Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Factorise fully: common factor first, then the bracket
Algebra
CCSS HSA.SSE.A.2England: GCSE Higher Algebra
Objective and success criteria
Students will: Factorise fully: common factor first, then the bracket.
- 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: Take out the greatest common factor of a polynomial; Difference of two squares; 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 · 5 min
- Quick retrieval from earlier learning (Take out the greatest common factor of a polynomial; Difference of two squares; Factorise quadratics x² + bx + c). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Complete the factorisation: 2x⁵ − 10x⁴ − 14x³ = 2x³( … ). Type what goes inside the bracket. → x^2-5x-7Prompt: Divide each term by 2x³.
- Factorise: 9x² − 121 (3(x + 11)(x − 11) / (3x + 11)(3x − 11) / (3x − 11)² / (3x + 11)²) → (3x + 11)(3x − 11)Prompt: This is a difference of two squares: A² − B² = (A + B)(A − B).
- Factorise: x² − 64 ((x − 8)(x + 8) / (x − 8)(x − 8) / (x)(x + 1) / (x + 8)(x − 8)) → (x − 8)(x + 8)Prompt: Find two numbers that multiply to −64 and add to 0.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Factorise fully: common factor first, then the bracket. 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 fully: 2x² + 8x + 6
- Step 1: 2(x² + 4x + 3)
- Step 2: 2(x + 1)(x + 3)
- Answer: 2(x + 1)(x + 3)
- 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 fully: 3x² − 33x + 90 ((3x − 6)(x − 5) / 3(x + 6)(x + 5) / 3(x² − 11x + 30) / 3(x − 6)(x − 5)) → 3(x − 6)(x − 5)Prompt: Every coefficient is a multiple of 3: take it out first.
- Factorise fully: 4x² − 64 (4(x² − 16) / (4x + 4)(x − 4) / 4(x + 4)(x − 4) / (x + 16)(x − 4)) → 4(x + 4)(x − 4)Prompt: Take out the common factor.
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.
- Elena says x³ − 9x = x(x² − 9) is fully factorised. What is the full factorisation? (x(x² − 9) / (x + 3)(x − 3) / x(x + 3)(x − 3) / x(x − 3)²) → x(x + 3)(x − 3)Prompt: A bracket can often be factorised further.
- Factorise fully: 2x² − 98 ((2x + 7)(x − 7) / (x + 14)(x − 7) / 2(x − 7)² / 2(x + 7)(x − 7)) → 2(x + 7)(x − 7)Prompt: Take out the common factor.
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: Take out the greatest common factor of a polynomial.
- 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-9.
Free lesson plan from eurekami.com/lesson-plan-builder