When adding two-digit numbers, the ones column may sum to 10 or more. When this happens, we regroup — trading 10 ones for 1 ten and carrying that ten to the tens column. For example, 47 + 35 requires regrouping because 7 + 5 = 12 ones, so we write 2 ones and carry 1 ten. Understanding place value is essential: the carry represents a full group of ten.
Use base-ten blocks to physically trade 10 unit cubes for a tens rod before moving to the written algorithm. Have students predict whether regrouping will be needed (ones digits sum ≥ 10) before computing. Practice with open number lines alongside the standard algorithm so students understand what is happening, not just the procedure.
You already know how to add two-digit numbers when the ones column stays below 10 — you simply add ones to ones, then tens to tens. Regrouping is what happens when the ones column "overflows." The key idea comes directly from your knowledge of place value: our number system groups things in tens. When you have 10 or more ones, you can always trade them for a ten, because that's what tens *are*.
Here's the core example. Add 47 + 35. Start with the ones: 7 + 5 = 12. But "12 ones" can't stay in the ones place — there's only room for a single digit there. So you regroup: trade 10 of those 12 ones for 1 ten, keeping 2 ones in the ones place. Write the 2 ones in the ones column and carry the new ten up to the tens column as a small "1." Now add the tens: 4 + 3 + 1 (the carried ten) = 8 tens. The answer is 82.
What makes regrouping work — and what students often miss — is that *nothing is being added or removed*. You're only renaming the same quantity. 12 ones and 1 ten + 2 ones are exactly the same amount, just as a dozen eggs is 12 eggs regardless of how they're arranged. The total value is preserved; only the representation changes. This is why base-ten blocks are so helpful: when you physically trade 10 unit cubes for a tens rod, you can see and feel that the total amount hasn't changed.
Before computing, you can predict whether regrouping will be needed: if the ones digits sum to 10 or more, you'll regroup. 6 + 7 = 13 (regroup), 8 + 5 = 13 (regroup), 3 + 4 = 7 (no regroup). Building this habit of previewing a problem helps you stay alert during computation. Every multi-digit addition you encounter in later grades — with hundreds, thousands, and beyond — applies exactly this same principle, column by column, moving from right to left.