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Use constant multiplicative relationships for recipes and length scales, with consistent units and checks.
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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Connect & Check
Direct proportion: corresponding quantities have a constant ratio. Scale factor: multiplier from one length to another. Scale 1:n: one unit on the drawing represents n of the same units in reality. Unit rate: amount for one unit.
Intentional practice feedback after your attempt
2:3; 20 and 30.
Equivalent ratios preserve the relationship.
Intentional practice feedback after your attempt
300 cm; 1.5 kg.
100 cm per metre; 1000 g per kilogram.
Intentional practice feedback after your attempt
450.
300÷2×3.
Present
If a recipe for 4 people needs 300 g, the same recipe for 6 needs 300×(6/4)=450 g. Both quantities scale together. On a 1:500 plan, 1 cm represents 500 cm=5 m. A labelled scale is a relationship; printed diagram size can change when a page is resized.
State corresponding quantities and units. Use a unit rate or one scale factor across a direct-proportion table. For scale lengths, multiply drawing by n to get real length, or divide real length by n for drawing length, after converting to matching units.
Optional scaffold
Find the amount for one person.
Intentional practice feedback after your attempt
750 g.
Scale 8 to 10 by 5/4, or use 75 g per person.
Optional scaffold
Check the quotient stays constant.
Intentional practice feedback after your attempt
25.
Multiply the first value by 2.5.
Optional scaffold
Convert centimetres to metres last.
Intentional practice feedback after your attempt
35 m.
7×500=3500 cm.
Optional scaffold
Convert 15 m to 1500 cm first.
Intentional practice feedback after your attempt
3 cm.
1500÷500=3.
Apply
Optional scaffold
One centimetre represents five metres.
Intentional practice feedback after your attempt
5 m; 15 m; 30 m.
All lengths scale by the same factor.
Intentional practice feedback after your attempt
360 g; 4 cm.
40 g per person; 800 cm÷200.
Optional scaffold
Convert each dimension separately.
Intentional practice feedback after your attempt
30 m; 20 m; perimeter 100 m.
2×(30+20)=100; lengths scale before perimeter.
Optional check after A3: 6×500÷100=30 m; 4×500÷100=20 m; 2×(30+20)=100 m. Drawings are schematic and not for measuring. Print resizing does not change the labelled lengths.
Apply and extend
Intentional practice feedback after your attempt
Only A. A costs £0 at 0 km and doubles when distance doubles; B has a fixed £4 charge.
A constant rate plus a fixed charge is not direct proportion.
Optional scaffold
A 2 cm line becomes 4 cm for the same 10 m.
Intentional practice feedback after your attempt
1:250. Each printed centimetre now represents half the previous real distance.
The original written scale is no longer correct for ruler measurements.
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 unit rate is an amount for one unit. Compare like units, such as price per notebook or per kilogram. In L015, the lower unit price will help identify the better buy when the product and conditions are comparable.
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
200,000 cm=2 km.
Deep challenge
Check after attempting
Area factor 1.5²=2.25, since both dimensions scale.