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Math lesson plan · 9th grade (Year 10 in England) · 60 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 · 6 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.
  1. Expand: 5(x − 2) → 5x-10Prompt: Multiply every term inside the bracket by the number outside.
  2. Simplify: (3x)(2x⁵) → 6x^6Prompt: Multiply the numbers.
  3. Expand: −3(5x + 2) → -15x-6Prompt: The negative outside multiplies every term inside.

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 polynomial by a monomial. 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: 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 · 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.
  1. Expand: 5x(5x² − 3x + 1) → 25x^3-15x^2+5xPrompt: Multiply every term inside the bracket by the term outside.
  2. Expand: −3x²(5x² + 2x − 7) → -15x^4-6x^3+21x^2Prompt: Multiply the numbers and add the exponents for each term.

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.
  1. Expand: 4x³(2x² + 6x − 7) → 8x^5+24x^4-28x^3Prompt: Multiply the numbers and add the exponents for each term.
  2. Expand: −5x(−5x² + 2x − 6) → 25x^3-10x^2+30xPrompt: Multiply every term inside the bracket by the term outside.

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

eurekami

Multiply a polynomial by a monomial

Name

Date

Score/ 8

  1. Question 1

    Expand: −4x²(x² + 5x + 4)

    Answer

  2. Question 2

    Omar expanded −5x(5x − 7) and got −25x² − 35x. What should the answer be?

    • A. −25x² − 7
    • B. −25x² + 35x
    • C. −25x² − 35x
    • D. −25x + 35
  3. Question 3

    Expand: −3x(−x² − 6x + 6)

    Answer

  4. Question 4

    Expand: 4x²(−5x² + 6x − 4)

    Answer

  5. Question 5

    Lucia expanded −3x(4x − 8) and got −12x² − 24x. What should the answer be?

    • A. −12x + 24
    • B. −12x² − 24x
    • C. −12x² + 24x
    • D. −12x² − 8
  6. Question 6

    Expand: x(−3x² + 6)

    Answer

  7. Question 7

    Expand: 4x²(−5x² − 4x + 5)

    Answer

  8. Question 8

    Omar expanded −3x(3x − 6) and got −9x² − 18x. What should the answer be?

    • A. −9x² + 18x
    • B. −9x + 18
    • C. −9x² − 18x
    • D. −9x² − 6

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Answer key: Multiply a polynomial by a monomial

  1. 1. -4x^4-20x^3-16x^2

  2. 2. B. −25x² + 35x

  3. 3. 3x^3+18x^2-18x

  4. 4. -20x^4+24x^3-16x^2

  5. 5. C. −12x² + 24x

  6. 6. -3x^3+6x

  7. 7. -20x^4-16x^3+20x^2

  8. 8. A. −9x² + 18x