Math lesson plan · 9th grade (Year 10 in England) · 30 minutes
Take out the greatest common factor of a polynomial
Algebra
CCSS HSA.SSE.A.2England: GCSE Foundation Algebra
Objective and success criteria
Students will: Take out the greatest common factor of a polynomial.
- 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 linear expressions; Divide monomials using exponent laws
Leads to: Factorise four-term expressions by grouping; Factorise fully: common factor first, then the bracket
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 linear expressions; Divide monomials using exponent laws). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- What is the highest common factor of the terms in 32x + 72? → 8Prompt: Find the largest number that divides both coefficients.
- Simplify: −20x⁵ ÷ 4x² → -5x^3Prompt: Divide the numbers.
- Which is 8x + 72 fully factorised? (2(4x + 36) / 8(x + 72) / 8x(x + 9) / 8(x + 9)) → 8(x + 9)Prompt: Take out the highest common factor of both terms.
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Take out the greatest common factor of a polynomial. 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: Complete the factorisation: 6x⁴ + 10x³ − 4x² = 2x²( … ). Type what goes inside the bracket.
- Step 1: 6x⁴ + 10x³ − 4x² = 2x²(3x² + 5x − 2)
- Step 2: 3x² + 5x − 2
- Answer: 3x^2+5x-2
- 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.
- Complete the factorisation: 2x⁵ + 4x⁴ + 4x³ = 2x³( … ). Type what goes inside the bracket. → x^2+2x+2Prompt: Divide each term by 2x³.
- What is the greatest common factor of 8x³y and 14xy⁴? (2xy / 56xy / 8xy / 2x) → 2xyPrompt: Find the HCF of the numbers.
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.
- Complete the factorisation: 30x⁴ − 12x³ − 12x² = 6x²( … ). Type what goes inside the bracket. → 5x^2-2x-2Prompt: Divide each term by 6x².
- Factorise by taking out −2x: −6x² + 2x = −2x( … ). Type what goes inside the bracket. → 3x-1Prompt: Divide each term by −2x.
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 linear expressions.
- 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: Factorise four-term expressions by grouping; Factorise fully: common factor first, then the bracket.
- 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