Mastering Algebraic Factorisation

Learning Context

This Year 8 maths lesson is designed under UK National Curriculum guidelines, specifically within the strand of Algebra. Pupils will develop foundational skills required for algebraic manipulation, focusing on factorisation principles. The lesson caters to the age-appropriate progression in algebra and builds upon their existing knowledge of multiplication and common factors (Year 7). The primary aim is to help pupils confidently rewrite and simplify algebraic expressions using factorisation, enhancing their problem-solving abilities.

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Learning Objectives

• LO1: To factorise single brackets in algebraic expressions.
• LO2: To identify and use common factors in algebra confidently.
• LO3: To rewrite algebraic expressions effectively using factorisation.
• LO4: To solve real-life and mathematical problems through factorisation.

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Curriculum Links

• Mathematics Curriculum (Key Stage 3): Develop algebraic manipulation skills, including simplifying expressions and factorising into single brackets. This lesson is geared to ensure fluent use of algebra in preparation for GCSE content.
• Problem-Solving and Reasoning: Apply algebraic knowledge to solve structured and unstructured mathematical challenges. Supports mastery in contextual problem-solving from the UK curriculum.

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Recall Phase

(20 minutes)

1. Quickfire Starter Quiz:

   • A set of 5 fluency questions is displayed (e.g., Calculate the greatest common factor of 12 and 18, Find the product of 4 × (x + 3)).
   • Pupils answer on mini whiteboards to immediately engage them and identify what they recall about expanding brackets and common factors.

2. Group Think-Pair-Share:

   • Pose the question: “What do you already know about brackets in algebra? How do we undo multiplication?”
   • Facilitate a brief discussion to refresh key ideas such as distributive property, common multipliers, and reverse operations.

3. Briefly revisit expanding brackets (e.g., 2(x + 4) = 2x + 8) to remind pupils of the relationship between expansion and factorisation.

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Scaffolding Phase ("We")

(30 minutes)

• Present visual examples of factorisation with incremental difficulty. Begin with numeric common factors only (e.g., 6x + 12 → 6(x + 2)), progressing to simple algebraic terms (5x^2 + 10x → 5x(x + 2)).
• Guided Practice:
  • Work through 2 scaffolded examples as a class on the interactive whiteboard. Verbally reason the process of identifying a common factor while students follow step-by-step.

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Modelling Phase ("I")

(30 minutes)

1. Teacher-led demonstration of systematic factorisation:

   • Use a worked example: 9xy + 6x → 3x(3y + 2).
   • Key focus:
     • Identify numeric factor first.
     • Check for common variables.
     • Rewrite the expression.

2. Highlight error traps (e.g., forgetting to factorise fully, misunderstanding coefficients) by showing a “common mistake” example and actively correcting it.

3. Relate factorisation to practical scenarios (e.g., grouping objects into packets).

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Key Knowledge

1. Definitions:

   • Factorisation: Rewriting an expression as a product of simpler terms.
   • Common Factor: A number/variable that divides two or more terms without remainder.

2. Steps to Factorisation:

   • Step 1: Identify the common factor (numeric and/or algebraic).
   • Step 2: Factorise using brackets.
   • Step 3: Double-check by expanding.

3. Where It’s Used:

   • Simplifying algebraic expressions.
   • Solving equations.
   • Practical problem-solving (structured and word problems).

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Success Criteria

By the end of this lesson, pupils will:

1. Accurately factorise simple algebraic expressions using single brackets.
2. Identify the greatest common factor in numeric and algebraic terms.
3. Confidently simplify and rewrite algebraic expressions.
4. Demonstrate application of factorisation in contextual problems (e.g., geometry or patterns).

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Personalising Learning

• Scaffold Support: Offer partially completed examples for pupils who need extra support.
• Stretch Activities: Introduce factorisation involving 3 terms for high-achievers (e.g., 6x^2y + 9xy^2 → 3xy(2x + 3y)).
• Incorporate real-life data problems for kinaesthetic learners.

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Critical Questions

1. How do we determine the greatest common factor in an algebraic expression?
2. What happens if an expression is already simplified?
3. Why do we factorise - how does it help us solve problems?
4. What kinds of mistakes might we make when factorising brackets?

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Vocabulary

• Tier 2: Identify, factor, simplify, expand.
• Tier 3: Algebraic expression, coefficient, variable, common factor.

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Lesson Flow

Hour 1: Introducing Factorisation (LO1 & LO2)

1. Starter recall quiz (mini whiteboards).
2. Think-pair-share: Revisiting expanding brackets.
3. Scaffolding examples - work through "we do" examples as a class.

Hour 2: Guided Practice (LO2 & LO3)

1. Modelling phase ("I do") - teacher demonstrates step-by-step.
2. Group work: Pupils factorise 8 structured examples in pairs (teacher circulates).
3. Whole-class review and feedback.

Hour 3: Problem-Solving Applications (LO3 & LO4)

1. Solve word problems: Factorise expressions for contextual questions (e.g., area/geometry).
2. Small groups create and swap their own factorisation problems.

Hour 4: Independent Practice and Plenary

1. Solo challenge worksheet: Mixed problem set, including error-spotting questions.
2. Plenary: Class-wide Kahoot quiz to assess key takeaways.

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Assessment for Learning (AfL) Strategies

1. Targeted Questioning throughout scaffolding and group work.
2. Mini Whiteboards for immediate feedback during the recall and modelling phase.
3. Peer marking during group activity (using success criteria).
4. End-of-lesson Kahoot to assess understanding and confidence.

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This lesson plan engages students with structured, practical, and contextual problem-solving approaches. It incorporates visual, collaborative, and independent learning techniques to ensure mastery of factorisation.