Combining Like Terms

Overview

This 60-minute lesson is designed for a Year 10 student to master the skill of combining like terms in algebraic expressions. It is the third lesson in a unit titled Mastering Algebraic Concepts. The lesson follows the National Curriculum for England, Key Stage 4 content regarding algebraic manipulation.

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Curriculum Links

National Curriculum Reference:

• Mathematics programmes of study, Key Stage 4 (Years 10-11)
• Algebra
  • "Use algebraic methods to solve problems, including simplifying and manipulating algebraic expressions (including expanding and factorising), solving equations and inequalities, and formulae."
  • Specifically:
    • Simplify and manipulate algebraic expressions by collecting like terms.

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Learning Objectives

By the end of the session, the student will be able to:

1. Identify like terms in algebraic expressions involving single and multiple variables.
2. Correctly combine like terms to simplify expressions.
3. Apply these skills to simplify at least 5 different algebraic expressions accurately.

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Success Criteria

The student can:

• Recognise which terms in an expression are like terms based on variables and powers.
• Correctly add or subtract coefficients of like terms.
• Simplify algebraic expressions with confidence, giving fully simplified final answers.
• Complete at least 5 algebraic simplifications with 100% accuracy.

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Resources Needed

• Whiteboard and markers
• Student notebook and pen/pencil
• Pre-prepared algebraic expressions on worksheets with progressive difficulty
• Algebra tiles or virtual algebra manipulatives (optional but recommended for concrete visualisation)
• Mini-whiteboard (for formative assessment and quick feedback)

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Lesson Structure

1. Starter (10 minutes) – Algebraic Terminology Recap

• Quick Q&A to recap algebraic terms: coefficient, variables, constants, like terms, unlike terms, and powers.
• Use mini-whiteboard to have the student write down definitions/examples as a quick formative check.
• Example prompts:
  • What makes two terms "like terms"?
  • Identify like terms in: 3x, 5x, 2y, -x, 7.

2. Introduction & Modelling (10 minutes) – Combining Like Terms

• Teacher explains the process of combining like terms:
  • Terms must have exactly the same variables with the same powers.
  • Only the coefficients are added or subtracted.
• Model combining simple expressions:
  • Example: 3x + 5x = 8x
  • 4a - 2a + 7 = 2a + 7
• Write at least 3 examples on the board increasing in complexity:
  • 2x + 3y + 4x
  • 5m - 3n + 2m - n

3. Guided Practice (15 minutes) – Active Combining

• Provide worksheet or on-the-fly expressions for student to combine like terms.
• Suggest students verbalise their thinking process to reinforce understanding.
• Examples to cover single variable terms and multiple variables, including negative coefficients:
  1. 6a + 2a
  2. 4x - 7x + 3
  3. 5p + 3q + 2p - q
  4. -2m + 4m - m + 5
  5. 7x² + 3x - 2x² + x
• Teacher provides immediate feedback, correcting any misconceptions.

4. Independent Practice (15 minutes) – Challenge Expressions

• Student simplifies 5 progressively harder expressions independently (with increasing difficulty, e.g., including decimals, negatives, multiple variables).
• Examples:
  • 3a + 4b - 2a + 5 - b
  • 0.5x + 2x - 3 + 4 - 1.5x
  • 8m² + 3m - 2m² + 7m - 4
  • -3x + 6 + 2x - 5
  • 10p - 3q + 4p + q - 2
• Teacher monitors; provides hints if needed while encouraging independence.

5. Plenary (10 minutes) – Success Check & Reflection

• Choose 3 expressions (new ones) and ask the student to combine the like terms aloud or on a mini-whiteboard.
• Check they meet the success criteria fully.
• Discuss challenges and clarify any misunderstandings.
• Student self-assesses their understanding against the success criteria.
• Teacher sets a micro-goal for next lesson (e.g., factorising after combining like terms).

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Differentiation

• For the single student, adapt difficulty in real-time based on their responses.
• Use algebra tiles or visual aids if the student is struggling with abstract notation.
• Introduce negative coefficients and decimals for stretch and challenge.

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Assessment

• Formative assessment via questioning and mini-whiteboard activities during lesson.
• Independent practice mini-quiz results.
• End-of-lesson verbal and written summary of at least 5 correct simplifications.

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Extension & Homework Ideas

• Find and simplify like terms in algebraic expressions from real-life contexts (e.g., formulae in physics).
• Prepare for next lessons involving expanding brackets and factorisation.

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Notes on Teaching Style

• Encourage student to verbalise reasoning to deepen conceptual understanding.
• Use questioning strategies to promote critical thinking.
• Provide instant feedback to consolidate learning.
• Combine traditional pen-and-paper with visual aids for an engaging multisensory experience.

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This lesson plan ensures full coverage of the algebraic manipulation aspect of the National Curriculum for England at Key Stage 4 and meets the required success criteria. The one-to-one tailored approach maximises student engagement and understanding.