Patterns and Relationships: Grade 5 Math Worksheet Answer Key – PDF Download

Grade 5 Patterns Worksheet Answer Key: problems 1–5

Problem 1: Start at 0, add 3

Start at 0 and add 3 each time: \(0 + 3 = 3\), \(3 + 3 = 6\), \(6 + 3 = 9\), \(9 + 3 = 12\).

The terms are \(0, 3, 6, 9, 12\).

Problem 2: Start at 0, add 5

Start at 0 and add 5 each time: \(0 + 5 = 5\), \(5 + 5 = 10\), \(10 + 5 = 15\), \(15 + 5 = 20\).

The terms are \(0, 5, 10, 15, 20\).

Problem 3: Start at 4, add 2

Start at 4 and add 2 each time: \(4 + 2 = 6\), \(6 + 2 = 8\), \(8 + 2 = 10\), \(10 + 2 = 12\).

The terms are \(4, 6, 8, 10, 12\).

Problem 4: Start at 1, add 7

Start at 1 and add 7 each time: \(1 + 7 = 8\), \(8 + 7 = 15\), \(15 + 7 = 22\), \(22 + 7 = 29\).

The terms are \(1, 8, 15, 22, 29\).

Problem 5: Complete the table

Pattern A adds 2: \(0, 2, 4, 6, 8, 10\).

Pattern B adds 4: \(0, 4, 8, 12, 16, 20\).

Grade 5 Patterns Worksheet Answer Key: problems 6–10

Problem 6: Add 5 and add 10

Pattern A: \(0, 5, 10, 15, 20\).

Pattern B: \(0, 10, 20, 30, 40\).

Compare corresponding terms: \(5 \to 10\), \(10 \to 20\), \(15 \to 30\). Each term of B is 2 times the corresponding term of A.

Problem 7: Add 3 and add 9

Pattern A: \(0, 3, 6, 9, 12, 15\).

Pattern B: \(0, 9, 18, 27, 36, 45\).

Compare corresponding terms: \(3 \to 9\), \(6 \to 18\), \(9 \to 27\). Each term of B is 3 times the corresponding term of A.

Problem 8: Add 4 and add 8

Pattern A: \(0, 4, 8, 12, 16\).

Pattern B: \(0, 8, 16, 24, 32\).

Compare corresponding terms: \(4 \to 8\), \(8 \to 16\), \(12 \to 24\). Each term of B is 2 times the corresponding term of A.

Problem 9: A is a multiple of B

Compare corresponding terms: \(6 \to 2\), \(12 \to 4\), \(18 \to 6\), \(24 \to 8\). Each A term divided by 3 gives the B term.

Each term of A is 3 times the corresponding term of B. For the first terms, \(3 \times 0 = 0\).

Problem 10: B is one more

Pattern A starts at 0 and adds 2. Pattern B starts at 1 and adds 2.

Compare corresponding terms: \(0 \to 1\), \(2 \to 3\), \(4 \to 5\), \(6 \to 7\), \(8 \to 9\). Each term of B is 1 more than the corresponding term of A.

Grade 5 Patterns Worksheet Answer Key: problems 11–15

Problem 11: Add 10 and add 5

Pattern A: \(0, 10, 20, 30, 40\).

Pattern B: \(0, 5, 10, 15, 20\).

Each term of A is 2 times the term of B, so each term of B is half of the corresponding term of A.

Problem 12: Write ordered pairs

Write the term of A first and the term of B second: \((0, 0), (3, 6), (6, 12), (9, 18)\).

Problem 13: Read a graph

1. Read across, then up: \((0, 0), (2, 4), (4, 8), (6, 12)\).
2. The first numbers are \(0, 2, 4, 6\): pattern A adds 2. The second numbers are \(0, 4, 8, 12\): pattern B adds 4.
3. Each second number is 2 times the first number.

Problem 14: Plot the pairs

Pattern A: \(0, 1, 2, 3, 4\). Pattern B: \(0, 3, 6, 9, 12\).

The ordered pairs are \((0, 0), (1, 3), (2, 6), (3, 9), (4, 12)\).

Problem 15: Graph and describe

Pattern A: \(0, 5, 10, 15\). Pattern B: \(0, 10, 20, 30\). The ordered pairs are \((0, 0), (5, 10), (10, 20), (15, 30)\).

The points line up in a straight line going up. Every second number is 2 times the first number.

Grade 5 Patterns Worksheet Answer Key: problems 16–20

Problem 16: Is it a pair?

1. \(12\) is the 5th term of A. The 5th term of B is \(24\). So yes, \((12, 24)\) is formed by corresponding terms.
2. \(9\) is the 4th term of A. The 4th term of B is \(18\), not \(12\). So no.

Problem 17: Find missing terms

Pattern A adds 4, so the 4th term is \(8 + 4 = 12\). Pattern B adds 8, so the 3rd term is \(8 + 8 = 16\).

Check: \(12 \to 24\) and \(8 \to 16\) both show B as 2 times A.

The missing terms are 12 and 16.

Problem 18: Seventh terms

Pattern A: \(0, 6, 12, 18, 24, 30, 36\). Pattern B: \(0, 3, 6, 9, 12, 15, 18\).

The 7th term of A is 36 and the 7th term of B is 18. The A term is 2 times the B term.

Problem 19: Saving each week

Priya: \(0, 4, 8, 12, 16\). Diego: \(0, 8, 16, 24, 32\).

Each of Diego’s amounts is 2 times Priya’s matching amount, because he adds twice as much each week.

Problem 20: School store packs

Pencils: \(6, 12, 18, 24\). Erasers: \(2, 4, 6, 8\).

Ordered pairs: \((6, 2), (12, 4), (18, 6), (24, 8)\).

The number of pencils is 3 times the number of erasers.

Grade 5 Patterns Worksheet Answer Key: problems 21–24

Problem 21: Block towers

1. Mei: \(0, 3, 6, 9, 12\). Liam: \(0, 6, 12, 18, 24\).
2. \((0, 0), (3, 6), (6, 12), (9, 18), (12, 24)\)
3. Liam always has 2 times as many blocks as Mei, because he adds twice as many each step.

Problem 22: Different starting numbers

Pattern A: \(2, 5, 8, 11, 14\). Pattern B: \(4, 10, 16, 22, 28\).

Compare: \(2 \to 4\), \(5 \to 10\), \(8 \to 16\), \(11 \to 22\), \(14 \to 28\). Each term of B is 2 times the corresponding term of A.

Problem 23: Bike miles

Noah: \(0, 2, 4, 6, 8, 10\). Maya: \(0, 6, 12, 18, 24, 30\).

Ordered pairs: \((0, 0), (2, 6), (4, 12), (6, 18), (8, 24), (10, 30)\).

Maya’s miles are 3 times Noah’s miles. The pair with 8 is \((8, 24)\), so Maya has ridden 24 miles.

Problem 24: Find the mistake

Pattern A: \(0, 4, 8, 12\). Pattern B: \(0, 8, 16, 24\).

Hannah’s idea works for \(4 \to 8\) but fails for the first terms \(0 \to 0\) and for \(8 \to 16\), which differ by 8. A relationship must work for every pair.

The correct relationship is that each term of B is 2 times the corresponding term of A.

How to use this grade 5 patterns worksheet answer key

Read this grade 5 patterns worksheet answer key after trying each problem yourself, and redo any problem you missed.

See every chapter on the Grade 5 math page.