The Discount Trap
Sale day at the mall. This jacket looks like 50% off. But is it real — or a fake 50%?
Concept
A "30% off + extra 20% off" sign looks like 50% off, but it isn't — because the second discount only applies to what's already been discounted, not the original price. Kid discovers stacked percentage discounts don't add, they compound, and the real total is always less than the naive sum.
The Experience
Kid sees a $100 jacket tagged "30% OFF + EXTRA 20%!" and guesses whether the total discount is 50%, more than 50%, or less than 50% — the correct answer is less.
Kid drags a slider to apply the first 30% discount to the $100 jacket, watching a live dollar readout, confirming that 30% of $100 is $30 off.
Kid is asked which amount the extra 20% applies to — the $70 left, the whole $100, or the $30 already taken off — and confirms it's the $70 left, not the original price.
Kid drags a second slider to find 20% of the remaining $70, landing on exactly $14 — so the two discounts together are $44 off, not $50.
Kid builds the real discount percentage as a fraction, placing $44 over the original $100 to get 44% — confirming that "30% + 20%" is really only 44% off.
Twist: kid is asked what the second discount would need to be for a real 50% off, correctly guesses "more than 20%," then works it out directly — computing that a true 50% off $100 is $50, and that reaching $50 after the first $30 discount needs $20 more off the remaining $70, which works out to about 29%, not 20%.
Closing screen compares "The deal" (30% + 20% = 44% off) against "A real 50%" (30% + 29% = 50% off), with the takeaway: "So next time you're shopping, don't add the discounts — do the math."
What Math Does The Kid Do?
- Calculates a percentage of a whole (30% of $100, 20% of $70) using a hands-on slider tied to a live dollar readout.
- Identifies the correct base amount a percentage applies to (the reduced price, not the original).
- Builds and evaluates a percent formula as a fraction (discount ÷ full price × 100).
- Compares an intuitive "add the percentages" answer against the actual compounded result.
- Works backward from a target outcome to solve for the discount rate needed to reach it.
Why This Matters
A "30% + 20% off" sign won't fool you again — you can compute the real, compounded discount yourself and explain exactly why stacked percentages don't simply add up.
Frequently asked questions
The Discount Trap is tagged for Grades 6-10.
No — The Discount Trap plays directly in the browser, right on this page. No login, no download.
No — The Discount Trap is free to play, no sign-up needed.