Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Factorise x² + bx + c when c is negative
Algebra
CCSS HSA.SSE.A.2England: GCSE Foundation AlgebraEngland: GCSE Higher Algebra
Objective and success criteria
Students will: Factorise x² + bx + c when c is negative.
- 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: 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 (Factorise quadratics x² + bx + c). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Factorise: x² − 2x − 35 ((x − 7)(x − 5) / (x − 7)(x + 5) / (x + 7)(x − 5) / (x − 35)(x + 1)) → (x − 7)(x + 5)Prompt: Find two numbers that multiply to −35 and add to −2.
- Factorise fully: x² − 12x + 32 → (x-8)(x-4)Prompt: Two numbers: product 32, sum −12.
- Factorise: x² − 16x + 63 ((x − 16)(x + 1) / (x + 9)(x + 7) / (x − 9)(x − 7) / (x − 9)(x + 7)) → (x − 9)(x − 7)Prompt: Find two numbers that multiply to 63 and add to −16.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Factorise x² + bx + c when c is negative. 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: x² − 2x − 15 = (x + 3)(x + ☐). What number goes in the box?
- Step 1: 3 × (−5) = −15, 3 + (−5) = −2
- Step 2: −5
- Answer: -5
- 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.
- x² − 5x − 6 = (x + 1)(x + ☐). What number goes in the box? → -6Prompt: The two numbers multiply to −6.
- Factorise: x² + x − 42 ((x + 6)(x − 7) / (x − 6)(x − 7) / (x − 6)(x + 7) / (x + 6)(x + 7)) → (x − 6)(x + 7)Prompt: A negative constant means the two numbers have opposite signs.
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: x² + 3x − 88 ((x + 8)(x + 11) / (x − 8)(x + 11) / (x + 8)(x − 11) / (x − 8)(x − 11)) → (x − 8)(x + 11)Prompt: A negative constant means the two numbers have opposite signs.
- x² − 3x − 40 = (x + 5)(x + ☐). What number goes in the box? → -8Prompt: The two numbers multiply to −40.
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
- 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