Math lesson plan · 10th grade (Year 11 in England) · 30 minutes
Factorise ax² + bx + c
Algebra
CCSS HSA.SSE.A.2England: GCSE Higher Algebra
Objective and success criteria
Students will: Factorise ax² + 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: Factorise quadratics x² + bx + c
Leads to: the next skill in this area.
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 4 min
- Quick retrieval from earlier learning (Factorise quadratics x² + bx + c). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Factorise: x² − 3x − 28 ((x − 7)(x − 4) / (x − 7)(x + 4) / (x − 3)(x + 1) / (x − 28)(x + 1)) → (x − 7)(x + 4)Prompt: Find two numbers that multiply to −28 and add to −3.
- Factorise fully: x² + x − 20 → (x-4)(x+5)Prompt: Two numbers: product −20, sum 1.
- Factorise: x² + 3x − 28 ((x − 28)(x + 1) / (x + 7)(x − 4) / (x + 7)(x + 4) / (x + 3)(x + 1)) → (x + 7)(x − 4)Prompt: Find two numbers that multiply to −28 and add to 3.
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Factorise ax² + bx + c. Read the success criteria together.
I do: model it · 7 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Factorise: 5x² − 8x − 21
- Step 1: (5x + 7)(x − 3)
- Answer: (5x + 7)(x − 3)
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 6 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: 2x² + 2x − 12 ((x − 4)(2x + 3) / (2x + 4)(x − 3) / (2x − 4)(x + 3) / (2x + 3)(x − 4)) → (2x − 4)(x + 3)Prompt: Multiply a × c = −24. Find two numbers with that product and sum 2.
- Factorise: 4x² − 23x + 15 ((4x − 5)(x − 3) / (4x + 3)(x + 5) / (x − 3)(4x − 5) / (4x − 3)(x − 5)) → (4x − 3)(x − 5)Prompt: Multiply a × c = 60. Find two numbers with that product and sum −23.
You do: independent practice · 7 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 6 questions are on the student sheet below, with answers in the key.
Exit ticket · 3 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Factorise: 3x² + 3x − 6 ((x − 3)(3x + 2) / (3x − 3)(x + 2) / (3x + 3)(x − 2) / (3x + 2)(x − 3)) → (3x − 3)(x + 2)Prompt: Multiply a × c = −18. Find two numbers with that product and sum 3.
- Factorise: 5x² + 20x − 25 ((5x − 5)(x + 5) / (5x + 5)(x − 5) / (x − 5)(5x + 5)) → (5x − 5)(x + 5)Prompt: Multiply a × c = −125. Find two numbers with that product and sum 20.
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: Factorise quadratics x² + bx + c.
- 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
- 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-10.
Free lesson plan from eurekami.com/lesson-plan-builder