A student solves 256 + 178. In the ones column, she calculates 6 + 8 = 14 and writes '14' in the ones place, then continues to the tens column. What is her error?
AShe should have started with the hundreds column, not the ones
BShe wrote both digits of 14 in the ones place; she should write 4 in the ones place and carry 1 to the tens column
CShe made an arithmetic mistake; 6 + 8 does not equal 14
DShe should have written 14 in the tens column instead
The ones place can only hold a single digit (0–9). When a column sum reaches 10 or more, you cannot write the two-digit result in one column. Instead, write the ones digit (4) in the ones place and carry the tens digit (1) to the next column to the left — this is regrouping. Writing '14' in the ones place implicitly squeezes a tens-place digit into the wrong column, producing a wildly incorrect answer. The carry represents the real-world trade: 14 ones = 1 ten and 4 ones.
Question 2 Multiple Choice
What is the correct answer to 487 + 365?
A742
B752
C852
D842
Ones: 7 + 5 = 12; write 2, carry 1. Tens: 8 + 6 + 1 (carried) = 15; write 5, carry 1. Hundreds: 4 + 3 + 1 (carried) = 8. Answer: 852. The two most common errors are forgetting to add the carried digit in the tens column (giving 742 or 752 without the second carry) and mishandling two separate carries in the same problem.
Question 3 True / False
When adding three-digit numbers, it is possible to need to regroup twice in the same problem — once in the ones column and once in the tens column.
TTrue
FFalse
Answer: True
True. Each column is evaluated independently. If the ones column produces a sum of 10 or more, you carry 1 to the tens column. Then the tens column adds its two digits plus the carried 1 — and if that sum also reaches 10 or more, you carry 1 to the hundreds column. Both carries can occur in the same problem. Handling them one at a time, column by column from right to left, keeps the process manageable.
Question 4 True / False
When you 'carry' a digit in addition, you are changing the total value of the numbers you are adding.
TTrue
FFalse
Answer: False
False. Carrying does not change the value — it reorganizes the same value into proper place-value notation. When ones-column sum equals 12, writing '2' in ones and carrying '1' to tens is just writing 12 as '1 ten and 2 ones,' which equals 12. The total is preserved; you are simply expressing it in a way that fits the positional system. This is why carrying is not a trick — it is the same ten-for-one trade you have been doing with base-ten blocks all along.
Question 5 Short Answer
Why is 'carrying' in column addition not a separate trick, but rather the same trade you have been doing with place value all along?
Think about your answer, then reveal below.
Model answer: Carrying is just the written expression of the trade '10 ones = 1 ten' (or '10 tens = 1 hundred') that you've practiced physically with base-ten blocks. When a column sums to 12, you can't write two digits in one place, so you trade 10 of those units for 1 of the next larger unit — the same trade as swapping 10 unit cubes for 1 rod. The algorithm records this by writing the leftover units in the current column and moving the bundled unit to the next column as a carried digit.
Seeing carrying as a familiar concept (not a new rule) helps students understand *why* the algorithm works rather than memorizing steps blindly. When students understand that a carry represents a real trade — the same trade they made with physical blocks — they are less likely to forget the carried digit and more likely to apply the procedure correctly even in new situations like three-carry problems or multi-digit subtraction with borrowing.