Your learning journey
Collect like terms, expand a single bracket and factorise a common factor. Explain how these equivalent forms are connected.
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
Like terms: identical variable part including powers. Expand: multiply out a bracket. Factorise: express as a product. Common factor: divides every term. Equivalent: same value for all allowed inputs.
Intentional practice feedback after your attempt
20.
12+8.
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6.
Largest shared positive factor.
Intentional practice feedback after your attempt
6.
Product of two negatives is positive.
Present
The distributive law a(b+c)=ab+ac shares multiplication across a sum. Thus 3(x+2)=3x+6. Reversing this gives factorisation. Collecting 3x+2x counts five x units; x and x² are different units.
Group only like terms. Multiply every term inside a bracket, including its sign. To factorise, take a common factor from every term. Expand again and substitute a value to check.
Optional scaffold
Count the coefficients.
Intentional practice feedback after your attempt
3a+4.
Collect a terms; the constant stays separate.
Optional scaffold
Multiply both terms.
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4y−12.
4×(−3)=−12.
Optional scaffold
Keep the factor sign.
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−3a−6.
Multiply the positive 2 by −3.
Optional scaffold
Expand to check both terms.
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4(2a+3).
HCF of coefficients is 4.
Apply
Optional scaffold
Compare powers as well as letters.
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5x; 3x+2y; 5x²; 3x²+2x.
Only identical letter parts combine.
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5x−10; 8x−6.
Expand first, then collect terms.
Optional scaffold
Write all four sides before collecting.
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2(x+2)+6=2x+10 cm.
Two lengths and two widths.
Optional check after C2: substitute x=2 in 3(x+4)−2(x+1) and x+10; both give 12. Numerical agreement is a check, not proof for every x.
Apply and extend
Intentional practice feedback after your attempt
Expanding gives 6x+72. Correct: 6(x+2).
Divide every original term by the factor.
Intentional practice feedback after your attempt
3x+12−2x−2=x+10.
Algebra proves all values; a substitution only checks one.
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 equation states that two expressions are equal. Solve by applying the same inverse operation to both sides, then substitute the solution into the original equation.
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.
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Optional extension activities
Stretch
Check after attempting
6x−15−2x−8=4x−23.
Deep challenge
Check after attempting
3x(2x+3).