Strategy #1: Count Back

The counting on strategy for subtraction involves starting at the smaller number and counting up to the larger number to find the difference. Counting back means starting at the larger number and counting backward by ones, tens, or other steps to reach the smaller number. A number line helps visualize subtraction by showing jumps backward (or forward, if counting on), making it easier to track and understand the difference between numbers.

Subtracting on a Number Line

Counting Back to Subtract

Strategy #2: Inverse Operations

Using inverse operations means solving subtraction problems by thinking of the related addition fact. For example, to solve 12 − 5, you can think, “What number plus 5 equals 12?” Since 7 + 5 = 12, the answer to 12 − 5 is 7.

Addition and Subtraction Fact Families

Addition and subtraction fact families are sets of related math facts that use the same numbers to show how addition and subtraction are connected. For example, if you know that 7 + 5 = 12, you can also use that fact to understand the related subtraction facts: 12 − 7 = 5 and 12 − 5 = 7. These facts show how subtraction "undoes" addition, and learning them helps make solving problems easier. Understanding fact families helps build a strong foundation in math by showing how numbers work together in different ways.

Strategy #3: Use Partials

Using partial differences to subtract means breaking the numbers into place values and subtracting each part separately. For example, to subtract 73 − 46, you subtract the tens (70 − 40 = 30), then the ones (3 − 6 = -3), and finally combine the partial differences (30 + (–3) = 27).

Strategy #4: Compensation

Compensation in subtraction involves adjusting the numbers to make the problem easier to solve, then correcting the answer. For example, in 52 − 29, you can round 29 up to 30, subtract 52 − 30 = 22, then add back the 1 you subtracted too much, giving a final answer of 23.

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