My 6th grader repeatedly makes this mist
Question
My 6th grader repeatedly makes this mistake when dividing fractions on homework:
1) 2/3 ÷ 4/5 = (2*4)/(3*5) = 8/15 (she multiplied straight across instead of multiplying by the reciprocal)
2) 3/4 ÷ 2/3 = (3*2)/(4*3) = 6/12 = 1/2 (same mistake, forgot to invert the second fraction)
Can you help organize this into a structured mistake notebook card (prompt, wrong, right, tag, cause) and show a parallel problem for her to test tonight?
Answer
ecorded one card — both misses share the same cause (forgot to invert the divisor), so they cluster into one card instead of two. Card id `56d4861af486ddfa`.
Card — fraction division
- Prompt: `2/3 ÷ 4/5 = (2·4)/(3·5) = 8/15 ; 3/4 ÷ 2/3 = (3·2)/(4·3) = 6/12 = 1/2`
- Wrong move: Multiplied numerators straight across and denominators straight across; did not invert (take the reciprocal of) the divisor.
- ight move — parallel problem for tonight: `5/6 ÷ 2/3` — invert the divisor (`2/3 → 3/2`), then multiply across: `5/6 × 3/2 = 15/12 = 5/4`.
- Tag: `fraction division`
- Cause: For division of fractions, forgot to invert the divisor (the second fraction) before multiplying across.
Tonight's test (5–10 min): Have her work `5/6 ÷ 2/3` from memory first on a separate sheet; only then check her work against the worked answer above. If she inverts and lands on `5/4`, she passes; if she goes straight across again, that's the exact thing the next review will drill.
eminder: Your existing daily 19:00 reminder is already on, so tonight's review will fire on its own — I didn't add another.
Heads-up: there's also an older card `3/4 ÷ 2/5` tagged `fraction division` from a previous quiz (5 same-cause misses). Same root cause, but I kept it as a separate card — its own prompt and its own review day — rather than merging. When the older one comes due, it will pull the same fix.