My 6th grader made the exact same mistak
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My 6th grader made the exact same mistake on two fraction division homework problems tonight:
1. Problem: (2/3) ÷ (4/5)
Student wrote: (3/2) × (4/5) = 12/10 = 6/5
2. Problem: (3/8) ÷ (2/3)
Student wrote: (8/3) × (2/3) = 16/9
Instead of keeping the first fraction (the dividend) and multiplying by the reciprocal of the second fraction (the divisor), she keeps inverting the first fraction! She remembers the rule "flip a fraction to multiply," but flips the wrong one.
Our family is in America/Los_Angeles timezone. We want to record this into our personal mistake notebook so it doesn't get forgotten:
1. Please cluster these two instances into exactly one 5-line cause card (prompt / wrong / right / tag / cause) following the strict mistake-notebook structure without extra lecture.
2. What is a clean, parallel changed-number practice item for self-testing when this card comes due?
3. Schedule our daily 7:00 PM evening review reminder so the card re-appears on its scheduled repetition interval.
Answer
I'll handle this in three parts: cluster the card, set up the daily review, and answer the changed-number practice item. Let me first check the notebook's current state and the card format.
Got it — the format is clear and the notebook already has several cards on this exact "flip the wrong fraction" trap (the student has hit this before). I'll still append tonight's two-instance cluster as you asked, schedule the 7 PM review, and give you the parallel practice item.
Done — both pieces landed.
**1. One cause card written (both tonight's problems clustered onto it):**
| Line | Content |
|---|---|
| Prompt | Two problems, same trap tonight: (2/3) ÷ (4/5); (3/8) ÷ (2/3). Wrote (3/2)×(4/5)=6/5 and (8/3)×(2/3)=16/9. |
| Wrong | Flipped the dividend (the first fraction) instead of the divisor (the second one). |
| Right | Keep the dividend, flip only the divisor, then multiply across. Same-type practice: (3/7) ÷ (2/5) → (3/7)×(5/2) = 15/14. |
| Tag | fraction division |
| Cause | inverted-dividend-not-divisor |
**2. Parallel changed-number practice item — (3/7) ÷ (2/5)**
This is the same-type item now embedded as the "right" line. The two possible answers are reciprocals of each other, which is itself a useful sanity check:
- If she flipped the **wrong** fraction (first), she gets **14/15**.
- If she flipped the **right** fraction (second), she gets **15/14**.
Quick rule of thumb she can use while practicing: *right answer × wrong answer = 1.* If those two numbers she writes down don't multiply to 1, she flipped the wrong one.
The card will return on its standard repetition cadence (1, 3, 7, 14, 30 days), so the first self-test is tomorrow.
**3. Daily 7:00 PM reminder — scheduled**
Every evening at 7:00 PM America/Los_Angeles, the notebook will surface whatever cards are due that day (system staggers the exact trigger time by a few minutes, so it fires at 19:08 PT). Your new card first appears tomorrow's review slot.
To stop it, say "stop the 7 PM reminder" and I'll disable it.