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I.1 Subtraction patterns across place values

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What are subtraction patterns?

Subtraction patterns are number sequences that decrease by the same amount each time. You look at how much is taken away from one number to get the next.

Example:
  • 5000, 4000, 3000, 2000 → Each step subtracts 1000
Note

Always check the difference between each pair of numbers to find the subtraction pattern.

How to identify a subtraction pattern

To identify a subtraction pattern, compare each number in the sequence with the one before it. The difference tells you how much is subtracted each time.

Steps:
  • Look at the first two numbers: 12,345 → 11,345
  • Find the difference: 12,345 − 11,345 = 1,000
  • Check the next numbers: 11,345 → 10,345 (subtracting 1,000 again)
  • The pattern is subtract 1,000 each time
Note

The subtraction amount can be small (like 5) or large (like 10,000). Always use place value to guide your work.

Examples of subtraction patterns

Here are some common subtraction patterns with different place values:

Examples:
  • 9,875, 9,775, 9,675, 9,575 → Subtract 100 each time
  • 42,000, 41,000, 40,000, 39,000 → Subtract 1,000 each time
  • 7,654, 7,644, 7,634, 7,624 → Subtract 10 each time
Note

Look at the digit that changes each time. This shows which place value the subtraction pattern uses.

Using subtraction patterns to complete sequences

When part of a subtraction sequence is missing, find the subtraction rule and apply it step by step to complete the pattern.

Example:
  • Sequence: 25,000, 24,000, ____, 22,000
  • Find the rule: subtract 1,000 each time
  • Fill in the blank: 25,000 → 24,000 → 23,000 → 22,000
Note

Check your answer by subtracting again to see if each step follows the same pattern.

Why subtraction patterns are important

Understanding subtraction patterns helps you work with large numbers, recognize place value, and prepare for algebraic thinking in more advanced math.

Example:
  • Pattern: 100,000, 90,000, 80,000, 70,000 → Subtracting 10,000 each time shows the tens of thousands place decreasing.
Note

Patterns in subtraction make problem solving faster and build number sense across place values.