Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Factorise four-term expressions by grouping
Algebra
CCSS HSA.SSE.A.2England: GCSE Higher Algebra
Objective and success criteria
Students will: Factorise four-term expressions by grouping.
- 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
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). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Complete the factorisation: 8x⁴ + 8x³ + 36x² = 4x²( … ). Type what goes inside the bracket. → 2x^2+2x+9Prompt: Divide each term by 4x².
- What is the greatest common factor of 12x³y and 30x²y? (6x² / 60x²y / 6x²y / 6x³y) → 6x²yPrompt: Find the HCF of the numbers.
- Factorise by taking out −5x: −20x² + 15x = −5x( … ). Type what goes inside the bracket. → 4x-3Prompt: Divide each term by −5x.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Factorise four-term expressions by grouping. 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 by grouping: x³ + 3x² − 2x − 6
- Step 1: x²(x + 3) − 2(x + 3)
- Step 2: (x² − 2)(x + 3)
- Answer: (x² − 2)(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 by grouping: x³ − x² + 2x − 2 ((x² − 1)(x + 2) / (x² + 2)(x + 1) / (x² + 2)(x − 1) / (x − 1)(x + 2)) → (x² + 2)(x − 1)Prompt: Group the first two terms and the last two terms.
- Factorise: xy − 2x + 2y − 4 ((x + 2)(y + 2) / (x + 2)(y − 2) / (x − 2)(y + 2)) → (x + 2)(y − 2)Prompt: Take x out of the first pair and a number out of the second pair.
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 by grouping: 2x² + 6x + 5x + 15 ((2x + 3)(x + 5) / (2x + 5)(x + 3) / (x + 5)(x + 3) / (2x + 15)(x + 1)) → (2x + 5)(x + 3)Prompt: Group as (2x² + 6x) + (5x + 15).
- Factorise: xy + 3x + 2y + 6 ((x + 3)(y + 2) / (x − 2)(y − 3) / (x + 2)(y + 3) / (x + 2)(y − 3)) → (x + 2)(y + 3)Prompt: Take x out of the first pair and a number out of the second pair.
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