? 47
Page 36Review students’ work.
1. 2,268 pencils
2. 25 bags
3. 31 boxes
4. 4,080 paintbrushes
Page 37Review students’ work.
1. 34 rolls of tickets
2. 42 boxes of cups
3. 13 books
4. 39 times
Page 391. One half
2. 1_2
3. 25 times
4.–5. Answers will vary.
Page 40Review students’ work.
1. 980
2. 24 students
3. 60
4. 2,475
Page 411. a. 1_
2
b. 3_4
c. 1_8
d. 0
e. 1
f. 1_4
2. B
Page 42Review students’ work.
1. 3,572
2. 8,411
3. 18
4. 24 R17
Page 43Students should fi ll in the recording sheet based on game play.
Page 44There is not enough money to buy everyone a T-shirt.
There is enough money to buy everyone a water bottle.
Answers for both will vary.
Sample answer:
There is enough money to buy a water bottle for 90 students and T-shirts for 11 students.
Page 451. 20 times
2.–3. Answers will vary.
4. B
Page 471. Answers will vary.
Page 482. Explanations will vary.
Page 49Explanations will vary.
1. Game 1 is fair.
2. Game 2 is fair.
3. C
Page 50Review students’ work.
1. $18.88
2. 29 boxes; $464
3. 9-pack for $3.59
4. Gym A
Page 511. Explanations will vary.
Version A: not fair
Version B: fair
Version C: not fair
2. Answers will vary.
Sample answer: r
impossible unlikely maybe likely certain
0 1 __ 2 0.5
1
d c f a b e
impossible unlikely maybe likely certain
0 1 __ 2 0.5
1
d c f a b e
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