Mental math strategies for addition include making 10, using doubles and near-doubles, counting on, and decomposing numbers. By learning multiple strategies, students become flexible thinkers who can choose the most efficient method for each problem.
You already know how to make 10 — you can take a number like 8 and figure out that it needs 2 more to reach 10. And you know near-doubles like 6 + 7, where you recognize that 6 + 6 = 12, so 6 + 7 must be one more, which is 13. These two strategies are the foundation of mental math for addition, and this topic is about becoming fluent with all of them and knowing when to use which one.
The counting on strategy is the simplest: when you add 9 + 3, you start at 9 in your head and count forward three steps: 10, 11, 12. This works well when one number is much bigger than the other. It saves you from starting at 1 and counting all the way up — that would take forever. The key move is to always count on from the larger number. Adding 2 + 9? Don't start at 2 and count nine steps. Flip it: start at 9 and count two steps. You learned this from the commutative property.
Making 10 is the most powerful strategy for speed. Ten is a special number because our number system is built in groups of ten. When you see 8 + 5, notice that 8 is only 2 away from 10. So break the 5 into 2 + 3: give the 2 to the 8 to make 10, and then add the leftover 3. Now you have 10 + 3 = 13. This works because you're not changing the total — you're just rearranging it to pass through 10, which is easy to work with. The same idea works with bigger numbers later on.
Decomposing (breaking apart) numbers gives you flexibility. 7 + 6 is tricky — but you might notice that 7 = 5 + 2 and 6 = 5 + 1. So 7 + 6 = (5 + 5) + (2 + 1) = 10 + 3 = 13. You don't have to decompose exactly this way — whatever lets you see a pair of numbers that adds cleanly. The big idea across all these strategies is that numbers are flexible: you can pull them apart, rearrange the pieces, and put them back together in whatever shape makes the addition easiest. A good mental math thinker does not memorize one fixed method — they read the problem, notice which strategy fits, and apply it quickly.