Your learning journey
Compare prices using a common unit. Interpret the best buy in terms of cost, quantity needed and waste.
Work without a calculator except for an invited check. Keyboard - means the same as −. Attempt before opening a scaffold or intentional practice explanation.
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Ready.
Connect & Check
Unit rate: amount per one unit. Unit price: cost for one item or unit of mass. Comparable: measured on the same basis. Budget: maximum available spending.
Intentional practice feedback after your attempt
0.75 kg.
Divide by 1000.
Intentional practice feedback after your attempt
£0.50 each.
Cost per item.
Intentional practice feedback after your attempt
£0.80.
One fifth of four pounds.
Present
Dividing cost by quantity gives a unit price because equal quantities carry equal shares of the price. £3 for 6 items is £0.50 per item. For mass, convert to the same unit first. The lowest unit price need not give the lowest bill for a small purchase.
Choose a common unit and label it. Divide each cost by its quantity, compare unrounded results, then consider the amount actually needed. Multiply back to check.
Optional scaffold
Divide total cost by number.
Intentional practice feedback after your attempt
£0.60 per apple.
4.80÷8=0.60; 8×0.60=4.80.
Optional scaffold
Convert 750 g to 0.75 kg.
Intentional practice feedback after your attempt
£4.80/kg.
3.60÷0.75=4.80.
Optional scaffold
Double the 500 g price.
Intentional practice feedback after your attempt
500 g pack is cheaper per kg: £4 versus £4.20.
Compare equal masses, not ticket prices.
Optional scaffold
Compare the actual purchase cost.
Intentional practice feedback after your attempt
Three loose items cost less: £1.50.
The pack has a lower unit price but a higher bill.
Apply
Optional scaffold
Scale to 1000 g.
Intentional practice feedback after your attempt
All £6/kg.
Quantity and cost scale together.
Intentional practice feedback after your attempt
£4.50/kg and £4/kg; 600 g is better value.
Both prices use one kilogram.
Optional scaffold
List complete pack totals.
Intentional practice feedback after your attempt
Three packs of 5 cost £9; two packs of 8 cost £10. Choose packs of 5.
Round pack counts up; leftovers are allowed.
Calculator check after A2: enter 1.80÷0.4 and 2.40÷0.6. Expect 4.5 and 4. Keep unrounded values when comparing; money answers use pounds and pence.
Apply and extend
Intentional practice feedback after your attempt
Example: 500 g for £2 is £4/kg; 1 kg for £5 is £5/kg.
One valid counterexample disproves always.
Intentional practice feedback after your attempt
A £6/kg; B £4/kg. B is cheaper per kg.
20% is applied to the £5 price, not to the mass.
Access, Scaffold, Core and Stretch support the same goal. Stretch deepens reasoning for either qualification tier.
Recall & Review
Retrieval without notes
Six retrieval points. Enter a number, decimal, fraction such as 3/2, or mixed number such as 1 1/2. Equivalent numeric values are accepted. Unsupported notation goes to teacher review. For rounding, also communicate the requested accuracy in written work; numerical scoring cannot judge significant trailing zeros.
Not checked.
Independent exit evidence
P1–P2: five minutes, no notes, 4 marks. Your teacher reviews working and explanations. Full assessment solutions are not embedded.
Recall & Review and prepare
A ratio shares a total into equal parts. Proportion scales corresponding amounts by the same factor. Decide whether the given number is a total, one share or a difference before calculating.
Retrieve F1 again in one week. Bring your working and one question.
Your progress summary
Completion records attempts, not mastery. Retrieval points describe the latest checked attempt. Your teacher reviews P1–P2 separately and checks retained understanding after a delay.
Restore a backup
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Optional extension activities
Stretch
Check after attempting
£3.20/kg versus £3.00/kg, so 1.2 kg pack.
Deep challenge
Check after attempting
750 g pack becomes £1.92, or £2.56/kg; it is now cheaper per kg.