Math lesson plan · 9th grade (Year 10 in England) · 45 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 · 5 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 35x + 63? → 7Prompt: Find the largest number that divides both coefficients.
- Simplify: −36x³ ÷ 6x → -6x^2Prompt: Divide the numbers.
- Which is 25x + 10 fully factorised? (5(5x + 10) / 5(5x + 2) / 5(6x + 2) / 25(x + 2)) → 5(5x + 2)Prompt: Take out the highest common factor of both terms.
Hook · 5 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 · 10 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 · 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.
- Complete the factorisation: 8x⁴ − 20x³ + 16x² = 4x²( … ). Type what goes inside the bracket. → 2x^2-5x+4Prompt: Divide each term by 4x².
- What is the greatest common factor of 4x⁵y³ and 12x⁴y²? (4x⁴y² / 4x⁵y³ / 4x⁴ / 8x⁴y²) → 4x⁴y²Prompt: Find the HCF of the numbers.
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.
- What is the greatest common factor of 9x²y and 21x³y²? (9x²y / 3x² / 63x²y / 3x²y) → 3x²yPrompt: Find the HCF of the numbers.
- Factorise by taking out −5x: −5x² + 25x = −5x( … ). Type what goes inside the bracket. → x-5Prompt: Divide each term by −5x.
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