Math lesson plan · 11th grade (Year 12 in England) · 45 minutes
Expand three binomials
Algebra
CCSS HSA.APR.A.1England: GCSE Higher Algebra
Objective and success criteria
Students will: Expand three binomials.
- 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: Multiply a binomial by a trinomial
Leads to: Factorise sums and differences of cubes; Find a coefficient in a binomial expansion
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 (Multiply a binomial by a trinomial). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Expand and simplify: (x − 3)(x² − 5) → x^3-3x^2-5x+15Prompt: Multiply x by every term of the trinomial, then the number by every term.
- Expand and simplify: (4x + 3)(x² − 5x + 3) → 4x^3-17x^2-3x+9Prompt: Use a grid: 2 rows × 3 columns.
- Without expanding fully, find the coefficient of x in (x² − 3x − 4)(x² − x − 2). → 10Prompt: Which pairs of terms multiply to give an x term?
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Expand three binomials. 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 − 4)(x + 4)(x − 2)
- Step 1: (x − 4)(x + 4) = x² − 16
- Step 2: (x² − 16)(x − 2)
- Step 3: x³ − 2x² − 16x + 32
- Answer: x^3-2x^2-16x+32
- 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 + 4)(x + 1)(x − 3) → x^3+2x^2-11x-12Prompt: Expand two of the brackets first.
- Expand: (x − 3)³ → x^3-9x^2+27x-27Prompt: (x − 3)³ = (x − 3)(x − 3)(x − 3).
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: (x + 4)³ → x^3+12x^2+48x+64Prompt: (x + 4)³ = (x + 4)(x + 4)(x + 4).
- Find the coefficient of x² in (2x − 1)(x + 2)(x + 5). → 13Prompt: An x² term uses an x from two brackets and a number from the third.
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: Multiply a binomial by a trinomial.
- 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 sums and differences of cubes; Find a coefficient in a binomial expansion.
- 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-11.
Free lesson plan from eurekami.com/lesson-plan-builder