Math lesson plan · 9th grade (Year 10 in England) · 60 minutes
Solve quadratics by factorising
Algebra
CCSS HSA.REI.B.4.BCCSS HSA.SSE.B.3.AEngland: GCSE Foundation AlgebraEngland: GCSE Higher Algebra
Objective and success criteria
Students will: Solve quadratics by factorising.
- 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: Graphs of quadratics: roots, vertex, intercepts; The quadratic formula; Quadratic inequalities
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 6 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 + 4x − 45 ((x + 9)(x + 5) / (x − 45)(x + 1) / (x + 9)(x − 5) / (x − 9)(x + 5)) → (x + 9)(x − 5)Prompt: Find two numbers that multiply to −45 and add to 4.
- Factorise fully: x² − 9x + 14 → (x-2)(x-7)Prompt: Two numbers: product 14, sum −9.
- Factorise: x² + 13x + 42 ((x + 7)(x + 6) / (x − 7)(x − 6) / (x + 13)(x + 1) / (x + 7)(x − 6)) → (x + 7)(x + 6)Prompt: Find two numbers that multiply to 42 and add to 13.
Hook · 6 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Solve quadratics by factorising. Read the success criteria together.
I do: model it · 12 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Solve: x² + 7x − 18 = 0. Give both solutions, separated by a comma.
- Step 1: (x − 2)(x + 9) = 0
- Step 2: x = 2 or x = −9
- Answer: x = -9 or x = 2
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 12 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Solve: x² + 11x + 28 = 0. Give both solutions, separated by a comma. → x = -7 or x = -4Prompt: Factorise: find two numbers that multiply to 28 and add to 11.
- Solve: x² − 12x = 0. Give both solutions, separated by a comma. → x = 0 or x = 12Prompt: Take out the common factor x.
You do: independent practice · 17 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 · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Solve: x² − 3x − 18 = 0. Give both solutions, separated by a comma. → x = -3 or x = 6Prompt: Factorise: find two numbers that multiply to −18 and add to −3.
- Solve: x² + 3x − 11 = 7. Give both solutions, separated by a comma. → x = -6 or x = 3Prompt: First rearrange so that one side is 0.
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
- Move on to: Graphs of quadratics: roots, vertex, intercepts; The quadratic formula; Quadratic inequalities.
- 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