Lesson Plan

• Describe the purpose of substitution in transforming non‑standard equations into quadratic form.
• Apply a step‑by‑step procedure to substitute, solve, and back‑substitute for the original variable.
• Check derived solutions against the original equation to identify extraneous roots.
• Solve a range of practice problems using substitution with confidence.

• Projector or interactive whiteboard
• Prepared slide showing the substitution procedure
• Worksheet with guided example and practice questions
• Graph paper and calculators for checking solutions
• Sticky notes for exit tickets

Begin with a quick “Do‑Now” asking students to solve \(x^2-5x+6=0\) and notice the ease of factoring. Review the quadratic formula and remind learners that many complex equations hide a quadratic pattern. Explain that today they will learn a systematic substitution method and will be able to state the success criteria: correctly identify a substitution, solve the resulting quadratic, and verify solutions.

1. Do‑Now & discussion (5') – Students share answers to the warm‑up quadratic and identify the pattern.
2. Mini‑lecture (10') – Present the six‑step substitution algorithm with a visual slide.
3. Guided example (15') – Work through the provided \(\frac{1}{x}+\frac{1}{x^{2}}=6\) problem, prompting students to suggest each step.
4. Partner practice (12') – Learners attempt the three practice equations on the worksheet, using the algorithm checklist.
5. Check & feedback (8') – Review answers as a class, highlighting common errors and the importance of checking solutions.
6. Exit ticket (5') – Students write one example of a substitution they could use in a new problem.

Summarise the substitution cycle: identify, rewrite, form a quadratic, solve, back‑substitute, and verify. Collect exit tickets to gauge understanding and assign homework: three additional substitution problems from the textbook. Remind students that mastering this technique expands the range of equations they can tackle confidently.