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H.1 Addition patterns across place values

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What is an addition pattern?

Addition patterns are number sequences that increase by the same amount each time. You find the pattern by adding the same number repeatedly.

Examples:
  • 2, 4, 6, 8, 10 → add 2 each time
  • 15, 25, 35, 45 → add 10 each time
Note

Every term in the pattern is created by adding the same number to the previous term.

How to identify an addition pattern

Look at the numbers in the sequence and check the difference between one number and the next. If the difference is the same, it is an addition pattern.

Steps:
  • Take the first two numbers: 120, 130
  • Find the difference: 130 − 120 = 10
  • Check the next numbers: 140 − 130 = 10
  • The pattern adds 10 each time.
Note

The “rule” of the pattern is the number you add each time. Always check more than one step to confirm the rule.

Examples with larger numbers

Patterns can use small or large numbers, even up to five digits. The rule stays the same: add the same amount each step.

Examples:
  • 1,250 → 1,350 → 1,450 → 1,550 (add 100 each time)
  • 9,000 → 9,200 → 9,400 → 9,600 (add 200 each time)
  • 45,120 → 45,220 → 45,320 → 45,420 (add 100 each time)
Note

When numbers get larger, line them up by place value to check the difference more easily.

Using place value in addition patterns

Addition patterns often change across place values (ones, tens, hundreds, thousands, ten-thousands). Knowing place value helps you recognize how the numbers grow.

Examples:
  • 500, 600, 700, 800 → pattern increases in the hundreds place
  • 8,000, 9,000, 10,000, 11,000 → pattern increases in the thousands place
  • 23,450, 23,460, 23,470, 23,480 → pattern increases in the tens place
Note

Pay attention to which place value is changing. This helps you predict the next number quickly.

Applying addition patterns

Completing addition patterns helps you build number sense, recognize rules, and solve problems more efficiently.

Examples:
  • Finish the pattern: 2,450 → 2,550 → 2,650 → ? → ?
    Rule: add 100 each time → 2,750, 2,850
  • Finish the pattern: 10,000 → 10,500 → 11,000 → ?
    Rule: add 500 each time → 11,500
Note

Always state the rule in words (for example: “add 500 each time”) and then use it to continue the sequence.

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