Factorising Single Brackets

National Curriculum References

• Key Stage 3 Mathematics Programme of Study: Year 9
• Topic: Algebra – Expressions and Formulae
• Focus: Factorising algebraic expressions
• Relevant NC Statements:
  • "Use algebraic methods to simplify and manipulate algebraic expressions, including expanding products of two binomials and factorising quadratic expressions" (NC Maths Framework, Year 9)
  • "Understand and use the distributive law to multiply a single term over a bracket and to factorise expressions by taking out a common factor"
• Assessment Standards:
  • Students should factorise linear expressions fully by identifying a common factor (low-attaining focus on single brackets)

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Learning Objectives

By the end of the lesson, students will:

1. Understand what factorising a single bracket means in algebra (taking out a common factor).
2. Identify the greatest common factor (GCF) in algebraic expressions.
3. Successfully factorise simple linear expressions with one bracket (e.g., 3x + 6 → 3(x + 2)).
4. Apply factorising skills to solve simple algebra problems.
5. Demonstrate understanding through independent and group tasks.

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Resources Needed

• Whiteboard and markers
• Mini whiteboards for each student
• Printed worksheets with practice and challenge questions
• Factorising algebra cards for group activity (pre-prepared)
• Visual aids - diagrammatic examples showing factorisation
• Timer or stopwatch

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Lesson Structure (50 minutes)

1. Starter Activity (5 minutes)

• Aim: Activate prior knowledge about multiplication and common factors.
• Activity: Write the numbers 12, 16, and 20 on the board and ask students in pairs to find the greatest common factor (GCF).
• Purpose: Connect numeric factors to algebraic factorising.

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2. Introduction & Explanation (10 minutes)

• Objective: Introduce factorising single brackets.

• Teacher input:

  • Explain factorising as the “reverse” of expanding.
  • Write a simple expression on the board (e.g., 4x + 8).
  • Ask students what multiplication facts they know for 4 and 8.
  • Highlight the GCF (4) and how to write the expression as 4(x + 2).

• Use visual aids:

  • Use a number factor tree (e.g., 12 = 3 × 4) alongside algebraic factor trees.
  • Write factor pairs to visually show common factors for terms.

• Key vocabulary:

  • Factor, common factor, bracket, term, coefficient

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3. Guided Practice (15 minutes)

• Activity 1: Mini whiteboard exercise

  • Students work on factorising expressions such as:
    • 5x + 10
    • 6y + 9
    • 8a + 12
  • Circulate to give instant feedback.

• Activity 2: Group card sort

  • In groups of 4, students receive mixed cards: some with expressions (e.g., 7m + 21), some with factorised forms (7(m + 3)).
  • They match pairs and explain their reasoning to the group.
  • Encourage discussion of possible mistakes (e.g., missing a factor or incorrect bracket).

• Differentiation: Provide scaffold cards for lower attaining students that highlight the GCF already.

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4. Independent Work (15 minutes)

• Worksheet:
  Students complete a worksheet graded for low attaining learners:

  • Tasks begin with very simple expressions and progress slightly.
  • Example questions:
    • Factorise 3p + 9
    • Factorise 10x + 5
    • Factorise 4m + 16
  • Include very basic word problems requiring factorising to solidify understanding.

• Support:

  • Teacher and teaching assistant circulate to assist.
  • Encourage students to verbally explain their steps to a peer or adult.

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5. Plenary & Assessment (5 minutes)

• Quick quiz:

  • Use mini whiteboards for students to answer “What is the factorised form of 12n + 18?”
  • Ask a few students to explain their answer aloud.

• Formative Assessment Questions:

  • What is the common factor in 9x + 15?
  • Why do we take out the common factor before the bracket?

• Exit ticket:

  • On a small slip, students write one thing they found easy and one thing they found tricky about factorising today.

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Differentiation and Support

• For low attaining students:
  • Use concrete examples and visual aids.
  • Provide partially completed factorisation to scaffold.
  • Allow paired work and discussion.
• For stretch:
  • Introduce factorising expressions with negative signs (e.g., -4x - 8).
  • Briefly explore expanding to relate both skills.

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Reflection for Next Lessons

• Assess the exit tickets to identify common difficulties.
• Plan follow-up activities targeting misconceptions.
• Introduce factorising expressions with multiple terms once confident with single brackets.

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This lesson plan ensures alignment with the National Curriculum for England, focuses on low-attaining learners at Year 9, and incorporates varied engaging activities and continuous assessment which will support teachers in effectively delivering the topic of factorising single brackets.