Questions: Two-Digit Addition with Regrouping

Question 1

A student adds 38 + 47 and writes '15' in the ones place because 8 + 7 = 15. What should she do instead?

• A. Write 1 in the ones place and carry the 5 to the tens column
• B. Write 5 in the ones place and carry the 1 ten to the tens column
• C. Start over and add the tens column first
• D. Round both numbers to the nearest 10 before adding

Answer: (B)

When the ones column sums to 10 or more, you must regroup: trade 10 ones for 1 ten. 8 + 7 = 15 ones — that's 1 ten and 5 ones. Write the 5 in the ones place (the remaining ones), and carry the 1 ten to the tens column. Writing '15' in the ones place is the classic error: the ones place can only hold a single digit. The regrouped ten must move to the tens column because that's where tens belong.

Question 2

When you carry the '1' to the tens column during regrouping, what does that 1 represent?

• A. One extra one that was left over from the ones column
• B. One ten, formed by trading 10 ones — it belongs in the tens column
• C. A placeholder so the tens column is not empty
• D. The first digit of the ones-column sum

Answer: (B)

The carried '1' represents one ten — a full group of 10. When the ones column sums to 10 or more, you can trade 10 ones for 1 ten (because that's what a ten is). That new ten gets recorded in the tens column. Students often think of it as 'just a 1,' but understanding it as 1 ten explains why it goes to the tens column and why it must be added there — it's the same unit as the other tens.

Question 3

Regrouping during addition changes the total value of the sum — the carried 1 adds extra to the answer.

• T. True
• F. False

Answer: False

This is the central misconception about regrouping. Regrouping does NOT change the total value — it only renames it. 12 ones and 1 ten + 2 ones represent the exact same amount; you have simply reorganized how they're expressed to fit the place-value system. The carried 1 is not extra — it came from the ones column. Nothing is added or removed. Base-ten blocks make this visible: trading 10 unit cubes for a tens rod doesn't change how many you have.

Question 4

You can predict whether regrouping will be needed by checking if the ones digits of both numbers sum to 10 or more.

• T. True
• F. False

Answer: True

Regrouping is triggered exactly when the ones-column sum reaches 10 or more, because 10 ones can be traded for 1 ten. If the ones digits sum to 9 or less, no trading is needed and the result fits directly in the ones place. Developing the habit of previewing this before computing — 'do the ones digits together reach 10?' — deepens understanding of what regrouping is about and helps catch errors before they happen.

Question 5

Explain what it means to 'regroup' in addition and why it doesn't change the total.

Model answer: Regrouping means trading 10 ones for 1 ten when the ones column adds up to 10 or more. The total doesn't change because 10 ones and 1 ten are the same amount — just expressed differently. For example, in 47 + 35, the ones give 12, which is renamed as 1 ten and 2 ones. The 2 stays in the ones place; the 1 ten is added to the tens column. The value is preserved; only the representation changes.

The key insight is that regrouping is renaming, not changing. Our number system is built on groups of 10, so whenever a column accumulates 10 or more of its unit, you can always trade them up: 10 ones become 1 ten, 10 tens become 1 hundred. This trade is completely value-neutral. The total quantity stays the same; only how it's expressed in place-value form changes. This is why carrying always produces a correct answer — you're reorganizing the total, not altering it.