Your learning journey
Demonstrate cumulative number understanding, diagnose the cause of an error and verify a repair independently.
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
Checkpoint: evidence at one point in learning. Diagnostic: used to choose teaching. Reference whole: quantity treated as 1 or 100%. Method mark: credit for a valid mathematical step.
Intentional practice feedback after your attempt
−5; 7/12.
Record the first incorrect decision if either fails.
Intentional practice feedback after your attempt
6; 7/20.
Separate factor and conversion evidence.
Intentional practice feedback after your attempt
12; £80.
The second answer uses 64÷0.8.
Present
Different errors need different repairs. Adding denominators is a unit error; reversing a percentage with the wrong base is a reference error; a decimal factor error is a place-value error. First identify the decision, then choose a representation and check.
Complete R1–R3 unaided as a short checkpoint. Tag each error: units, operation, scale or reference whole. Use the matching D example, then A and P tasks without the prompt. Record a fresh delayed check; do not infer a grade or fixed tier from this lesson.
Optional scaffold
Use common units.
Intentional practice feedback after your attempt
5/6.
4/6+1/6 counts sixths.
Optional scaffold
Estimate: answer must be below half of 48.
Intentional practice feedback after your attempt
6.
12.5%=1/8.
Optional scaffold
Reverse the reduction multiplier.
Intentional practice feedback after your attempt
£72.
54 is three quarters; one quarter is 18.
Optional scaffold
Use the original problem forwards.
Intentional practice feedback after your attempt
72×0.75=54.
A useful check reproduces the stated final value.
Apply
Optional scaffold
Use twelfths for the sum.
Intentional practice feedback after your attempt
11/12; 9/2.
Addition needs equal parts; division uses the reciprocal.
Intentional practice feedback after your attempt
42; 3/5; 30.
Select the method from the demand, not nearby questions.
Optional scaffold
Keep the order of the two actions.
Intentional practice feedback after your attempt
£66; no, voucher first gives £67.20.
0.8×90−6=66; 0.8×84=67.2.
Optional check after A3: enter 90×0.8−6 and (90−6)×0.8. Expect 66 and 67.2. Brackets record the order. Use calculator results to check arithmetic, not to replace explanation.
Apply and extend
Intentional practice feedback after your attempt
Independent explanation and a fresh delayed problem; e.g. recover original from £45 after 25% off: £60.
Remembering an answer is not the same as choosing a method.
Optional scaffold
Compare the products of the multipliers.
Intentional practice feedback after your attempt
Yes: 1.25×0.8=1. A 25% fall gives £93.75.
Reciprocal multipliers reverse a change; equal percentage rates need not.
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
Ratio a:b compares the first quantity with the second in that order. To share £50 in the ratio 2:3, there are five equal parts. Each part is £10, so the shares are £20 and £30.
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
Original Reach for the Star. Not an official or endorsed Pearson resource. Separate teacher package contains assessment solutions. Local saving is browser-dependent; no account or dashboard service is included.
Optional extension activities
Stretch
Check after attempting
x=70 and x=90.
Deep challenge
Check after attempting
Multipliers 1.5×0.5=0.75, a 25% net decrease.