Test solutions with the detailed point scale. Add up your points and spot what to review.
1 Multiplicative comparisons / 3 pts
- “56 is 8 times as many as 7” and “56 is 7 times as many as 8.” (1 pt)
- \( 4 \times 12 = 48 \). The sailboat is 48 feet long. (1 pt)
- \( 72 = n \times 8 \), so \( n = 72 \div 8 = 9 \). The tower is 9 times as tall as the statue. (1 pt)
2 Add or multiply / 3 pts
- \( 4 \times 9 = 36 \) dollars. (1 pt)
- \( 9 + 4 = 13 \) dollars. (1 pt)
- \( 36 - 13 = 23 \). Eli saves 23 dollars more than Fay. (1 pt)
3 Factors of 54 / 4 pts
- 1 and 54, 2 and 27, 3 and 18, 6 and 9 (we stop at 6 since 7 and 8 are not factors; 4 and 5 are not factors either). (2 pts)
- 1, 2, 3, 6, 9, 18, 27, 54. (1 pt)
- No: \( 8 \times 6 = 48 \) and \( 8 \times 7 = 56 \), so 54 falls between two multiples of 8. (1 pt)
4 Multiples of 12 / 3 pts
- 12, 24, 36, 48, 60. (1 pt)
- Yes, \( 12 \times 8 = 96 \). (1 pt)
- \( 12 \times 9 = 108 \) and \( 12 \times 8 = 96 \), \( 12 \times 10 = 120 \), so the answer is 108. (1 pt)
5 Prime or composite / 4 pts
- 31 is prime. 57 is composite (\( 3 \times 19 \)). 73 is prime. 85 is composite (\( 5 \times 17 \)). (2 pts)
- The number 2. (1 pt)
- The number 1 has only one factor, itself. A prime needs exactly two factors and a composite more than two. (1 pt)
6 Divisibility and patterns / 3 pts
- It ends in 8, so it is divisible by 2 and not by 5. (1 pt) The digits add to \( 7 + 1 + 2 + 8 = 18 \), a multiple of 9, so it is divisible by 9. (1 pt)
- 5, 13, 21, 29, 37. (1 pt)
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