Discount math game: which offer really costs less?

Separate the saving from the sale price

For a $40 item at 25% off, the saving is $40 × 0.25 = $10. The sale price is $40 − $10 = $30. A card asking for the sale price expects $30, not $10. An equivalent method is $40 × 0.75 = $30.

For two successive reductions, apply the second percentage to the reduced price. A $100 item at 20% off, then 10% off the reduced price, costs $80 × 0.90 = $72. It does not cost $70. Each card below states the offer terms; real store coupons can use different conditions.

Run the offer comparison

1. Minutes 0–4: model the $40 example and ask teams to label original price, saving and sale price.
2. Minutes 4–19: play the ten cards. Before calculating, have teams predict whether the answer is above or below a simple benchmark such as half the original price.
3. Award one paper point for the correct number and one for a correct explanation of the offer terms. Keep the score on your host sheet; a close estimate alone does not demonstrate the percent calculation.
4. Minutes 19–25: ask each group to design two offers for the same item with equal final prices, such as 25% off $40 and $10 off $40. Another group checks the equivalence.

Ten sale-price challenge cards

1. 1. Ten percent off

   A notebook set costs $30 before a 10% discount. What is the sale price?

   Host answer and explanation

   $27.00

   10% of $30 is $3. Subtract $3 to get $27.

2. 2. A quarter off

   A backpack costs $48 before 25% off. What is the sale price?

   Host answer and explanation

   $36.00

   One quarter of $48 is $12; $48 − $12 = $36.

3. 3. Half price

   A lamp costs $35 before a 50% discount. What is the sale price?

   Host answer and explanation

   $17.50

   Half of $35 is $17.50. The saving and sale price happen to be equal in this round.

4. 4. Saving or spending?

   A $60 jacket is discounted by 15%. How many dollars are saved?

   Host answer and explanation

   $9.00

   $60 × 0.15 = $9 saved. Its sale price would be $51, but the card asks for the saving.

5. 5. Same starting price

   A $50 game set is offered at either 20% off or $8 off. What is the lower final price?

   Host answer and explanation

   $40.00

   20% off saves $10, making $40. The dollar-off offer costs $42. Submit the lower final price, not the $2 difference.

6. 6. Different starting prices

   The same bag is $80 with 25% off at Shop A and $70 with 10% off at Shop B. How many dollars cheaper is the lower offer?

   Host answer and explanation

   $3.00

   Shop A: $80 × 0.75 = $60. Shop B: $70 × 0.90 = $63. The difference is $3.

7. 7. Two percentages in sequence

   A $100 kit is reduced by 20%, then by another 10% of the reduced price. What is the final price?

   Host answer and explanation

   $72.00

   First $100 × 0.80 = $80; then $80 × 0.90 = $72. The combined reduction is 28%, not 30%.

8. 8. Dollar coupon first

   An $80 item allows a $10 coupon first, then 25% off the remaining amount. What is the final price?

   Host answer and explanation

   $52.50

   $80 − $10 = $70. Then $70 × 0.75 = $52.50. The order is part of the offer.

9. 9. Percentage first

   The same $80 item instead takes 25% off first, then the $10 coupon. What is the final price?

   Host answer and explanation

   $50.00

   $80 × 0.75 = $60; $60 − $10 = $50. Compare with the previous card: changing the order changes the saving by $2.50.

10. 10. A cent-level finish

    A $19.99 puzzle has 15% off. What is the sale price rounded to the nearest cent?

    Host answer and explanation

    $16.99

    $19.99 × 0.85 = $16.9915. Round the final result to $16.99. Do not round the original price to $20 for the exact answer.

Use the wrong answers as useful evidence

An answer of $10 to the opening example confuses the saving with the price paid. An answer of $70 in the sequential-discount card adds percentages that apply to different amounts. Ask students to show the amount each percentage acts on rather than simply memorizing a shortcut.

For an easier set, play cards 1–5 and use 10%, 25% and 50% benchmarks. For an extension, keep the same prices but ask students to write precise coupon terms that make one of two results correct. Avoid presenting the fictional offers as real promotions or promising that this activity identifies the best purchase for everyone.