For mental math with two-digit numbers, use strategies like counting on by tens and ones, making tens, or decomposing numbers. For example, 34+28 can be solved as 34+30-2 or 30+20 + 4+8.
Teach one strategy at a time (make a ten, count on, decompose). Let students choose which strategy works best for each problem. Use number lines and drawings to show thinking.
You've already practiced adding and subtracting tens in your head — jumping from 30 to 50, or from 70 down to 40. Mental math strategies for two-digit addition take that skill and stretch it to handle the ones digits too. The big idea is this: you don't have to add both digits at once. You can break the problem into steps that are each easy enough to hold in your head.
The decompose into tens and ones strategy is the most direct. To add 34 + 28, split both numbers: 30 + 4 and 20 + 8. Add the tens first (30 + 20 = 50), then the ones (4 + 8 = 12), then combine (50 + 12 = 62). Each step involves only a small calculation. The add tens, then ones strategy keeps the first number whole and adds in parts: 34 + 20 = 54, then 54 + 8 = 62. You're taking one mental step at a time, which keeps you from losing track.
A third strategy is make a ten: look for a way to rewrite the problem so that one number becomes a round ten. For 34 + 28, you could borrow 2 from 34 to give to 28, turning it into 32 + 30 = 62. This works because you know that 28 needs 2 more to reach 30, and round tens are easy to add. The prerequisite skill — adding tens in your head — is doing most of the work here.
No single strategy is best for every problem. Choosing well is part of the skill. For 50 + 37, just add directly — decomposing wastes time. For 48 + 25, making a ten (50 + 23) is cleaner. The goal is to look at a problem, notice which numbers are near a ten or easy to split, and select the path that requires the fewest mental steps. Flexibility — not just accuracy — is what mental math is really about.
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