Worked Example 1
Rule from Position
Position: 1, 2, 3, 4 → Value: 5, 9, 13, 17
- 1The values go up by 4 each time, so the rule uses 4 × n.
- 24 × 1 = 4, but the first value is 5, so add 1.
- 3Check: 4 × 3 + 1 = 13.
Answer: 4 × n + 1
Florida Grade 5 Math · Algebraic Reasoning
MA.5.AR.3.1: Rules for number patterns
What this Grade 5 benchmark means, worked examples, common mistakes, and a free printable worksheet.
Created by a Florida mom · Published by Tropical Learning LLC
What Is Benchmark MA.5.AR.3.1?
In Grade 5, students look at a numerical pattern, find the rule, and write the rule as an expression.
A rule can describe how to get from one term to the next ("add 4") or how to find any term from its position (4 × n + 1). Writing it as an expression lets you find terms far down the pattern.
Official benchmarkGiven a numerical pattern, identify and write a rule that can describe the pattern as an expression.
On the FAST test: part of the Grade 5 reporting category Algebraic Reasoning, which is about 23–29% of the test.
Worked Examples
Worked Example 2
A Multiplying Pattern
3, 6, 12, 24, ...
- 16 ÷ 3 = 2, 12 ÷ 6 = 2, 24 ÷ 12 = 2.
- 2Each term is 2 times the one before.
- 3The next term is 24 × 2 = 48.
Answer: Multiply by 2
Common Mistakes to Watch For
Assuming every pattern adds
Wrong:3, 6, 12, 24 → next is 27
Check the change between each pair: 3, 6, 12 are not the same. Each term doubles, so next is 48.
Using only the step, not the start
Wrong:5, 9, 13, 17 → rule is 4 × n
4 × 1 = 4, not 5. Adjust for the start: 4 × n + 1.
Helpful Math Tip
Test your rule on at least two terms. A rule that works for only the first term is not the rule.
Related Grade 5 Skills
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