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Using Mental Math to Subtract Up to 20

This lesson teaches strategies for subtracting mentally within 20, including counting back on a number line, thinking in terms of addition, and breaking numbers apart to make ten first.

Why Use Mental Math for Subtraction?

Subtracting numbers up to 20 comes up constantly, whether you're figuring out how many crayons are left in a box or how many minutes remain before recess. Counting on fingers works, but it is slow and easy to lose track of once numbers get past ten. Mental math strategies let you find the answer to problems like \( 15 - 4 \) or \( 12 - 7 \) quickly and confidently, without needing paper or a number line every time.

The goal is not to memorize every single fact by rote, but to notice patterns and relationships between numbers so subtraction becomes something you can reason through in your head.

Strategy 1: Counting Back

When the number you are subtracting is small (usually 1, 2, or 3), it is fastest to start at the larger number and count back that many steps. For \( 15 - 4 \), start at 15 and hop back four times: 14, 13, 12, 11. The answer is 11.

Counting back works best for small hops. Once the number being subtracted gets larger than 3, another strategy is usually faster and less error prone.

Strategy 2: Think Addition (Counting Up)

Every subtraction fact has a matching addition fact. Since \( 7 + 5 = 12 \), it must also be true that \( 12 - 7 = 5 \). Instead of counting backward through a big gap, ask "what do I add to 7 to reach 12?" and count up: 8, 9, 10, 11, 12. That is five steps, so \( 12 - 7 = 5 \).

This "think addition" trick is especially useful when the two numbers in the subtraction are close together, or when the number you are subtracting is close to the total.

Strategy 3: Make a Ten First

Ten is the easiest number to work with in your head, so a powerful strategy is to break the smaller number apart so you land on 10 first. For \( 13 - 5 \), split the 5 into 3 and 2. Subtract the 3 first to get to 10, then subtract the remaining 2.

The same idea works for addition. If you have already practiced using mental math to add up to 20, you will recognize this "make a ten" idea from building sums, since it uses the same friendly-number thinking in reverse.

Strategy 4: Use Doubles and Near Doubles

If you already know a doubles fact, such as \( 8 + 8 = 16 \), you can use it to solve nearby subtraction facts almost instantly. For \( 16 - 8 \), recognize that 16 is double 8, so the missing number must also be 8. For \( 16 - 7 \), notice that 7 is one less than 8, so the answer will be one more than 8, giving 9.

Leaning on facts you already know well, instead of solving every problem from scratch, is what makes mental math fast.

Choosing the Best Strategy

Skilled mental math is really about flexibility: looking at the two numbers and picking whichever strategy fits best.

If the number being subtracted is 1, 2, or 3, count back.
If the number being subtracted is close to the total, think addition and count up instead.
If crossing over 10 feels tricky, break the smaller number apart to make a ten first.
If a doubles fact is nearby, use it to jump straight to the answer.

These same strategies show up again once subtraction problems are wrapped inside a story, so once this feels comfortable, try applying it in mental math word problems.

Worked Examples

Example 1: \( 18 - 3 \). Count back three from 18: 17, 16, 15. So \( 18 - 3 = 15 \).

Example 2: \( 14 - 9 \). Think addition: what plus 9 makes 14? Count up 10, 11, 12, 13, 14, which is five steps, so \( 14 - 9 = 5 \).

Example 3: \( 17 - 8 \). Make a ten: split 8 into 7 and 1. \( 17 - 7 = 10 \), then \( 10 - 1 = 9 \), so \( 17 - 8 = 9 \).

Before checking a mental math answer with a written method, it can also help to get a quick sense of the size of the answer using estimating differences, which is a good habit for catching mistakes.

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