Problem
Discount rate is the discount over the original price
A table gives the original and sale price of three items. We need which item has the biggest discount rate.
Ratios
Your answer
How to solve
Strategy Organize Information in More Ways — The discount amounts cannot be compared directly, because each is taken from a different starting price. Turn each into a rate against its own original price and the three become comparable.
1STEP 1
Find each discount amount
Subtract the sale price from the original price for each item.
1500 - 1050 = 450, 4000 - 3000 = 1000, 1200 - 960 = 240
The biggest discount in won is the set square.
6.RP.A.3Identify Subproblems2STEP 2
See why the amounts cannot be compared
The 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.
(discount rate) = (discount) ÷ (original)
Each needs its own base.
7.RP.A.3Analyze The UnitsThe three discounts cannot be compared as amounts of money.
Why?
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.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
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.
🧱One-to-one correspondenceIf each thing here pairs with exactly one thing there, the two groups are the same size.
3STEP 3
Work out the three rates
Divide each discount by its own original price and write it as a percent.
450 ÷ 1500 = 0.3, 1000 ÷ 4000 = 0.25, 240 ÷ 1200 = 0.2
30%, 25% and 20%.
7.RP.A.3Organize Information In More Ways4STEP 4
Pick the largest
Now the three are measured the same way, so they can be compared directly.
30 ＞ 25 ＞ 20
The colored pencil is discounted most.
7.RP.A.3Identify SubproblemsAnswer
The colored pencil
Check one: 30% off 1500 is 450 won, leaving 1050 won, exactly the sale price given.
Takeaway
A discount only means something next to the price it came off -- compare rates, not amounts.
- Find each discount amount
- See why the amounts cannot be compared
- Work out the three rates
- Pick the largest