Lesson Plan

• Solve linear equations and inequalities, applying correct algebraic manipulations and sign‑change rules.
• Solve systems of linear equations using both substitution and elimination methods.
• Solve quadratic equations by factorising, completing the square, and using the quadratic formula.
• Interpret solution sets, including number‑line representation and discriminant analysis.
• Communicate solutions clearly and verify answers by substitution.

• Projector and screen
• Whiteboard and markers
• Worksheet packets with practice problems
• Scientific calculators
• Graph paper and rulers
• Handout of key formulae (linear, quadratic, discriminant)

Begin with a quick “mystery number” challenge to spark curiosity about solving for unknowns. Review that students already know how to isolate a variable in simple equations. Explain that today they will extend this to inequalities, systems, and quadratics, and will be able to check every answer by substitution.

1. Do‑now (5 '): Students solve two short linear equations on mini‑whiteboards; peer‑check.
2. Mini‑lecture (10 '): Present forms of linear equations and inequalities, emphasise sign‑reversal rule; work through one example of each.
3. Guided practice (15 '): Pairs solve a set of linear equations and inequalities from the worksheet; teacher circulates and provides immediate feedback.
4. Simultaneous equations (15 '): Demonstrate substitution then elimination with a worked system; students attempt a new system individually.
5. Quadratic techniques (20 '): Brief overview of factorising, completing the square, and the quadratic formula; students solve one problem using each method.
6. Consolidation quiz (10 '): Exit‑ticket containing one linear equation, one inequality, one system, and one quadratic; quick peer review.

Recap the four families of problems tackled and the key steps for each. Collect exit‑tickets to gauge understanding and assign a worksheet for homework that reinforces all methods covered.