Math lesson plan · 9th grade (Year 10 in England) · 45 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 · 5 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.

Factorise: x² + x − 6 ((x + 3)(x + 2) / (x − 6)(x + 1) / (x − 3)(x + 2) / (x + 3)(x − 2)) → (x + 3)(x − 2)Prompt: Find two numbers that multiply to −6 and add to 1.
What is √196? → 14Prompt: Which number multiplied by itself gives this?
Factorise fully: x² − 13x + 42 → (x-6)(x-7)Prompt: Two numbers: product 42, sum −13.

Hook · 5 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 · 10 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 · 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.

Factorise: 25x² − 121 (5(x + 11)(x − 11) / (5x + 11)(5x − 11) / (5x − 11)² / (5x + 11)²) → (5x + 11)(5x − 11)Prompt: This is a difference of two squares: A² − B² = (A + B)(A − B).
Use the difference of two squares to work out 31² − 29² without a calculator. → 120Prompt: a² − b² = (a + b)(a − b).

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.

Use the difference of two squares to work out 39² − 27² without a calculator. → 792Prompt: a² − b² = (a + b)(a − b).
Factorise: 4x² − 144 ((2x + 12)(2x − 12) / 2(x + 12)(x − 12) / (2x − 12)² / (2x + 12)²) → (2x + 12)(2x − 12)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