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Additional Practice
Answers
ACTIVITY 1.1
1. Answers may vary. Sample answers:
a. 3, 5, 7, 9
b. 4, 8, 12, 16
c. 8, 16, 24, 32
2. a. 1, 2, 3, 4, 6, 12
b. 1, 5, 25
11. Answers may vary. Sample answer: Two
examples of composite numbers are 6 and 8.
The factors of 6 are 1, 2, 3, and 6; the factors
of 8 are 1, 2, 4, and 8. These numbers are
composite because they have factors other
than 1 and themselves.
ACTIVITY 1.2
c. 1, 19
12. 12, 36, 42, 63, 90
d. 1, 2, 3, 4, 6, 8, 12, 24
13. Answers may vary. Sample answer: Three
three-digit numbers that are divisible by 9
are 153, 279, and 666. I chose these numbers
because the sum of their digits is a number
divisible by 9.
3. 6 is a factor of 36. This is true because 36 is
6 × 6.
4. Joanne’s claim is incorrect because numbers
that are perfect squares have an odd number
of factors. For example, 16 has five factors:
1, 2, 4, 8, and 16. (Accept any correct
counterexample to Joanne’s claim, with or
without the observation that the number
happens to be a perfect square.)
5. 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
6. 2, 3, 5, 11, 13
7. 4, 6, 8, 9, 10, 12, 14, 15
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UNIT 1
8. Answers may vary. Sample answer: You
can determine if a number is prime or
composite by listing the number’s factors.
If the number has factors other than itself
and 1, then it is composite. If the number’s
only factors are 1 and itself, then the number
is prime.
9. There is only one even prime number, 2.
This is true because for every even number
greater than 2, 2 is a factor of that number.
10. a. 1, 2, 3, 4, 6, 9, 12, 18, 36; composite
b. 1, 7, 11, 77; composite
c. 1, 97; prime
14. The divisibility rules for 3 and 9 are similar
in that they both are determined by finding
the digit sum. They are different because to
be divisible by 3 a number’s digit sum must
be divisible by 3 and to be divisible by 9, a
number’s digit sum must be divisible by 9.
15. 54, 126, 738
16. 1, 2, 7, 11, 14, 22, 77, 154
17. Answers may vary. Sample answer: 60,
120, 180
18. Answers may vary. Sample answer: 216
and 456 because their last two digits form
a number that is divisible by 4.
19. Answers may vary. Sample answer: 230 and
740 because they both end in 0.
20. 24 and 72
ACTIVITY 1.3
21. 2 × 2 × 3 × 3, or 22 × 32
22. 26
23. 2 × 2 × 2 × 2 × 3 × 3, or 24 × 32
Level 1, Unit 1 • Number Concepts
1
Additional Practice
Answers
24. 34; 9 is not a prime number
25. 3 × 7; 1 is not a prime number and is not
included when writing a prime factorization.
26. 23 × 32 × 5
27. 2 × 32 × 73
28. 2 × 2 × 2 × 7 × 3 × 3 × 3 × 3
29. 32 × 5
30. 112
3
3
2
31. 27 matches 3 ; 8 matches 2 ; 25 matches 5 ;
32 matches 25; 49 matches 72.
32. 15: 1, 3, 5, 15
63: 1, 3, 7, 9, 21, 63
33. 12: 2 × 2 × 3
Common factor: 3
34.
16
3
9
4
64
32
2
8
18
64
35. Answers may vary. Sample answer: The
methods all help you to find the factors that
the numbers have in common and then you
can find the greatest common factor. They
are different in how they have you find the
common factors.
36. Jake can give equal numbers of tiles of each
color to each of four friends
37. 48
38. 720
2
42. Answers may vary. Sample answer: 10 and
20 have a greatest common factor of 10.
43. 12 boxes, each containing two oranges and
three fruit snacks
45: 5 × 3 × 3
6
40. Robbie is not correct because 60 is not a
factor of 12. It appears that Robbie found the
LCM by mistake.
41. Linda is not correct because 12 is not a
multiple of 60. It appears that Linda found
the GCF by mistake.
