Your learning journey
Substitute into formulae and change the subject by inverse operations. State necessary restrictions and check with values.
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
Formula: equation connecting quantities. Subject: isolated variable. Rearrange: express the same relationship with a different subject. Restriction: excluded value such as a zero divisor.
Intentional practice feedback after your attempt
x=5.
Subtract 4 then divide by 3.
Intentional practice feedback after your attempt
11.
Substitute then calculate.
Intentional practice feedback after your attempt
2x+10.
Both terms are multiplied.
Present
Changing the subject uses the same balanced operations as solving, but retains letters. From y=3x+4, subtract 4 to obtain y−4=3x, then divide by 3: x=(y−4)/3. Brackets show that the whole difference is divided.
Identify the required subject and undo operations in reverse order on both sides. Keep grouped numerators in brackets. Check by substitution into both versions; do not divide by zero.
Optional scaffold
Undo subtraction.
Intentional practice feedback after your attempt
a=b+7.
Add 7 on both sides.
Optional scaffold
Keep brackets around C−2.
Intentional practice feedback after your attempt
n=(C−2)/5.
Subtract 2 then divide the whole difference.
Optional scaffold
Two equivalent forms are allowed.
Intentional practice feedback after your attempt
w=(P−2l)/2 or P/2−l.
Subtract 2l then divide by 2.
Optional scaffold
State the non-zero condition.
Intentional practice feedback after your attempt
t=d/v.
vt=d, then divide by v; original t≠0.
Apply
Optional scaffold
Start with the outermost operation.
Intentional practice feedback after your attempt
(y−3)/2; y/2−3; 2(y−3).
Read the complete operation chain.
Intentional practice feedback after your attempt
h=2A/b; h=12.
Multiply by 2 then divide by b.
Optional scaffold
Keep units with the result.
Intentional practice feedback after your attempt
d=(C−4)/3; 7 km.
Remove the fixed cost before finding distance.
Optional check: choose x=2 in y=3x+4 to give y=10. Enter (10−4)÷3 to recover 2. Parentheses must reflect the written numerator.
Apply and extend
Intentional practice feedback after your attempt
Yes: divide both terms of P−2w by 2.
Distribution of division over a sum/difference.
Intentional practice feedback after your attempt
At y=10 it gives −2/3, but x=2 is correct. Use x=(y−4)/3.
Subtract before dividing.
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 inequality describes a set of values. An open circle excludes an endpoint; a filled circle includes it. A number line shows which side of the endpoint is allowed.
Retrieve F1 again in one week. Bring your working and one question.
Higher alternative: Rearranging when the subject occurs twice
Higher route: replace the 2-minute A3 feedback and the two 4-minute Challenge discussions with this 10-minute taught extension. Retain core P1–P2. Set HX1–HX2 as the final four minutes of that alternative, and use the shared challenges later if needed. The core route remains 60 minutes; the extension is not an additional compulsory ten minutes. Route choice reflects tier curriculum, not temporary support needs.
Make x the subject of y=ax+cx+d: subtract d, then factorise x to get y−d=x(a+c). Divide by a+c: x=(y−d)/(a+c), provided a+c≠0. If a+c=0 the original reduces to y=d: every x works when y=d, and none when y≠d. A different example, p=3x+qx, gives p=x(3+q), so x=p/(3+q), provided q≠−3.
Intentional Higher practice feedback
4+k; x=y/(4+k), k≠−4.
Intentional Higher practice feedback
t=(v−2)/(a+b), provided a+b≠0.
HX1–HX2: teacher review. Completion is not mastery.
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
r=√(A/π), so r=7 cm.
Deep challenge
Reveal a worked check after attempting
t=(v−u)/a, provided a≠0.