Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Factorise quadratics x² + bx + c
Algebra
CCSS HSA.SSE.A.2CCSS HSA.SSE.B.3.AEngland: GCSE Foundation Algebra
Objective and success criteria
Students will: Factorise quadratics x² + bx + c.
- I can answer questions on today's skill on my own, without help.
- I can explain each step and say why it works.
- I can check my answer and spot a mistake.
Before and after
Needs first: Multiply binomials (expand double brackets); Factorise linear expressions
Leads to: Difference of two squares; Solve quadratics by factorising; Factorise ax² + bx + c
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Multiply binomials (expand double brackets); Factorise linear expressions). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Expand and simplify: (x + 9)(x − 8) → x^2+x-72Prompt: Multiply each term in the first bracket by each term in the second (FOIL).
- What is the highest common factor of the terms in 18x − 8? → 2Prompt: Find the largest number that divides both coefficients.
- Expand and simplify: (2x − 1)(3x − 6) → 6x^2-15x+6Prompt: Use a grid or FOIL: four multiplications.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Factorise quadratics x² + bx + c. Read the success criteria together.
I do: model it · 10 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Factorise: x² + 15x + 56
- Step 1: 8 × 7 = 56 and 8 + 7 = 15
- Step 2: (x + 8)(x + 7)
- Answer: (x + 8)(x + 7)
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 10 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Factorise: x² − 6x − 16 ((x + 8)(x − 2) / (x − 8)(x − 2) / (x − 8)(x + 2) / (x − 16)(x + 1)) → (x − 8)(x + 2)Prompt: Find two numbers that multiply to −16 and add to −6.
- Factorise fully: x² − x − 42 → (x-7)(x+6)Prompt: Two numbers: product −42, sum −1.
You do: independent practice · 10 min
- Students work on the student sheet. Circulate and check the first two answers of every student early.
- Students who finish: write a question of their own for a partner, with the answer.
The 8 questions are on the student sheet below, with answers in the key.
Exit ticket · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Factorise: x² + x − 6 ((x − 6)(x + 1) / (x + 1)(x + 1) / (x − 3)(x + 2) / (x + 3)(x − 2)) → (x + 3)(x − 2)Prompt: Find two numbers that multiply to −6 and add to 1.
- Factorise fully: x² + 9x + 8 → (x+1)(x+8)Prompt: Two numbers: product 8, sum 9.
Watch out for
- Doing an operation to one side of an equation but not the other.
- Reading 3x as 3 + x, or thinking x always stands for one particular number.
Support and stretch
Support
- Review first: Multiply binomials (expand double brackets).
- Use concrete materials: balance scales or a balance drawing.
- Give the first step of each question, or a partly worked example to finish.
- Pair with a confident partner for the guided practice.
Stretch
- Move on to: Difference of two squares; Solve quadratics by factorising; Factorise ax² + bx + c.
- Explain a common mistake in writing and how to fix it.
- Write a word problem that uses today's skill, then solve a partner's.
Homework and more practice
Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-9.
Free lesson plan from eurekami.com/lesson-plan-builder