Solving linear equations

AQA GCSE Maths

8 ready-made resources for teaching Solving linear equations, written for AQA GCSE Maths. Slides, worksheets, mark schemes, homework, an assessment and retrieval quizzes, all with SEN-friendly scaffolding built in as standard. Below is what the topic requires and where students usually go wrong, free to read whether or not you sign up.

Get these 8 files free

What is in this bundle

Assessment mark schemeWord, editable
End-of-topic assessmentWord, editable
HomeworkWord, editable
Retrieval-practice quizzesWord, editable
SlidesPowerPoint, editable
Starter & exit ticketWord, editable
Tiered worksheetWord, editable
Worksheet mark schemeWord, editable

Foundation tier

Solve one-step and two-step equations with the unknown on one side (e.g. 3x + 5 = 20).
Solve equations involving a single bracket that needs expanding first (e.g. 2(x + 3) = 16).
Solve equations with the unknown on both sides (e.g. 5x - 2 = 2x + 10).
Solve simple equations involving a fraction of the unknown (e.g. x/4 + 1 = 6).
Form a linear equation from a short worded description and solve it.
Check a solution by substituting it back into the original equation.

Higher tier, in addition

Solve equations with brackets and fractions combined, including the unknown appearing in a denominator (e.g. 3/(x+1) = 2).
Solve equations arising from more complex worded/contextual problems (e.g. perimeter, angle, or rate problems) where setting up the equation is the harder step, not solving it.
Rearrange a linear formula to change the subject before solving for a value.

Where students go wrong

Treating "=" as an instruction to compute rather than a statement of equality (carrying operations across without applying them to both sides).
Sign errors when moving a term across the equals sign (forgetting to flip the operation).
Expanding a bracket incorrectly when a negative sits outside it (e.g. -2(x - 3) → losing the sign on the second term).
Dividing only part of one side by a coefficient, rather than the whole side.
Stopping after isolating a multiple of x (e.g. leaving 3x = 12 unsolved).

How it gets asked in the exam

"Solve", "Find the value of x", "Work out", "Show that x = ...", short worded-context problems ("The perimeter of this rectangle is 30cm... find x").

Key vocabulary

Equation, unknown, term, coefficient, expand, bracket, solve, substitute, inverse operation, balance.

Assumed prior knowledge

Confident with negative number arithmetic (addition, subtraction, multiplication).
Understands that the "=" sign means both sides hold equal value, not just "the answer follows."
Can expand a single bracket (distributive law).
Basic fraction operations (for the fractional-equation content).

How Speca scaffolds this topic

Balance-scale visual model is highly effective for dual-coding the "do the same to both sides" principle: worth a recurring visual motif across the whole topic's slides.
Worked examples should show every intermediate line (no skipped mental-maths steps), since skipped steps are a common source of lost marks and confusion for students who need explicit modelling.
Colour-coding matching terms on each side of the equation (e.g. same colour for terms being moved) supports students who struggle to track multi-step rearrangement.
Chunk multi-step equations into "one new idea per slide" (one-step → two-step → brackets → both-sides → fractions) rather than introducing several complexity layers at once.

Every file, free to start

Three full bundles a month at no cost, no card needed. Speca can also write a resource for a topic we have not built yet, and mark a photo of a student's working against the mark scheme.

Start free