4th Grade Factors, Multiples, Prime and Composite Test Solutions and Scoring (PDF)

\(1 \times 40\), \(2 \times 20\), \(4 \times 10\), \(5 \times 8\).

1 and 40, 2 and 20, 4 and 10, 5 and 8

Scoring: 2 points for all four pairs; 1 point for three pairs or for four pairs with one wrong extra pair; 0 points otherwise.

Count by 9: 9, 18, 27, 36, 45, 54, 63.

27 and 54

Scoring: 1 point for each correct missing number.

7 rows of 3: \(7 \times 3 = 21\). Factor pairs: \(1 \times 21\), \(3 \times 7\).

\(7 \times 3\) = 21; factors 1, 3, 7, 21

Scoring: 1 point for a correct equation; 1 point for all four factors.

(a) 27 = \(3 \times 9\): composite. (b) 31 has only factors 1 and 31: prime. (c) 49 = \(7 \times 7\): composite. (d) 61 has only factors 1 and 61: prime.

(a) composite (b) prime (c) composite (d) prime

Scoring: 2 points for four correct; 1 point for two or three correct.

\(9 \times 7 = 63\), \(9 \times 8 = 72\), \(9 \times 11 = 99\). 85 and 91 are not (\(9 \times 9\) = 81, \(9 \times 10\) = 90, \(9 \times 11\) = 99).

63, 72, 99

Scoring: 2 points for all three and no extra numbers; 1 point if one is missing or one wrong number is included.

A prime number has exactly two factors. The number 1 has only one factor, 1 itself.

Mia is not correct. 1 has one factor, so it is not prime.

Scoring: 1 point for saying Mia is not correct; 1 point for a reason that mentions the number of factors.

(a) \(8 \times 7 = 56\).

(b) The primes between 80 and 90 are 83 and 89. 8 + 3 = 11, 8 + 9 = 17.

(c) The only multiple of 5 between 10 and 20 is 15. It is odd and 15 = \(3 \times 5,\) so it is composite.

(a) 56 (b) 83 (c) 15

Scoring: 1 point for each correct number.

The last digit is 5.

(a) no (b) yes (c) no

Scoring: 2 points for three correct; 1 point for two correct.

(a) Factor pairs of 32: \(1 \times 32,\) \(2 \times 16,\) \(4 \times 8\). Rows and desks per row both at least 2: \(2 \times 16,\) \(4 \times 8,\) \(8 \times 4,\) \(16 \times 2\).

(b) 32 has more than two factors (1, 2, 4, 8, 16, 32).

(a) \(2 \times 16,\) \(4 \times 8,\) \(8 \times 4,\) \(16 \times 2\) (b) composite

Scoring: (a) 2 points for four arrangements, 1 point for two or three; (b) 1 point for composite with a reason.