Grades Grade 4 Operations & Algebraic ThinkingGenerating & Analyzing Number Patterns

Generating & Analyzing Number Patterns

🧠 Operations & Algebraic Thinking

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Generating & Analyzing Number Patterns

Spot the rule in a sequence, extend it, and describe what you see!

A NUMBER PATTERN is a sequence of numbers that follow a specific rule. The rule can involve adding, subtracting, multiplying, or dividing. Spotting the rule lets you predict what comes next and describe the overall behavior of the pattern.

🔢Additive pattern

3, 7, 11, 15, 19, …
Rule: Add 4 each time.
Next term: 19 + 4 = 23.

✖️Multiplicative pattern

2, 6, 18, 54, …
Rule: Multiply by 3 each time.
Next term: 54 × 3 = 162.

How to analyze a number pattern:

1List the terms and find the difference (or ratio) between consecutive terms

2Check if the difference stays the same → additive pattern

3Check if the ratio stays the same → multiplicative pattern

4State the rule clearly: "Start at ___, then ___"

5Use the rule to extend the pattern or fill in missing terms

Two patterns side by side:

Pattern A: 5, 10, 15, 20, 25 (rule: +5)Pattern B: 5, 10, 20, 40, 80 (rule: ×2)

Both start at 5, but Pattern B grows MUCH faster because multiplication compounds quickly.

Features of even-number outputs

Always end in 0, 2, 4, 6, or 8Sum of two oddsDivisible by 2

Features of odd-number outputs

Always end in 1, 3, 5, 7, or 9Sum of an odd and an evenNot divisible by 2

Pattern analysis often reveals properties like "all terms are even" or "every other term is odd."

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Remember This!

Patterns appear in real life too! Multiplication tables are patterns. Clock times follow patterns. Identifying patterns is one of the most powerful skills in all of mathematics.

✏️ Try It!

What is the next number in this pattern: 4, 8, 16, 32, ___?

Take Quiz 📝 — 25 Questions