Multi-digit addition extends single-digit addition by working place value by place value, starting from the ones. When the sum in any column exceeds 9, we "regroup" (carry) into the next place -- this is why understanding that 10 ones = 1 ten is essential. Students at this level add numbers up to the millions, managing multiple regroupings across columns. The standard algorithm is efficient, but it only makes sense when students understand that they are combining like units (ones with ones, tens with tens) and trading 10 of one unit for 1 of the next.
Start with base-ten blocks: physically combine ones, trade 10 ones for a ten-rod, combine ten-rods, trade 10 for a hundred-flat. Then transition to the written algorithm, linking each step back to what the blocks showed. Partial sums (adding each place separately, then combining) is a useful bridge strategy. Practice with real-world contexts -- combining distances, costs, populations -- reinforces meaning.
You already know two things that make multi-digit addition straightforward: how to add single-digit numbers, and how place value works (ones, tens, hundreds, thousands, and so on). Multi-digit addition is just those two ideas applied together. The central rule is that you can only combine like units — ones with ones, tens with tens, hundreds with hundreds. This is why you write numbers aligned by place value before adding.
Always start from the ones column and move left. When you add the ones, you might get a sum of 10 or more. You cannot write a two-digit number in a single column, so you write the ones digit in the column and "carry" the tens digit to the next column — this is regrouping. What you are really doing is trading 10 ones for 1 ten, the same trade you made physically with base-ten blocks when 10 unit cubes became a ten-rod.
The most common mistake is forgetting to include the carried digit in the next column. Think of a carry as an obligation: the moment you write it above a column, you must add it when you get there. A good habit is to write carry digits small above the column so they stay visible. The second most common mistake is misaligning columns — writing 976 so that its 9 lines up under the thousands digit of 1,248 instead of under the hundreds digit.
This algorithm scales to any number of digits without any new rules. Whether you are adding five-digit numbers or ten-digit numbers, each column works exactly like the ones column. That unlimited scalability is one of the most remarkable features of base-ten positional notation — the same simple procedure handles any size of number you could ever encounter.