Math lesson plan · 11th grade (Year 12 in England) · 45 minutes
Add, subtract and multiply polynomials
Algebra
CCSS HSA.APR.A.1
Objective and success criteria
Students will: Add, subtract and multiply polynomials.
- 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 binomials (expand double brackets)
Leads to: Remainder and factor theorems; Multiply a binomial by a trinomial
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 binomials (expand double brackets)). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Expand and simplify: (x + 5)(x + 7) → x^2+12x+35Prompt: Multiply each term in the first bracket by each term in the second (FOIL).
- Expand and simplify: (5x + 6)(4x + 5) → 20x^2+49x+30Prompt: Use a grid or FOIL: four multiplications.
- Expand: (x + 6)² → x^2+12x+36Prompt: (x + 6)² means (x + 6)(x + 6).
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Add, subtract and multiply polynomials. 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: Simplify: (5x² + 4x − 9) − (−5x² − 2x + 1)
- Step 1: 10x² + 6x − 10
- Answer: 10x^2+6x-10
- 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.
- Simplify: (5x² + 8x) − (−2x² + 7x) → 7x^2+xPrompt: Subtracting a bracket changes the sign of every term inside it.
- Expand and simplify: (x − 5)(x² + 3x − 3) → x^3-2x^2-18x+15Prompt: Multiply each term of the first bracket by every term of the second.
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.
- Simplify: (x² − 8x + 6) + (−4x² − 8x) → -3x^2-16x+6Prompt: Remove the brackets.
- Expand and simplify: (−4x − 3)(x² − 4x + 5) → -4x^3+13x^2-8x-15Prompt: Multiply each term of the first bracket by every term of the second.
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 binomials (expand double brackets).
- 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: Remainder and factor theorems; Multiply a binomial by a trinomial.
- 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