My 5th-grade son is working on his fract
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My 5th-grade son is working on his fraction addition homework tonight.
For the problem 1/3 + 1/4, he wrote 2/7 (adding 1+1 on top and 3+4 on bottom).
I want him to understand why this doesn't work rather than just handing him the answer.
Could you provide:
1. The exact name of this common misconception/mistake type.
2. 1-2 diagnostic Socratic questions I can ask him tonight so he discovers the contradiction himself, along with how I'll know his thinking clicked.
3. One parallel changed-number practice problem without giving away any answers.
4. One single clarifying question (placed at the very end) that would change how we approach his homework tonight.
Answer
### 1. The name of the mistake
This is **"adding numerators and denominators separately"** — sometimes called the **"add-tops, add-bottoms"** rule, and in the research literature it's part of **whole-number bias** in fraction work. The bar between the two numbers is doing real work — it means "out of pieces this size" — and his mental model has dropped it. He's treating the top number and the bottom number of each fraction as two independent integers and applying the addition rule he already trusts.
The one line you can say out loud tonight, in his own words' neighborhood: *"In a fraction, the top and the bottom aren't two separate numbers — the bottom tells you what size the pieces are, and they have to match before you can add the tops."*
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### 2. Two diagnostic questions (ask the first; only move to the second if he's still stuck)
**Q1.** *"You and I each have a chocolate bar the same size. Yours is cut into 3 pieces, mine into 4. You eat one of yours and I eat one of mine. Can we just count the pieces and say together we ate 2 pieces out of 7?"*
**You'll know it clicked when** he can tell you *why* the pieces can't just be added — usually something about "the pieces are different sizes" or "we have to cut them the same size first." If he just says "no, that's wrong" without a reason, that's a guess, not understanding — push him with *"why are the pieces different sizes if the bars are the same?"*
**Q2.** *"Your answer was 2/7. Pick any number between 0 and 1 — say 1/2 — and tell me: is 2/7 more or less than 1/2? Now if you actually had 1/3 of a pie and I gave you 1/4 of a pie, would you have more or less than half a pie?"*
**You'll know it clicked when** he notices the two answers point opposite ways and starts asking which part of his work is wrong. If he agrees they're on the same side of 1/2 and calls it done, the contradiction hasn't landed — go back to Q1.
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### 3. One changed-number parallel problem (no answer key)
`1/2 + 1/6 = ?`
Same shape as his page (different denominators, small unit fractions). If he's still using the "add tops, add bottoms" rule, he'll write `2/12` or `2/8` — that's the signal that the misconception is still running and the next move is the visual / common-denominator step, not another page of these. If he pauses and starts thinking about the pieces before he writes, Q1 landed.
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### 4. One clarifying question for tonight
Has his class already been introduced to **equivalent fractions or making a common denominator** (the LCD method), or is this page his first time adding unlike denominators? That changes how I'd frame Q1 — visual model first if he hasn't seen LCD yet, vs. "what's the smallest number both bottoms fit into?" if he has.