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Math lesson plan · 9th grade (Year 10 in England) · 60 minutes

Difference of two squares

Algebra

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

Objective and success criteria

Students will: Difference of two squares.

  • 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: Factorise quadratics x² + bx + c; Square roots and cube roots

Leads to: Factorise fully: common factor first, then the bracket; Simplify algebraic fractions by factorising; Factorise sums and differences of cubes

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 (Factorise quadratics x² + bx + c; Square roots and cube roots). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. Factorise: x² − 8x + 15 ((x − 5)(x + 3) / (x − 5)(x − 3) / (x − 8)(x + 1) / (x + 15)(x + 1)) → (x − 5)(x − 3)Prompt: Find two numbers that multiply to 15 and add to −8.
  2. What is ∛216? → 6Prompt: Which number, used three times in a multiplication, gives this?
  3. Factorise fully: x² − 49 → (x-7)(x+7)Prompt: Two numbers: product −49, sum 0.

Hook · 6 min

  • Show a "think of a number" puzzle and ask the class to work out the starting number.
  • Share the objective: Difference of two squares. 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: Factorise: 9x² − 16
  • Step 1: (3x + 4)(3x − 4)
  • Answer: (3x + 4)(3x − 4)
  • 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. Factorise: 16x² − 25 ((4x + 5)(4x − 5) / (4x − 5)² / 4(x + 5)(x − 5) / (4x + 5)²) → (4x + 5)(4x − 5)Prompt: This is a difference of two squares: A² − B² = (A + B)(A − B).
  2. Use the difference of two squares to work out 33² − 29² without a calculator. → 248Prompt: a² − b² = (a + b)(a − b).

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. Use the difference of two squares to work out 47² − 43² without a calculator. → 360Prompt: a² − b² = (a + b)(a − b).
  2. Factorise: x² − 25 ((x + 5)(x − 5) / (x − 5)² / (x + 5)² / (x + 25)(x − 1)) → (x + 5)(x − 5)Prompt: This is a difference of two squares: A² − B² = (A + B)(A − B).

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: Factorise quadratics x² + bx + c.
  • 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: Factorise fully: common factor first, then the bracket; Simplify algebraic fractions by factorising; Factorise sums and differences of cubes.
  • 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

Difference of two squares

Name

Date

Score/ 8

  1. Question 1

    Factorise: x² − 16

    • A. (x + 4)(x − 4)
    • B. (x + 4)²
    • C. (x − 4)²
    • D. (x + 16)(x − 1)

  2. Question 2

    Use the difference of two squares to work out 90² − 84² without a calculator.

    Answer

  3. Question 3

    Factorise: x² − 144

    • A. (x + 12)(x − 12)
    • B. (x − 12)²
    • C. (x + 12)²
    • D. (x + 144)(x − 1)

  4. Question 4

    Use the difference of two squares to work out 72² − 64² without a calculator.

    Answer

  5. Question 5

    Factorise: x² − 64

    • A. (x + 64)(x − 1)
    • B. (x − 8)²
    • C. (x + 8)²
    • D. (x + 8)(x − 8)

  6. Question 6

    Use the difference of two squares to work out 42² − 26² without a calculator.

    Answer

  7. Question 7

    Factorise: x² − 25

    • A. (x + 5)²
    • B. (x + 5)(x − 5)
    • C. (x + 25)(x − 1)
    • D. (x − 5)²

  8. Question 8

    Use the difference of two squares to work out 46² − 44² without a calculator.

    Answer

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Answer key: Difference of two squares

  1. 1. A. (x + 4)(x − 4)

  2. 2. 1044

  3. 3. A. (x + 12)(x − 12)

  4. 4. 1088

  5. 5. D. (x + 8)(x − 8)

  6. 6. 1088

  7. 7. B. (x + 5)(x − 5)

  8. 8. 180