Adding or subtracting a multiple of 10 from any two-digit number changes only the tens digit, leaving the ones digit unchanged. To compute 47 + 30, think: 4 tens + 3 tens = 7 tens, so the result is 77. Similarly, 82 − 50 = 32 because 8 tens − 5 tens = 3 tens. This mental strategy is faster than the written algorithm and builds number sense.
Use a hundred chart and have students move up or down rows (each row = 10) to visualize adding or subtracting tens. Then practice mentally, gradually removing the chart. Emphasize the pattern: 'only the tens digit changes.'
You already know how place value works: a two-digit number like 47 is made of 4 tens and 7 ones. That structure is the key to mental addition and subtraction with tens. When you add a multiple of 10 — a number like 20, 30, or 50 — you are only adding to the tens part of the number. The ones part stays exactly the same.
Imagine a hundred chart laid out in front of you. Every row is a group of 10. When you add 30, you jump down three rows. Your column — your ones digit — never changes. If you start at 47 (column 7, row 4), jumping down three rows lands you at 77. The ones digit is still 7. This is why the rule works: adding tens only changes the tens digit.
The same idea runs backwards for subtraction. To compute 82 − 50, ask: "8 tens minus 5 tens is how many tens?" The answer is 3 tens — and the 2 in the ones place never moved. So 82 − 50 = 32. No writing required. You are doing tens arithmetic just like you learned to do ones arithmetic, using the same counting skills but applied one column to the left.
The one situation that requires extra care is when the tens digits add up to 10 or more, causing a carry into the hundreds. For example, 75 + 40: 7 tens + 4 tens = 11 tens = 110, plus the 5 ones = 115. The ones digit is still 5, but you now have a hundreds digit too. The strategy still works — you just need to handle the regrouping in your head, which gets easier with practice.