I am checking my 4th grader's math works
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I am checking my 4th grader's math worksheet tonight before signing off.
She has 10 three-digit subtraction problems. She got 8 correct, but she stumbled on the 2 problems that have a zero in the tens place.
Specifically, on 502 - 278, she wrote 334.
Looking at her vertical scratch work, she did 12 - 8 = 4 in the ones column, but she seems to have jumped straight from the 5 in the hundreds place (slashing 5 to 4) directly to the ones column, leaving the tens place untouched, and then subtracting in tens.
I want to sit with her at the table tonight, but:
1. Please do NOT give me the final correct numerical answer to 502 - 278 (withhold the answer so she can calculate it herself).
2. What is the specific arithmetic misconception / cause card name for this error?
3. What is 1 clear diagnostic question or ladder step I can ask out loud at the desk, and how will I know her response landed?
4. Give me 1 parallel practice problem with changed numbers (no answer key attached) so she can verify the concept on her own before bed.
Answer
I'll pull the relevant misconception card and the Socratic ladder so the cause name and the diagnostic question match what the skill actually uses, then read your cause-card and ladder in one go.
I'll quickly confirm which columns don't match (without the answer surfacing), then write the cause card and ladder for you.
The cause card is **A2 跨零退位链断裂** — *borrow-chain breaks at the zero*.
What you saw in her scratch work — slash 5→4 in hundreds, leave the 0 alone in tens, jump straight to ones, then try to handle the tens column — is the textbook version. The 0 gets treated as "nothing / skip me" instead of a placeholder that has to be walked through the chain (0 → 10 → 9). She's not failing the borrow; she's failing to *complete* it.
| Page summary | |
| --- | --- |
| ight | 8 (per your read-through) |
| Wrong, same cause | `502 − 278` = **334** → **A2 跨零退位链断裂** |
| Wrong, same cause | the other zero-in-tens problem → also A2; you don't need a second verdict, same card |
| Tonite's redo | `600 − 274` (the A2 同型) |
**Diagnostic question to say out loud at the desk:**
"After you changed the 5 to a 4, what number is *actually* sitting in the tens column right now — is it still 0, or has it become 10? And after you lend one of those tens to the ones, what does it become?"
**How you'll know it landed:** she should say **"10"** when you first ask (the hundred got unpacked into ten tens), then **"9"** after she lends one to the ones column. If she says **"0," "blank,"** or skips the tens column entirely when you ask her to name it — the misconception is still sitting there. A tighter self-check with no number attached: "Tell me, column by column left to right, what you're subtracting *from* at each step." If the tens column comes out as "nothing," she's still collapsing the zero.
**Parallel practice, no answer attached:**
`600 − 274`
Same shape as hers: a 0 in the tens place, top number smaller than bottom in the ones. If she still produces something like `426` or `436`, the card is confirmed and worth a one-line note to the teacher ("borrow chain breaks at the zero — A2"). If she gets a clean answer with the tens column going 0 → 10 → 9 on the page, she's got it for tonight.
One housekeeping note: the script confirms your reading — the mismatched columns on `502 − 278` are hundreds and tens. I'm holding back the correct value as you asked; she should be the one to land it.