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FF.1 Complete number patterns using rules

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What are number patterns?

Number patterns are sequences of numbers that follow a specific rule. Each number in the pattern is related to the one before it by that rule.

Examples:
  • 2, 4, 6, 8, 10 → Add 2 each time
  • 100, 90, 80, 70 → Subtract 10 each time
Note

Always look for what changes from one number to the next. The change tells you the rule.

How to find the rule in a number pattern

To find the rule, compare each number to the one before it. Check if you are adding, subtracting, multiplying, or dividing by the same amount each time.

Steps:
  • Look at the pattern: 3, 6, 12, 24
  • Ask: How do I get from 3 to 6? Multiply by 2.
  • Check if the same rule works for the rest. 6 × 2 = 12 and 12 × 2 = 24
  • The rule is “Multiply by 2.”
Note

If the same operation works for each step, you have found the correct rule. Always test your rule for every number in the pattern.

Common types of rules in number patterns

Most number patterns follow simple rules that use addition, subtraction, multiplication, or division.

Examples:
  • Addition pattern: 5, 10, 15, 20 → Add 5 each time
  • Subtraction pattern: 1,000, 900, 800, 700 → Subtract 100 each time
  • Multiplication pattern: 4, 8, 16, 32 → Multiply by 2 each time
  • Division pattern: 1,200, 600, 300, 150 → Divide by 2 each time
Note

Patterns can grow (increase) or shrink (decrease). Use place value and basic facts to help check your work.

Using rules to complete number patterns

Once you know the rule, apply it to find the missing numbers in the pattern. Continue using the same operation for each step.

Examples:
  • Rule: Add 250
    Pattern: 1,000, 1,250, 1,500, 1,750, 2,000
  • Rule: Divide by 5
    Pattern: 1,250, 250, 50, 10, 2
Note

When you apply a rule, make sure you use it correctly each time. Patterns are predictable—if one number looks wrong, recheck your rule.

Real-world connections

Number patterns appear in real life, such as in calendars, distances, scores, or prices. Recognizing patterns helps you predict and solve problems faster.

Examples:
  • Counting by 25s on coins: 25, 50, 75, 100 → Add 25
  • Measuring time: 5, 10, 15, 20 minutes → Add 5
  • Saving money: $10, $20, $40, $80 → Multiply by 2
Note

Finding patterns helps you think logically and solve problems in everyday situations, not just in math class.