Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Multiply a polynomial by a monomial
Algebra
CCSS HSA.APR.A.1England: GCSE Foundation Algebra
Objective and success criteria
Students will: Multiply a polynomial by a monomial.
- 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); Multiply monomials using exponent laws
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 (Expand brackets (distributive property); Multiply monomials using exponent laws). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Expand: 6(x + 3) → 6x+18Prompt: Multiply every term inside the bracket by the number outside.
- Simplify: (−x⁵)(4x⁴) → -4x^9Prompt: Multiply the numbers.
- Expand: −3(6x + 4) → -18x-12Prompt: The negative outside multiplies every term inside.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Multiply a polynomial by a monomial. 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: 6x(4x² − 6x + 4)
- Step 1: 24x³ − 36x² + 24x
- Answer: 24x^3-36x^2+24x
- 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: −3x(6x² + 2x + 1) → -18x^3-6x^2-3xPrompt: Multiply every term inside the bracket by the term outside.
- Expand: −x³(−x² + 3x + 5) → x^5-3x^4-5x^3Prompt: Multiply the numbers and add the exponents for each term.
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: −4x³(−3x² − 6x − 6) → 12x^5+24x^4+24x^3Prompt: Multiply the numbers and add the exponents for each term.
- Yuki expanded −5x(3x − 1) and got −15x² − 5x. What should the answer be? (−15x² + 5x / −15x² − 1 / −15x² − 5x / −15x + 5) → −15x² + 5xPrompt: Multiply −5x by each term, sign included.
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
- 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