Your learning journey
Read algebraic notation accurately. Substitute signed values and distinguish expressions, equations and identities.
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
Variable: letter representing a value. Coefficient: multiplying number. Term: part separated by addition/subtraction. Expression: calculation without an equality claim. Equation: equality to solve. Identity: equality true for all allowed values.
Intentional practice feedback after your attempt
14.
Multiply before adding.
Intentional practice feedback after your attempt
9.
Two negative factors.
Intentional practice feedback after your attempt
5.
Divide before adding.
Present
Juxtaposition means multiplication: 3x is 3×x, not 3+x. Substitution replaces every occurrence of a letter by the same value. Brackets protect a negative value: if x=−2, x²=(−2)²=4, whereas −x²=−4.
Write the replacement in brackets, then use operation priority. Keep multiplication distinct from powers. Check by a second calculation and state any excluded value when division is involved.
Optional scaffold
Replace b by a bracketed value.
Intentional practice feedback after your attempt
−10.
5×(−2).
Optional scaffold
Multiply first.
Intentional practice feedback after your attempt
−7.
3×(−3)+2=−9+2.
Optional scaffold
Write each multiplication.
Intentional practice feedback after your attempt
9 and −9.
The leading minus is outside the square.
Optional scaffold
Test values, then explain the structure.
Intentional practice feedback after your attempt
Identity: equal for every x.
Distribution gives 2x+6.
Apply
Optional scaffold
Use a substitution table.
Intentional practice feedback after your attempt
6,5,4; −6,1,4.
The square stays equal for opposite values.
Intentional practice feedback after your attempt
−13; −6.
2×(−2)−3×3; (−2)×3.
Optional scaffold
Label m as kilometres.
Intentional practice feedback after your attempt
£18. Fixed charge £4 and distance cost £14.
4+2×7; model assumes that tariff applies.
Optional check: enter (−3)² and then −(3²). Expect 9 and −9. Calculator models differ in negative-key precedence; use explicit brackets.
Apply and extend
Intentional practice feedback after your attempt
No: x=3 gives 9 versus 6. They agree at x=0 or x=2.
Agreement at one value does not prove an identity.
Intentional practice feedback after your attempt
2 is not 1/2. Division is not commutative.
The divisor and dividend have different roles.
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
Like terms have the same letter part: 3x+2x=5x. Unlike terms such as 3x+2y cannot normally be combined. A bracket is a group: 2(x+3) multiplies both parts by two.
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
Stretch
Check after attempting
12−10=2; 2×3=6.
Deep challenge
Check after attempting
3x²=12 while (3x)²=36.