Lesson Plan

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Lesson Plan
Grade: Date: 17/01/2026
Subject: Additional Mathematics
Lesson Topic: Know and use the remainder and factor theorems
Learning Objective/s:
  • State the Remainder Theorem and the Factor Theorem.
  • Apply synthetic (Horner’s) division to obtain remainders and quotients.
  • Determine whether a linear expression $x‑a$ is a factor of a given polynomial.
  • Factorise higher‑degree polynomials using the theorems.
  • Identify and correct common errors when using these theorems.
Materials Needed:
  • Projector or interactive whiteboard
  • Printed worksheets with practice questions
  • Synthetic‑division template handout
  • Graphing calculators (optional)
  • Whiteboard markers and erasers
 Introduction:
Begin with a quick “mystery‑polynomial” challenge to spark curiosity about hidden factors. Review students’ prior experience with long division of polynomials and the concept of a remainder. Explain that by the end of the lesson they will be able to state the two theorems, use synthetic division, and factor polynomials confidently.
Lesson Structure:
  1. Do‑now (5'): Quick mental recall – write the remainder when $f(x)$ is divided by $x‑a$.
  2. Mini‑lecture (10'): Introduce the Remainder Theorem and Factor Theorem with simple examples.
  3. Guided practice (12'): Demonstrate synthetic division step‑by‑step on $f(x)=2x^{3}-5x^{2}+3x-7$ divided by $x‑2$.
  4. Pair work (10'): Students complete practice questions 1 and 2 from the worksheet, using the template.
  5. Class discussion (5'): Review common mistakes listed in the source and correct them.
  6. Extension activity (8'): Factorise the cubic $h(x)=x^{3}-6x^{2}+11x-6$ using the Factor Theorem.
  7. Exit ticket (5'): Write one theorem statement and a brief example showing its use.
Conclusion:
Summarise how the two theorems provide a fast route to remainders and factorisation. Collect exit tickets to gauge understanding and assign homework: complete the remaining practice questions (3‑4) and bring any difficulties to the next lesson.