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Use multipliers for percentage change, recover an original value and distinguish simple interest from repeated growth.
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
Multiplier: scale factor for a change. Increase: add to the original. Decrease: subtract from the original. Reverse percentage: recover the original. Simple interest: interest calculated on the original principal each year.
Intentional practice feedback after your attempt
12; 0.2.
Percentage operators use the reference whole.
Intentional practice feedback after your attempt
40.
Divide by 0.75.
Intentional practice feedback after your attempt
1.25.
One whole and one quarter.
Present
A 20% increase leaves 120% of the original, so multiply by 1.20. A 20% decrease leaves 80%, so multiply by 0.80. If a sale price is £72 after a 20% reduction, £72 is 80% of the original: divide 72 by 0.8 to recover £90.
Identify which value represents 100%. Write new = original × multiplier, then multiply forwards or divide backwards. Percentage change = change ÷ original × 100%. Simple interest uses the same original principal each year; add the accumulated interest at the end.
Optional scaffold
Use 1−0.15.
Intentional practice feedback after your attempt
£68.
85% remains; 80×0.85=68.
Optional scaffold
Check 60×1.1.
Intentional practice feedback after your attempt
£60.
66 is 110%; divide by 1.1.
Optional scaffold
Do not divide by the final 72.
Intentional practice feedback after your attempt
20%.
The increase is 12 compared with original 60.
Optional scaffold
Use the original £300 each year.
Intentional practice feedback after your attempt
£324.
£12 each year; £24 interest plus £300.
Apply
Optional scaffold
Write the new percentage first.
Intentional practice feedback after your attempt
1.05→84; 0.95→76; 1.5→120; 0.5→40.
Retain 100% before adding or subtracting the change.
Intentional practice feedback after your attempt
£81; £80; 25%.
The relevant base is always the original.
Optional scaffold
Write the new reference amount after each step.
Intentional practice feedback after your attempt
£96: 100×1.2×0.8.
The fall is 20% of £120, which is £24.
Core examples are non-calculator friendly. Optional check after A3: 100×1.2×0.8=96. Keep intermediate values unrounded; use ordinary multipliers rather than a calculator-specific % key.
Apply and extend
Intentional practice feedback after your attempt
33 1/3%: the rise is 20/60=1/3 of the reduced price.
The original fall was 25%, but reversal uses a different base.
Optional scaffold
Name the reference amount for the second year.
Intentional practice feedback after your attempt
Simple: £120. Repeated growth: £121.
Simple adds £10 each year; repeated growth adds £10 then £11.
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
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Optional extension activities
Stretch
Check after attempting
0.85×original=68, so original=£80.
Deep challenge
Check after attempting
1.2×0.8=0.96, so the final price is 4% lower.