My 7th-grade son is working on percent i
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My 7th-grade son is working on percent increase/decrease homework tonight.
The question: 'A jacket originally costs $60. The price is marked up by 20%. Later, the new price is discounted by 20%. What is the final price?'
He immediately wrote down '$60' and said: 'Plus 20% and minus 20% cancel out, so it goes right back to the start.'
I want to guide him at the table without just telling him the answer or giving away the calculation.
Can you:
1. Name the misconception and explain where his thinking slipped?
2. Give me 1-2 diagnostic questions I can ask him so he discovers the shifting base on his own?
3. Provide a parallel problem with changed numbers (no answer included) for him to solve independently?
Answer
**Where his thinking slipped**
He treated +20% and −20% as inverse operations on the same base. They aren't. The markup moves the price off $60 to a higher number; the discount is then taken off *that* new number, not off the original $60. So the two 20%s aren't doing symmetric work — the second one starts from a different place than the first one ended.
A sentence you can say out loud, if you want one: *"The 20% off isn't off $60 — it's off whatever the price became after the markup."*
**Two questions, in this order**
1. **"What does the price become after the markup, before the discount even starts?"**
*How you'll know it landed:* He writes a number larger than $60 on paper. Any method is fine — adding 20% of $60, or multiplying $60 by 1.2. If he still writes $60, the misconception is still in charge and this question needs another minute.
2. **"When the sign says '20% off,' what number are we taking 20% of?"**
*How you'll know it landed:* He points to the post-markup number he just wrote, not back to $60. If he still says "$60," don't argue — point at the two numbers sitting on his paper and ask which one the discount sign is talking about.
Stop after question 2. Don't tell him whether the final price is higher or lower than $60 — let him compute it himself. The number is yours to confirm with your phone after.
**Same shape, different numbers — for him to do alone**
> A bike originally costs $200. The shop marks it up by 25%, then puts it on sale at 25% off. What is the final price? Show your work.
When he's done, ask question 2 again on his answer: *"What number is the 25% being taken off of?"* That second pass is the one that cements it.