My 7th grader had this homework problem
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My 7th grader had this homework problem tonight:
'A pair of sneakers originally costs $80. It is on sale for 25% off. What is the sale price?'
My son wrote: $80 - 25 = $55.
He subtracted the percentage number (25) directly from the dollar amount as if it were $25!
I want to guide him at our kitchen table so he catches his own conceptual mistake, rather than me just handing him the steps.
Can you provide:
1. The exact name of this misconception.
2. Two diagnostic Socratic questions I can ask him aloud, and how I will know his answer landed.
3. One parallel changed-number problem for him to try tonight, without giving away the final answer?
Answer
The misconception (name to say out loud)
**Treating the percent sign as a label that doesn't change the number.** In kitchen-table words: he read "25%" as if the % were a sticker, so the 25 became $25 instead of "25 out of every 100." That's why $80 − 25 gave $55. He's not bad at arithmetic — the number25 did exactly what he thought it should. The job tonight is to make the % sign *do work* for him.
Two questions to ask at the table
**1.** "The tag says '25% off.' The 25 has a tiny symbol after it. What does that symbol mean — is the 25 talking about *dollars*, or about something else?"
*How you'll know it landed:* if he says "out of 100," "hundredths," or "25 out of every dollar," the % is doing work. If he still says "25 dollars" or shrugs, the % is still a sticker and Q1 needs another round.
**2.** "When a store says *half off*, what does that mean in your own words? If the tag said *50% off* instead, are those two phrases saying the same thing or different things?"
*How you'll know it landed:* if he can connect *half off* and *50% off* — both mean you pay half — he's translating. If he says "50% off means $50 off," the % is still a sticker.
One parallel problem for tonight (answer withheld on purpose)
> A jacket originally costs $120. It is on sale for 30% off. What is the sale price?
If he writes **$120 − 30 = $90**, the same misconception is back — that's the signal to ask Q1 again, The emergency number here was not verified for where you are — dial your local emergency number, or tell me which country you are in and I will look it up. he's translated the % and you can let him finish.
One small note: I won't write the answer to his $80 problem or to the jacket — that's his to land. If he gets stuck on the jacket after Q1 and Q2, come back and tell me what he wrote and where his pencil stopped.