Your learning journey
Select and justify a proportion method. Diagnose whether the given amount is a total, a share or a difference.
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
Corresponding: quantities in matching roles. Total: sum of all shares. Difference: larger share minus smaller share. Direct proportion: constant ratio of corresponding quantities.
Intentional practice feedback after your attempt
15 and 25.
Eight equal parts.
Intentional practice feedback after your attempt
300 g.
Multiply by 6/4.
Intentional practice feedback after your attempt
£5/kg.
Double the quantity and cost.
Present
For A:B=2:3, the whole contains five equal parts but the difference contains one part. The number of parts depends on what the given amount describes. In direct proportion, multiplying one quantity by a factor multiplies the other by the same factor.
Label the ratio parts and the meaning of the known amount. Find one part or one unit; scale to the target. Check the original ratio and the stated total or difference.
Optional scaffold
Divide by the sum of the terms.
Intentional practice feedback after your attempt
24 and 32.
Seven parts; one part 8.
Optional scaffold
Match 15 to three parts.
Intentional practice feedback after your attempt
35.
One part 5; seven parts 35.
Optional scaffold
Divide by 5−3.
Intentional practice feedback after your attempt
A=21; B=35.
Two parts equal 14.
Optional scaffold
Find one serving first.
Intentional practice feedback after your attempt
600 g.
75 g per serving.
Apply
Optional scaffold
Label total, share or difference.
Intentional practice feedback after your attempt
16; 20; 16.
Divide by 5, 3 and 1 respectively to find one part.
Intentional practice feedback after your attempt
£40 and £32; £60 and £48.
The second given amount is one part.
Optional scaffold
Convert litres to millilitres.
Intentional practice feedback after your attempt
Need 300 ml syrup and 1200 ml water; short by 50 ml.
1500÷5=300 ml per part.
Optional check after A3: 1500÷5=300 and 300+1200=1500. The sum check is necessary but also check syrup:water=1:4.
Apply and extend
Optional scaffold
Scale both ratios to the same B value.
Intentional practice feedback after your attempt
No. Match B to 12: A:B:C=8:12:15, so A:C=8:15.
The two original B parts have different sizes.
Intentional practice feedback after your attempt
No in general. Flour:sugar 2:1 becomes 4:1 rather than 4:2.
All corresponding ingredients must scale together.
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
An algebraic expression records a calculation with a letter representing a number. For x=4, 3x+2 means 3×4+2, while 3(x+2) means 3×(4+2).
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
4×15/6=10 hours.
Deep challenge
Check after attempting
The inverse model assumes equal productivity and no coordination limits; those assumptions may fail.