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 − 8x − 9 ((x + 1)(x − 9) / (x + 1)(x + 9) / (x − 9)(x + 1) / (x − 8)(x + 1)) → (x + 1)(x − 9)Prompt: Find two numbers that multiply to −9 and add to −8.
- Factorise fully: x² − 10x + 21 → (x-3)(x-7)Prompt: Two numbers: product 21, sum −10.
- Factorise: x² − 4x − 5 ((x − 1)(x + 5) / (x + 1)(x − 5) / (x + 1)(x + 5) / (x − 5)(x + 1)) → (x + 1)(x − 5)Prompt: Find two numbers that multiply to −5 and add to −4.
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 − 36 = (x + 4)(x + ☐). What number goes in the box? → -9Prompt: The two numbers multiply to −36.
- Factorise: x² − 3x − 108 ((x − 9)(x − 12) / (x + 9)(x + 12) / (x − 9)(x + 12) / (x + 9)(x − 12)) → (x + 9)(x − 12)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.
- x² + x − 72 = (x + 9)(x + ☐). What number goes in the box? → -8Prompt: The two numbers multiply to −72.
- Factorise: x² − x − 56 ((x − 7)(x − 8) / (x + 7)(x − 8) / (x + 7)(x + 8) / (x − 7)(x + 8)) → (x + 7)(x − 8)Prompt: A negative constant means the two numbers have opposite signs.
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