Subtraction Bug in Place Value
During a place-value unit, Mr. Tran asks students to solve 502 - 178. Eleven students answer 324. Eight students answer 476 and explain: '2 minus 8 you can't do, so 8 minus 2 is 6; 0 minus 7 you can't do, so 7 minus 0 is 7; 5 minus 1 is 4.' These same eight students answer correctly when no regrouping is needed. They can build 502 with base-ten blocks but do not exchange a hundred for ten tens when subtracting. Mr. Tran has 25 minutes before specials and a worksheet of 12 similar subtraction problems ready to hand out.
1. Identify the error pattern and explain why the 12-problem worksheet is a poor instructional choice.
Read the worked answer
The eight students are consistently subtracting the smaller digit from the larger in each column and ignoring regrouping. Their explanation ('8 minus 2 is 6') shows they are not treating 502 as 5 hundreds, 0 tens, and 2 ones but as three independent digits. This is a conceptual place-value error, not a speed problem.
A worksheet of 12 similar problems is a poor choice because it lets them rehearse the bug 12 more times. Correct answers on no-regroup items will also reinforce the belief that their procedure is fine. The remedy needs a concrete exchange, not more repetition.
2. Describe what Mr. Tran should do in the 25 minutes.
Read the worked answer
Use base-ten blocks with a sequence that forces an exchange:
- Start with 52 - 27 so students must trade one ten for ten ones.
- Then build 502 and subtract 178. Have students physically trade one hundred for ten tens and one ten for ten ones before subtracting.
- Record each trade in the written algorithm beside the blocks. Ask: 'Where did the ten come from when we changed the 0 to 10?'
- Have one student explain the exchange aloud while another points to the blocks.
Skip the 12-problem worksheet. Assign two problems with a written explanation as homework. The goal in 25 minutes is to connect the written marks to quantity, not to cover many items.
3. How should Mr. Tran check whether the intervention transferred?
Read the worked answer
Give 703 - 256 and a story problem such as 'A theater has 402 seats. If 178 are filled, how many are empty?' Also use an error-analysis prompt: 'Marcus says 502 - 178 = 476. Use estimation to explain why he is wrong.'
Proceed when students can estimate (500 - 200 = 300) and explain the exchange. If they still subtract smaller-from-larger, reteach again in a small group with blocks. A correct answer alone is not sufficient evidence because students can sometimes get the right answer while still misunderstanding the exchange.