Solving Linear Equations

Overview

This is lesson 15 of 19 in the Year 9 Maths 2026 Plan. Students develop fluency solving and verifying linear equations by preserving equality and applying inverse operations, building from simple one-step equations towards brackets, like terms and variables on both sides.

Learning intentions

• WALT solve one- and two-step linear equations using inverse operations.
• WALT simplify equations involving brackets and like terms.
• WALT preserve equality while solving.
• WALT verify solutions by substituting them into the original equation.
• WALT connect equations to measurement and everyday situations.

Success criteria

• I can solve one- and two-step equations accurately.
• I can expand brackets and collect like terms before solving.
• I can explain why each operation preserves equality.
• I can substitute my answer into the original equation and show that both sides are equal.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge advanced learners and deepen understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: challenge questions aligned with classroom mathematics content.
• Mathematics and Statistics — Mathsteasers / Additional resources for advanced learners: opportunities for reasoning, explanation and non-routine problem-solving.

Lesson structure (60 minutes)

1. 0–5 min · Hook and retrieval. Display the opening question from the introduction and retrieval slides: “A mystery number is doubled and then increased by 5 to make 17. How could we find the number?” Students solve independently, compare methods with a partner, and identify the inverse operations used. Briefly state the WALT and success criteria.

2. 5–15 min · Balance-model demonstration. Use a physical balance or balance diagram from the balance-model slides to represent (x+4=11), then (2x+4=14). Teacher models removing or adding the same quantity to both sides, recording each equation line by line. Students explain why the balance remains level and use algebra tiles or drawn counters to model one example.

3. 15–25 min · Strategy sort and teacher check. Distribute the equation strategy and practice worksheet and display the sorting instructions in the strategy-sort slides. In pairs, students classify equation cards or worksheet examples by the first useful strategy: undo addition/subtraction, undo multiplication/division, simplify like terms, or expand brackets. Pause for hinge questions: “What must happen first in (3(x+2)=18)?” and “Which step would be illegal or unhelpful?” Address misconceptions before students continue.

4. 25–40 min · Partner solve and verify. Students solve a graduated set on the equation strategy and practice worksheet, including one- and two-step equations, brackets and like terms. Partners take turns as Solver and Checker: the Solver writes an inverse-operation explanation, while the Checker substitutes the answer into the original equation and confirms both sides. Teacher conferences with selected students, collecting examples of reasoning for feedback.

5. 40–52 min · Error spotting and applications. Show the worked examples in the error-spotting and application slides. Students identify and correct an error such as changing only one side of an equation or checking against a simplified rather than original equation. Then pairs choose one context from the worksheet, such as a perimeter, unknown length, phone-data cost or taxi fare, define the variable, form an equation, solve it and check whether the answer is sensible. Invite two pairs to explain their equations.

6. 52–60 min · Plenary and exit assessment. Revisit the success criteria using the plenary slides. Students complete the individual exit question on the worksheet: solve (4x-7=21), verify the solution in the original equation, and write one sentence explaining why the same operation must be applied to both sides. Students hand in the exit response and selected working.

Resources

• the complete linear-equations slide deck
• the equation strategy and practice worksheet
• Physical balance model or balance diagram
• Algebra tiles or counters
• Equation cards for sorting
• Mini-whiteboards and pens
• Calculators for checking, not replacing, algebraic reasoning
• Projector or interactive display

Assessment

• Use hinge questions during the balance demonstration and strategy sort to check whether students understand inverse operations and preserving equality.
• Listen to partner explanations and inspect whether students expand, simplify and solve in a logical order; use the error-spotting task to identify misconceptions.
• Mark the individual exit equation and verification. Collect selected work from students needing feedback on notation, operation choice or checking.

Differentiation

• Support learners with a visible inverse-operations reference, physical balance models, colour-coded equation sides and scaffolded equation strips showing one step per line.
• Provide deliberate practice beginning with positive integer one-step equations before moving to brackets, fractions or variables on both sides. Read instructions aloud and offer the worksheet in a dyslexia-friendly format: clear sans-serif font, generous spacing, uncluttered pages and highlighted operation symbols.
• Use mixed-readiness partnerships with explicit Solver and Checker roles. Offer oral rehearsal, sentence starters such as “I did this to both sides because…” and allow students to explain reasoning verbally or with diagrams.
• Extend advanced learners with equations containing variables on both sides, for example (5x+3=2x+18), and ask them to justify every operation, create a context for an equation and compare two valid solution methods.