Depth · one concept from first principles · step 2 of 4
The table shows the original price and the discounted price of items at a stationery shop. Which item has the highest discount rate?
| Item | Colored pencil | Set square | Memo pad |
|---|---|---|---|
| Original price (won) | |||
| Sale price (won) |
Subtract the sale price from the original price for each item.
The biggest discount in won is the set square.
6.RP.A.3Identify SubproblemsThe set square is cut by the most won, but it also started the dearest. A discount only means something against the price it came off.
Each needs its own base.
7.RP.A.3Analyze The UnitsThe three discounts cannot be compared as amounts of money.
A discount rate says how many hundredths of its own price came off, so each is measured against a different whole and the three answers are in different units.
Rewriting each as a share of its own price puts all three on the same scale of hundredths, and only then do the numbers mean the same thing.
Divide each discount by its own original price and write it as a percent.
30%, 25% and 20%.
7.RP.A.3Organize Information In More WaysNow the three are measured the same way, so they can be compared directly.
The colored pencil is discounted most.
7.RP.A.3Identify SubproblemsA discount only means something next to the price it came off -- compare rates, not amounts.
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