Support
Answer and teaching response
4 · One quarter of $16 is $4, leaving $12 to pay.
Compare a fractional discount with a fixed reduction
Calculate the amount removed and the amount paid for two offers on the same starting price, then check when a different starting price changes the result.
Get student and teacher materialsPrepare the group
Learning goal: Produce a two-offer comparison that identifies the reference price, reduction and final amount without confusing a saving with a payment.
You will need: Paper and pencil. Prices and offers are invented mathematics examples in dollars; assume identical items and ignore tax, fees and other conditions.
Work through an example
An item has the same $12 starting price in two offers. Offer A removes 1/4 of the price. Offer B removes $2. Which final price is lower, and by how much?
Offer A costs $9 and Offer B costs $10, so A is $1 lower. The quarter-price reduction is $3; it is not the amount paid.
- Confirm a common reference: both offers apply to an identical item starting at $12 under the stated assumptions. A comparison of different starting prices would need separate calculations.
- For Offer A, find the reduction first: one quarter of twelve dollars is three dollars. Subtract it from twelve to obtain a nine-dollar final price.
- For Offer B, subtract the fixed two-dollar reduction to obtain ten dollars. Compare nine and ten using the same dollar unit.
- Check each offer by adding reduction and final price to recover twelve dollars. Then state the lower final price and the one-dollar difference; naming only the larger reduction leaves the payment unstated.
Run the 15-minute workshop
- 3 minutes. Ask learners to label saving and payment as different quantities in a quarter-off offer.
- 4 minutes. Complete both rows of the worked comparison and reverse each subtraction to verify the starting price.
- 5 minutes. Solve support and core items before using the challenge to test whether the same offer always wins.
- 3 minutes. Complete the independent two-offer record, naming both final prices and their difference.
A useful error to discuss
A learner might say: A quarter-price discount means the final price is one quarter of the original price.
Distinguish a quarter off from paying a quarter. A quarter off removes one part and leaves three equal quarter-parts to pay.
Practise at your level, then check independently
Start with support or core practice, then try the challenge. Complete the independent check without help. Enter a number, fraction or mixed number, such as 3/4 or 1 1/4. The number check does not assess your drawing or explanation.
Core
Answer and teaching response
12 · The reduction is $6; $18 − $6 leaves $12.
Challenge
Answer and teaching response
4 · The fixed reduction gives $4, while a quarter off gives $4.50. The offer that won at $12 need not win at $6.
Independent check
Answer and teaching response
2 · The quarter-off price is $15 and the fixed-reduction price is $17; the difference is $2.
Transfer the idea
At what shared starting price do a quarter-off offer and a $2 reduction give the same final price? Explain using the reductions.
Discuss a possible response
At $8. One quarter of eight is two, so both offers remove $2 and leave $6. The equality concerns the same starting price and the stated assumptions.
Choose the next teaching step
- Calculates the reduction and payment separately.
- Compares offers from the same reference price and checks the result by recombining payment and reduction.
Support: Partition a drawn price bar into four equal parts, cross out the removed part and label the three remaining parts.
Extend: At a $10 starting price, compare one fifth off with $2 off: both final prices are $8. Explain why a fractional reduction depends on the starting amount.
Materials for your group
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