Your learning journey
Translate a context into a linear equation, solve it and interpret the result with appropriate units and constraints.
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
Model: mathematical representation of a situation. Unknown: quantity to find. Constraint: condition the answer must satisfy. Interpret: state what a numerical result means in context.
Intentional practice feedback after your attempt
x=5.
Subtract 2 then divide by 3.
Intentional practice feedback after your attempt
4x+8.
Expand then collect.
Intentional practice feedback after your attempt
20 cm.
2×7+2×3.
Present
An equation links two descriptions of the same quantity. If tickets cost £4 each plus a £3 fee and the bill is £23, 4n+3=23 models the bill. Solving gives n=5 tickets. The unit and any whole-number requirement matter.
Define the unknown with units. Translate each relationship, keeping one-off charges separate. Solve using balanced operations. Substitute and check the result against the context.
Optional scaffold
Subtract the fixed fee first.
Intentional practice feedback after your attempt
n=6 tickets.
5n+2=32.
Optional scaffold
Consecutive means one apart.
Intentional practice feedback after your attempt
11 and 12.
2n+1=23; n=11.
Optional scaffold
Add all four sides.
Intentional practice feedback after your attempt
7 cm and 10 cm.
4x+6=34; x=7.
Optional scaffold
Equate the two costs.
Intentional practice feedback after your attempt
n=4; both cost £16.
8+2n=4n.
Apply
Optional scaffold
Underline the operation words.
Intentional practice feedback after your attempt
x+6=20, x=14; 6x=30, x=5; 2x−6=20, x=13.
Word order and operation matter.
Intentional practice feedback after your attempt
Width 8 cm; length 13 cm.
2x+2(x+5)=42.
Optional scaffold
Let v be visits.
Intentional practice feedback after your attempt
7 visits; 6+3×7=27.
The fee is paid once.
Optional check after C2: enter 10+2×8 and 4×8. Expect 26 and 32. Check that the calculator expression matches the written cost model.
Apply and extend
Intentional practice feedback after your attempt
No. 2n+1=30 gives n=14.5, not a whole number.
Consecutive integer sums are odd.
Intentional practice feedback after your attempt
Equal at 5 visits (£20). At 8, A £26 and B £32, so A.
Equality alone does not decide every case.
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 formula links quantities. The subject is the letter isolated on one side. To make n the subject of C=3n+4, subtract 4 from both sides then divide by 3: n=(C−4)/3.
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
Allow 10–15 minutes if the main practice is secure. Show your method, explain a check and justify your conclusion.
Stretch
Reveal a worked check after attempting
3.50+1.80m=21.50, so m=10.
Deep challenge
Reveal a worked check after attempting
2w+2(w+3)=38, w=8; length=11 cm.