ACTIVITY 1.4
18
39. Answers may vary. Sample answer: In
both methods you find the least common
multiple of the numbers. In one method,
you multiply (or use repeated addition) to
get lists of multiples; in the other method,
you divide the numbers into their prime
factors and then multiply certain of those
factors to find the LCM.
SpringBoard® Mathematics with Meaning™ Level 1
44. 2
45. Answers may vary. Sample answer: 6 and 8.
46. 12 weeks from now
47. 50
48. Check students’ diagrams. GCF = 12 and
LCM = 180
49. Answers may vary. Students should give
their choice and show an example of finding
the GCF using whichever method they
chose.
50. 6
ACTIVITY 1.5
13 ; Sufia: ___
8
21 ; Tera: ___
51. Rod: ___
25
25
25
1 ; ten
52. Four boxes should be shaded for __
3
5 , and three
boxes should be shaded for __
6
1 . Ordered from
boxes should be shaded for __
4
5
1 , __
1 , __
least to greatest: __
4 3 6
© 2010 College Board. All rights reserved.
UNIT 1
Additional Practice
Answers
53. Answers may vary. Sample answers:
10 ___
15
a. ___
18 ; 27
6 ___
9
b. ___
14 ; 21
4 ___
6
c. ___
10 ; 15
5
54. __
8 . Sample explanations may include finding
common denominators and then comparing
numerators, or cross multiplying.
63.
0
42
64. ___
4
35
16
1
10
1
3
2
3
36
8
3
5
4
5
27 7___
2
___
8
3
11
3 ft; 67 in.; 65 in.; 5__
1 ft
65. 5__
4
4
66. a. <
73
___
b. <
c. >
55. a. <
b. <
67. 11
c. >
5
56. __
7
5
__
5 ___
5
___
2
57. __
3
__
4
__
11 13
6
__
7
7
7 7
17 ___
8 ___
3
11 __
58. ___
20 10 15 5
3 and ___
24 . Explanations may vary. Sample
59. __
8
64
answer: These are equivalent because each
can be converted to the other using the
Property of One.
© 2010 College Board. All rights reserved.
1
UNIT 1
9
ACTIVITY 1.6
2
60. a. 8__
9
b. 6
1
c. 3__
4
__
d. 3 2
3
17
___
61. a.
5
47
___
b. 7
71
c. ___
6
89
___
d. 10
37 ___
31
62. ___
16 8
ACTIVITY 1.7
68. a. 0.125
b. 0.4
c. 2.61
d. 6.07
e. 0.12
2
69. a. ___
25
17
b. 16___
20
1
c. 99____
100
3
d. __
5
3
e. 312___
50
70. 0.052 0.5
0.52
0.523
71. 3.2
2.32
2.3
72.
3.02
5
6 1.25
0
1
2
2
22
5
3
5
3
4
5
73. a. 8.8
3
4__
8
1
5__
4
b. 2.3
c. 6.7
Level 1, Unit 1 • Number Concepts
3
Additional Practice
Answers
UNIT 1
82.
74. a. 12.67
b. 24.68
-10
-8
-6
-4
-2
0
2
4
6
8
10
c. 0.45
75. Answers may vary. Sample answer: I would
25
convert the decimal part (0.25) to ____
100
1 . Then I would
and then reduce that to __
1 behind the 1 to4 form the mixed
put the __
4
number.
76. Answers may vary. Sample answer: I would
1 to 0.5 by dividing 1 by 2. I would
convert __
2
then put .5 behind the 3 to form the
decimal.
3 7
4 8
77.
0
1
2
2
7
10
4
3
3
100
4
83. a. -9, -8, 0, 2
b. -7, -5, 1, 10
c. -10, -3, 2, 10
84. a. 5
b. 6
c. -24
85. a. -4
b. -8
c. -3
86. -7°
5
78. 1:41.11; 1:41.24; 1:41.73
87. 137 ft
88. -10 dollars
ACTIVITY 1.8
79. a. 5
b. -40
c. 12
d. -4
a. a 10-foot drop in elevation
b. a 35-dollar deposit
c. your aunt gives you $20
d. the temperature is 8 degrees below zero
81. a. 45
b. 6
c. 18
d. 0
e. 8
4
SpringBoard® Mathematics with Meaning™ Level 1
© 2010 College Board. All rights reserved.
80. Answers may vary. Sample answers: