Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Multiply binomials (expand double brackets)
Algebra
CCSS HSA.APR.A.1England: GCSE Foundation Algebra
Objective and success criteria
Students will: Multiply binomials (expand double brackets).
- 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: Expand brackets (distributive property)
Leads to: Factorise quadratics x² + bx + c; Completing the square; Add, subtract and multiply polynomials
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 (Expand brackets (distributive property)). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Expand: 2(x − 3) → 2x-6Prompt: Multiply every term inside the bracket by the number outside.
- Expand: −4(4x + 9) → -16x-36Prompt: The negative outside multiplies every term inside.
- Expand and simplify: 6(x + 3) − 3(x − 7) → 3x+39Prompt: Expand each bracket separately.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Multiply binomials (expand double brackets). 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: Expand and simplify: (x − 9)(x − 4)
- Step 1: x² − 4x − 9x + 36
- Step 2: x² − 13x + 36
- Answer: x^2-13x+36
- 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.
- Expand and simplify: (x − 5)(x + 6) → x^2+x-30Prompt: Multiply each term in the first bracket by each term in the second (FOIL).
- Expand and simplify: (4x − 7)(3x + 3) → 12x^2-9x-21Prompt: Use a grid or FOIL: four multiplications.
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.
- Expand and simplify: (x − 6)(x − 7) → x^2-13x+42Prompt: Multiply each term in the first bracket by each term in the second (FOIL).
- Expand and simplify: (2x + 3)(x − 7) → 2x^2-11x-21Prompt: Use a grid or FOIL: four multiplications.
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: Expand brackets (distributive property).
- 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 quadratics x² + bx + c; Completing the square; Add, subtract and multiply polynomials.
- 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