5th Grade Patterns and Ordered Pairs Test Solutions and Scoring (PDF)

(a) 0, 4, 8, 12, 16

(b) 0, 8, 16, 24, 32

Scoring: 1 point for each pattern. Take off the point if the first term is not 0 or any term is wrong.

Pair the terms in the same position, with the A term first.

\((0, 0), (6, 2), (12, 4), (18, 6), (24, 8)\)

Scoring: 2 points for all five pairs correct. 1 point for three or four correct pairs, or for all pairs written with the numbers in the wrong order.

A: 0, 2, 4, 6. B: 0, 10, 20, 30. Each B term is \(10\div2=5\) times the A term, because \(10=5\times2\), \(20=5\times4\), \(30=5\times6\).

Answer: each B term is 5 times the A term

Scoring: 1 point for listing the terms, 1 point for the correct relationship (5 times).

(a) A: 0, 2, 4, 6. B: 0, 3, 6, 9. Pairs: \((0, 0), (2, 3), (4, 6), (6, 9)\).

(b) Plot each pair: right the first number, up the second.

Scoring: (a) 1 point for four correct pairs. (b) 2 points for four correct points; 1 point for two or three correct points.

A adds 5: \(10+5=15\).

B adds 15: \(15+15=30\).

Answer: 15 and 30

Scoring: 1 point for each missing number.

First numbers: 0, 3, 6, 9: start at 0, add 3. Second numbers: 0, 2, 4, 6: start at 0, add 2.

Next pair: first 12, second \(6+2=8\). Answer: 8

Scoring: 1 point for both rules, 1 point for 8.

(a) Pitchers: 0, 1, 2, 3, 4. Cups: 0, 8, 16, 24, 32. Pairs: \((0, 0), (1, 8), (2, 16), (3, 24), (4, 32)\).

(b) Cups are 8 times the pitchers: \(7\times8=56\). Noah makes 56 cups.

Scoring: (a) 2 points for all five pairs, 1 point for four correct. (b) 1 point.

(a) Minutes add 10 and pages add 4. After 50 minutes she has read 20 pages. After 60 minutes: \(16+4=20\), \(20+4=24\). Answer: 24 pages.

(b) Pages 16, 20: the next pair is \((50, 20)\). Answer: 50 minutes.

Scoring: (a) 1 point. (b) 2 points: 1 for continuing the pattern correctly, 1 for 50.

A: 0, 6, 12. B: 0, 10, 20. When A is 12, B is 20, not 18.

Answer: No, the correct pair is \((12, 20)\).

Scoring: 1 point for “no” with a correct reason.