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Math lesson plan · 9th grade (Year 10 in England) · 45 minutes

Factorise four-term expressions by grouping

Algebra

CCSS HSA.SSE.A.2England: GCSE Higher Algebra

Objective and success criteria

Students will: Factorise four-term expressions by grouping.

  • 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: Take out the greatest common factor of a polynomial

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 (Take out the greatest common factor of a polynomial). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. Complete the factorisation: 16x⁵ − 20x⁴ − 36x³ = 4x³( … ). Type what goes inside the bracket. → 4x^2-5x-9Prompt: Divide each term by 4x³.
  2. What is the greatest common factor of 28x³y and 8x²y? (4x² / 4x²y / 56x²y / 8x²y) → 4x²yPrompt: Find the HCF of the numbers.
  3. Factorise by taking out −4x: −20x² + 8x = −4x( … ). Type what goes inside the bracket. → 5x-2Prompt: Divide each term by −4x.

Hook · 5 min

  • Show a "think of a number" puzzle and ask the class to work out the starting number.
  • Share the objective: Factorise four-term expressions by grouping. 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: Factorise by grouping: x³ + 3x² − 2x − 6
  • Step 1: x²(x + 3) − 2(x + 3)
  • Step 2: (x² − 2)(x + 3)
  • Answer: (x² − 2)(x + 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.
  1. Factorise by grouping: x³ − 2x² + 6x − 12 ((x² + 6)(x − 2) / (x² + 6)(x + 2) / (x² − 2)(x + 6) / (x − 2)(x + 6)) → (x² + 6)(x − 2)Prompt: Group the first two terms and the last two terms.
  2. Factorise: xy + 2x + 2y + 4 ((x + 2)(y − 2) / (x − 2)(y − 2) / (x + 2)(y + 2)) → (x + 2)(y + 2)Prompt: Take x out of the first pair and a number out of the second pair.

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.
  1. Factorise by grouping: 2x² + 6x + 5x + 15 ((x + 5)(x + 3) / (2x + 5)(x + 3) / (2x + 15)(x + 1) / (2x + 3)(x + 5)) → (2x + 5)(x + 3)Prompt: Group as (2x² + 6x) + (5x + 15).
  2. Factorise: xy − 4x − 1y + 4 ((x − 1)(y + 4) / (x − 1)(y − 4) / (x − 4)(y − 1) / (x + 1)(y + 4)) → (x − 1)(y − 4)Prompt: Take x out of the first pair and a number out of the second pair.

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: Take out the greatest common factor of a polynomial.
  • 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

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Factorise four-term expressions by grouping

Name

Date

Score/ 8

  1. Question 1

    Factorise by grouping: 2x² + 6x + 5x + 15

    • A. (2x + 15)(x + 1)
    • B. (2x + 5)(x + 3)
    • C. (x + 5)(x + 3)
    • D. (2x + 3)(x + 5)

  2. Question 2

    Factorise: xy − 1x + 5y − 5

    • A. (x + 5)(y + 1)
    • B. (x − 5)(y + 1)
    • C. (x + 5)(y − 1)
    • D. (x − 1)(y + 5)

  3. Question 3

    Factorise by grouping: x³ + 2x² − 2x − 4

    • A. (x² − 2)(x − 2)
    • B. (x + 2)(x − 2)
    • C. (x² + 2)(x − 2)
    • D. (x² − 2)(x + 2)

  4. Question 4

    Factorise: xy − 5x + 5y − 25

    • A. (x + 5)(y − 5)
    • B. (x + 5)(y + 5)
    • C. (x − 5)(y + 5)

  5. Question 5

    Factorise by grouping: x³ − 3x² − 2x + 6

    • A. (x² − 2)(x − 3)
    • B. (x² − 2)(x + 3)
    • C. (x² − 3)(x − 2)
    • D. (x − 3)(x − 2)

  6. Question 6

    Factorise by grouping: 5x² + 5x − 6x − 6

    • A. (5x − 6)(x + 1)
    • B. (5x − 6)(x − 1)
    • C. (x − 6)(x + 1)
    • D. (5x + 6)(x − 1)

  7. Question 7

    Factorise: xy − 6x + 3y − 18

    • A. (x − 6)(y + 3)
    • B. (x + 3)(y − 6)
    • C. (x − 3)(y + 6)
    • D. (x + 3)(y + 6)

  8. Question 8

    Factorise by grouping: x³ − 6x² − 5x + 30

    • A. (x² − 6)(x − 5)
    • B. (x² − 5)(x + 6)
    • C. (x² − 5)(x − 6)
    • D. (x − 6)(x − 5)

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Answer key: Factorise four-term expressions by grouping

  1. 1. B. (2x + 5)(x + 3)

  2. 2. C. (x + 5)(y − 1)

  3. 3. D. (x² − 2)(x + 2)

  4. 4. A. (x + 5)(y − 5)

  5. 5. A. (x² − 2)(x − 3)

  6. 6. A. (5x − 6)(x + 1)

  7. 7. B. (x + 3)(y − 6)

  8. 8. C. (x² − 5)(x − 6)