4th Grade Number and Shape Patterns Test Solutions and Scoring (PDF)

8, 15, 22, 29, 36, 43.

8, 15, 22, 29, 36, 43

Scoring: 2 points for all six terms; 1 point if one term is wrong or one is missing.

\(3 \times 2 = 6\), \(6 \times 2 = 12\), \(12 \times 2 = 24\), \(24 \times 2 = 48\).

3, 6, 12, 24, 48

Scoring: 2 points for all five terms; 1 point if the first three terms are correct.

Each term is 8 more than the one before. \(36 + 8 = 44\), \(44 + 8 = 52\).

Add 8; 44 and 52

Scoring: 1 point for the rule; 1 point for both missing numbers.

\(10 – 4 = 6\), \(12 – 4 = 8\), \(15 – 4 = 11\), \(18 – 4 = 14\), \(20 – 4 = 16\).

6, 8, 11, 14, 16

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

\(3 \times 4 = 12\), \(5 \times 4 = 20\), \(7 \times 4 = 28\), \(9 \times 4 = 36\). The rule is multiply by 4.

\(11 \times 4 = 44\).

Multiply by 4; output 44

Scoring: 1 point for the rule; 1 point for 44.

(a) 4, 7, 10: add 3 each time, starting at 4.

(b) 13, 16, 19. Six squares need 19 toothpicks.

(c) The terms are 4, 7, 10, 13, 16, 19, 22, 25. Yes, 8 squares use 25 toothpicks.

(a) start at 4, add 3 (b) 19 (c) yes, 8 squares

Scoring: 1 point for each part.

5, 9, 13, 17, 21, 25.

Every term is odd, because adding an even number to an odd number always gives an odd number.

5, 9, 13, 17, 21, 25; all odd

Scoring: 1 point for the six terms; 1 point for a correct feature.

(a) 3, 7, 11, 15, 19.

(b) Continue: 23, 27, 31. Row 8 has 31 flowers.

(c) Every row has an odd number of flowers (3 is odd and 4 is even). 50 is even, so no row has 50.

(a) 3, 7, 11, 15, 19 (b) 31 (c) no, all rows are odd

Scoring: 1 point for each part.

2, 5, 8, 11, 14, 17.

The terms alternate even, odd, even, odd. Adding 3 (an odd number) changes odd and even each time.

Diego is not correct.

Scoring: 1 point for the six terms; 1 point for a correct conclusion with a reason.