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Using Mental Math to Add Up to 20

This lesson covers mental math strategies for adding numbers up to 20, including making a ten, using doubles facts, and counting on, so students can add quickly and confidently without paper or a calculator.

What Is Mental Math?

Mental math means solving a problem in your head, without writing anything down or using a calculator. When you're adding numbers up to 20, mental math strategies let you find the answer quickly by breaking the problem into smaller, friendlier pieces. Instead of counting one by one, you use number patterns you already know, like facts to 10, to jump straight to the answer.

Learning these strategies now makes every future addition problem faster, and it builds the number sense you'll use in estimating sums and in real-life word problems.

Strategy 1: Making a Ten

One of the most useful mental addition strategies is making a ten. Since adding to 10 is easy, you can break one addend apart so that part of it completes a ten, then add on what's left.

For example, to solve \( 8 + 5 \), think about how much 8 needs to reach 10. It needs 2 more. So split the 5 into \( 2 + 3 \):

\( 8 + 5 = 8 + 2 + 3 = 10 + 3 = 13 \)

Ten frames showing 8 and 5. Moving 2 counters into the first frame makes a full ten, leaving 3.

This same idea works for any pair of numbers close to 10 or 20, and it's especially handy when one addend is 7, 8, or 9.

Strategy 2: Doubles and Near-Doubles

Doubles facts, like \( 6 + 6 \), \( 7 + 7 \), and \( 9 + 9 \), are worth memorizing because they show up constantly and are easy to picture. Once you know a doubles fact, you can use it to solve a "near-double" problem, where the two addends are just one apart.

For example, if you know \( 7 + 7 = 14 \), then \( 7 + 8 \) is just one more:

\( 7 + 8 = 7 + 7 + 1 = 14 + 1 = 15 \)

Likewise, \( 6 + 8 \) is two away from the double \( 7 + 7 \), since 6 and 8 are each one step from 7:

\( 6 + 8 = 7 + 7 = 14 \)

Strategy 3: Counting On

When one number is small, usually 1, 2, or 3, it's often fastest to start at the larger number and count on. For \( 12 + 3 \), start at 12 and count up three more: 13, 14, 15.

Counting on from 12 by three jumps of 1 gives 13, 14, then 15.

Counting on works well for small second numbers, but for larger numbers making a ten or using doubles is usually quicker and less prone to mistakes.

Putting the Strategies Together

Good mental mathematicians don't use just one method. They glance at a problem, like \( 9 + 6 \), and pick whichever strategy fits best. Here, 9 is one away from 10, so making a ten works nicely: \( 9 + 1 + 5 = 10 + 5 = 15 \). For \( 8 + 8 \), a doubles fact gives the answer instantly: \( 16 \). For \( 13 + 2 \), counting on is simplest: \( 14, 15 \).

These same building blocks reappear when you start using mental math to subtract up to 20, since knowing a fact like \( 8 + 5 = 13 \) also tells you that \( 13 - 5 = 8 \).

Practice Problems

Try solving each of these in your head before checking the strategy suggested.

Problem	Suggested strategy	Answer
\( 9 + 7 \)	Make a ten: \( 9 + 1 + 6 \)	16
\( 6 + 6 \)	Doubles fact	12
\( 14 + 3 \)	Counting on	17
\( 8 + 9 \)	Near-double of \( 8 + 8 \)	17
\( 7 + 4 \)	Make a ten: \( 7 + 3 + 1 \)	11

Why These Strategies Matter

Mental addition to 20 is the foundation for almost every math skill that comes next, from larger addition and subtraction to solving mental math word problems. Once these facts feel automatic, they also support skills like estimating sums, where you use quick mental approximations instead of exact calculations. Keep practicing a mix of making ten, doubles, and counting on until picking the fastest strategy becomes second nature.

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