Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Add and subtract polynomials
Algebra
CCSS HSA.APR.A.1England: GCSE Foundation Algebra
Objective and success criteria
Students will: Add and subtract 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: Name polynomials by degree and number of terms
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 (Name polynomials by degree and number of terms). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- What is the degree of the polynomial −x⁶ − 7x³ + 4x⁵? → 6Prompt: The degree is the highest power of x.
- Which name describes −8x⁴ + 4x²? (quartic trinomial / cubic binomial / quadratic monomial / quartic binomial) → quartic binomialPrompt: Count the terms: 1 monomial, 2 binomial, 3 trinomial.
- Write −1 − 3x² − 7x in standard form (highest power first). What is the leading coefficient? → -3Prompt: Order the terms from the highest power of x to the lowest.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Add and subtract 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: (−6x² + 5x + 9) + (2x² − 3x − 6)
- Step 1: −4x² + 2x + 3
- Answer: -4x^2+2x+3
- 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: (x² + 7x − 9) + (3x² − 7x − 9) → 4x^2-18Prompt: Remove the brackets: adding doesn't change any signs.
- Simplify: (2x² + 8x − 9) − (−6x² − x + 4) → 8x^2+9x-13Prompt: Subtracting a bracket changes the sign of every term inside it.
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.
- Find the coefficient of x² in (−3x³ + 6x − 9) − (3x² − 5x − 5). → -3Prompt: Some powers are missing from one polynomial: their coefficient is 0.
- Simplify: (4x² + 6x − 1) − (−3x² + 6x − 4) → 7x^2+3Prompt: Subtracting a bracket changes the sign of every term inside it.
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: Name polynomials by degree and number of terms.
- 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