A student computes 63 − 28 and gets 45, writing '8 − 3 = 5' in the ones column and '6 − 2 = 4' in the tens column. What error did they make?
AThey subtracted the bottom digit from the top digit in the ones column regardless of which was larger
BThey forgot to carry a value into the tens column
CThey subtracted in the wrong order — tens before ones
DThey made an arithmetic error in the tens column
The student swapped the subtraction in the ones column: instead of computing 3 − 8 (which requires regrouping), they computed 8 − 3 = 5. This 'subtract the smaller from the larger' error is the most common mistake in two-digit subtraction. The correct approach is to recognize that 3 < 8, regroup (trade 1 ten for 10 ones), then compute 13 − 8 = 5 in ones and 5 − 2 = 3 in tens, giving 35.
Question 2 Multiple Choice
In the problem 53 − 27, after regrouping the tens column changes from 5 tens to 4 tens. Why?
AYou traded 1 ten for 10 ones so the ones column has enough to subtract from, leaving one fewer ten
BYou subtracted 1 from the tens column as the first step of finding the answer
CThe tens digit decreases whenever the ones digit in the subtrahend is larger
DIt is a procedural step with no connection to the value of the number
Regrouping means making an exchange: 1 ten is traded for 10 ones. The 53 is re-expressed as 4 tens and 13 ones — still the same total value, just represented differently. This exchange is why the tens column shows one fewer ten after regrouping. Understanding the exchange (not just the procedure) helps students catch the most common post-regrouping error: forgetting to reduce the tens digit before subtracting in the tens column.
Question 3 True / False
After regrouping in a subtraction problem, the total value of the number you started with has not changed — only how it is represented has changed.
TTrue
FFalse
Answer: True
Regrouping is an exchange, not a removal: 1 ten becomes 10 ones, so 53 becomes '4 tens + 13 ones,' which still equals 53. The total is preserved. This is why regrouping works: it rearranges the same quantity into a form that allows digit-by-digit subtraction. Students who don't grasp this sometimes think they are 'taking' something from the number, which can lead to confusion about why the tens digit must be updated.
Question 4 True / False
When solving a two-digit subtraction problem with regrouping, you should check the tens column first to decide whether regrouping is needed.
TTrue
FFalse
Answer: False
Always check the ones column first. Regrouping is triggered by a ones-column problem (the bottom ones digit is larger than the top ones digit), not by anything in the tens column. The useful habit is: before subtracting ones, ask 'Can I subtract?' If yes, proceed. If no, regroup first — borrow a ten, update the tens digit, then subtract. Checking the tens column first leads students to start subtracting there prematurely or to miss the need for regrouping entirely.
Question 5 Short Answer
Explain why regrouping (borrowing a ten) does not change the total value of the number, even though it changes the digits.
Think about your answer, then reveal below.
Model answer: Regrouping is an exchange based on the fact that 1 ten equals exactly 10 ones. When we regroup, we break apart one ten and add 10 to the ones column — the quantity is rearranged but not changed. For example, 53 can be expressed as 5 tens and 3 ones, or as 4 tens and 13 ones. Both representations equal 53. This is the same principle underlying place value: different combinations of tens and ones can represent the same total.
This understanding is what separates students who genuinely grasp regrouping from those who have only memorized the steps. If a student knows WHY the tens digit drops by 1, they will remember to update it — and they won't confuse regrouping in subtraction with regrouping in addition (where 10 ones bundle into a new ten, going the other direction).