Your learning journey
Use fractions and percentages as operators, recover a whole from a known fraction, and explain the chosen reference amount.
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
Operator: an instruction that scales a quantity. Reference amount: quantity treated as the whole or 100%. Unit fraction: one equal part. Original amount: quantity before a stated operation.
Intentional practice feedback after your attempt
60%; 0.15.
Use hundredths.
Intentional practice feedback after your attempt
1/2.
Cancel a common factor 3.
Intentional practice feedback after your attempt
16; 8.
Find one equal part.
Present
Three fifths of 80 is (80÷5)×3=48 because five equal parts make the whole. The same calculation is 80×0.6. For 15% of 80, 10% is 8 and 5% is 4, so the result is 12. A decimal multiplier gives 80×0.15=12.
Name the whole and write the fraction or decimal multiplier. Calculate, include units and check size. To recover a whole from a known fraction, find one part then all parts, or divide by the fraction. An operator above 1 increases the quantity.
Optional scaffold
Divide by 4, then multiply by 3.
Intentional practice feedback after your attempt
21.
One quarter is 7; three quarters are 21.
Optional scaffold
Find 10% and 5% first.
Intentional practice feedback after your attempt
£21.
30%=£18 and 5%=£3; or 0.35×60.
Optional scaffold
More than 100% must exceed the original.
Intentional practice feedback after your attempt
36.
100%=24 and 50%=12.
Optional scaffold
Divide the known part by 2, then multiply by 3.
Intentional practice feedback after your attempt
27.
One third is 9; three thirds are 27.
Apply
Optional scaffold
Combine benchmark percentages.
Intentional practice feedback after your attempt
8; 4; 12; 120.
150%=1.5, greater than 1.
Intentional practice feedback after your attempt
56; £6; 36.
12.5%=1/8; recover one quarter before four.
Optional scaffold
The second operator acts only on the walkers.
Intentional practice feedback after your attempt
3 learners.
12 walk; 25% of 12 is 3.
Optional check after A2: (7÷8)×64=56; 0.125×48=6; 27÷0.75=36. Use the ordinary decimal multiplier so calculator-specific percentage-key behaviour is avoided.
Apply and extend
Intentional practice feedback after your attempt
Yes, both 10; (20/100)×50=(50/100)×20.
Multiplication commutes; the same product is divided by 100.
Optional scaffold
Reverse the original scaling.
Intentional practice feedback after your attempt
50, since one fifth is 10. Multiplying again finds 3/5 of the part, not the whole.
Check (3/5)×50=30.
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
For a percentage increase, retain 100% and add the change. A 10% rise uses multiplier 1.10; a 10% fall uses 0.90. Recovering an original amount reverses this multiplier.
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
10%=£24, 5%=£12, so 35%=£84.
Deep challenge
Check after attempting
18/24=3/4=75%.