Mental math strategies for addition include making tens, counting on, breaking apart numbers, and using place value. For example, 28 + 15 = 28 + 2 + 13 = 30 + 13 = 43. Flexible strategies develop fluency and number sense.
You already know how to add two-digit numbers by writing them out in columns and regrouping — that's your prerequisite skill. Mental math is the same arithmetic, but performed entirely in your head by choosing clever ways to rearrange the numbers. The key insight is that addition doesn't care what order you group numbers in, so you can always split, rearrange, and simplify as long as the total stays the same.
The most powerful mental math strategy is making tens. Ten is easy to work with because our number system is base-10. To add 28 + 15, notice that 28 is only 2 away from 30. So split 15 into 2 + 13: now you have 28 + 2 = 30, and then 30 + 13 = 43. You've turned a hard problem into two easy ones by creating a round number along the way. Any time one of your numbers is close to a multiple of 10, making a ten is the fastest route.
Another strategy is counting on — start with the larger number and count up by the smaller one. 47 + 8 means starting at 47 and counting up 8 to land on 55. This works best when the number being added is small. Breaking apart numbers (also called decomposing) means splitting addends by place value: 34 + 52 becomes (30 + 50) + (4 + 2) = 80 + 6 = 86. You add the tens together, add the ones together, and combine the results.
The reason these strategies matter is not just speed — it's number sense. When you choose which strategy to use, you are thinking about the structure of numbers. A student who automatically breaks 37 + 25 into 37 + 3 + 22 = 40 + 22 = 62 is doing the same thing a mathematician does when simplifying a complex problem: find the structure that makes the calculation easy. Practice switching between strategies and you'll find that choosing the right approach becomes a kind of creative skill.