Math lesson plan · 11th grade (Year 12 in England) · 60 minutes
Multiply a binomial by a trinomial
Algebra
CCSS HSA.APR.A.1England: A-level Pure Mathematics
Objective and success criteria
Students will: Multiply a binomial by a trinomial.
- 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: Add, subtract and multiply polynomials
Leads to: Expand three binomials
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 (Add, subtract and multiply polynomials). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Simplify: (4x² − 9x − 7) − (2x² + 2x − 4) → 2x^2-11x-3Prompt: Subtracting a bracket changes the sign of every term inside it.
- Expand and simplify: (2x − 5)(x² + 2x + 1) → 2x^3-x^2-8x-5Prompt: Multiply each term of the first bracket by every term of the second.
- Simplify: (3x² + 2x + 6) − (3x + 3) → 3x^2-x+3Prompt: Subtracting a bracket changes the sign of every term inside it.
Hook · 6 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Multiply a binomial by a trinomial. 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: Expand and simplify: (x + 4)(x² − 4x − 9)
- Step 1: x(x² − 4x − 9) + 4(x² − 4x − 9)
- Step 2: x³ − 25x − 36
- Answer: x^3-25x-36
- 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.
- Expand and simplify: (x + 1)(x² − x + 1) → x^3+1Prompt: Multiply x by every term of the trinomial, then the number by every term.
- Expand and simplify: (3x + 4)(x² + 5x − 4) → 3x^3+19x^2+8x-16Prompt: Use a grid: 2 rows × 3 columns.
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.
- Expand and simplify: (x + 6)(x² + 4x − 1) → x^3+10x^2+23x-6Prompt: Multiply x by every term of the trinomial, then the number by every term.
- Without expanding fully, find the coefficient of x in (x² − x − 2)(x² − 4x + 3). → 5Prompt: Which pairs of terms multiply to give an x term?
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: Add, subtract and multiply polynomials.
- 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: Expand three binomials.
- 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