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Subtracting with Digits up to 20

This lesson covers subtracting whole numbers up to 20, showing how to use counting back, number lines, and subtraction facts to find differences accurately and build a strong number sense foundation.

What Does Subtracting with Digits up to 20 Mean?

Subtracting with digits up to 20 means finding the difference between two whole numbers where the larger number is no bigger than 20. For example, \(17 - 5 = 12\) is a subtraction problem within this range. Before working through these problems, it helps to be comfortable with understanding the subtraction sign, since the minus sign \( - \) always tells us we are taking away, comparing, or finding a missing part.

Subtraction can be thought of in three ways: taking objects away from a group, comparing two groups to see how many more one has than the other, or finding a missing part when the whole and one part are known. All three ideas use the same operation, just applied to different situations.

Strategy 1: Counting Back

One of the simplest ways to subtract is to start at the larger number and count backward by the amount being subtracted. To solve \(17 - 5\), start at 17 and count back five numbers: 16, 15, 14, 13, 12. The last number said is the answer, so \(17 - 5 = 12\).

Counting back works well for small numbers being subtracted, but it can get slow for larger amounts. That is why it helps to also learn subtraction facts up to 20, which lets students recall answers instantly instead of counting every single time.

Strategy 2: Using a Number Line

A number line gives a visual picture of subtraction. Starting at the larger number, each jump to the left represents subtracting one. The picture below shows \(17 - 5 = 12\) as five backward jumps starting at 17 and landing on 12.

Starting at 17 and jumping back five spaces lands on 12, so \(17 - 5 = 12\).

If this visual approach feels new, it is worth reviewing using number line to subtract up to 20, which walks through how to draw and read these jumps step by step.

Strategy 3: Breaking Apart Numbers

Another useful method is breaking the number being subtracted into friendlier parts. For example, to solve \(15 - 8\), break 8 into 5 and 3. First subtract 5 to reach a round number: \(15 - 5 = 10\). Then subtract the remaining 3: \(10 - 3 = 7\). So \(15 - 8 = 7\). Breaking numbers apart this way avoids long counting sequences and builds flexible number sense.

Worked Examples

Example 1: Solve \(19 - 6\).

Count back six numbers from 19: 18, 17, 16, 15, 14, 13. So \(19 - 6 = 13\).

Example 2: Solve \(14 - 9\).

Break 9 into 4 and 5. First, \(14 - 4 = 10\). Then, \(10 - 5 = 5\). So \(14 - 9 = 5\).

Example 3: Solve \(20 - 12\).

Using a number line, start at 20 and jump back 12 spaces to land on 8, so \(20 - 12 = 8\). Check it by adding: \(8 + 12 = 20\).

Checking Your Answer

A quick way to check any subtraction is to add the difference back to the number that was subtracted. If \(a - b = c\), then \(c + b\) should equal \(a\). For instance, since \(17 - 5 = 12\), adding \(12 + 5\) should give 17, and it does. This checking habit catches small counting mistakes and connects subtraction to addition, which is also the idea behind completing subtraction statements and filling in missing numbers in a subtraction sentence.

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