Mastering Inequalities

Overview

This 60-minute lesson aims to deepen Year 10 students’ understanding of inequalities in line with the National Curriculum for England (Mathematics Program of Study, Year 10). Students will explore solving linear inequalities, representing solutions on number lines, and interpreting inequalities in context.

National Curriculum Links

Key Stage 4:

• Use and interpret inequalities involving algebraic expressions (Non-statutory guidance for Years 9 to 11)
• Solve linear inequalities in one variable and represent solutions on a number line
• Understand sets of values satisfying inequalities and how they extend beyond strict equality
• Develop fluency and reasoning in manipulating inequalities and applying them to problem-solving contexts

(Reference: Department for Education, Mathematics programme of study, Key Stage 4)

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Learning Objectives

By the end of the lesson, students will be able to:

1. Solve linear inequalities algebraically and represent their solutions on number lines.
2. Understand and apply inequality notation (>, <, ≥, ≤) in problem-solving contexts.
3. Translate word problems into algebraic inequalities and interpret solutions.
4. Develop reasoning skills by comparing and combining inequalities.

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Resources Needed

• Whiteboard and markers
• Student workbooks or lined paper
• Pre-prepared inequality problem cards (with real-life contexts)
• Number line visuals (printed A3) and mini dry-wipe boards per pair
• Rulers for drawing number lines
• Projector or visualiser for examples and solutions
• Question mini-set for plenary assessment

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Lesson Breakdown

1. Starter Activity (10 minutes)

Activity: Inequality Matching Game

• Display a set of inequality expressions and a set of number line graphs on the board.
• Students work in pairs to match inequalities with correct shaded number line representations.
• Discuss answers and highlight key symbols and directions of inequalities.

Purpose: Activate prior knowledge from KS3 and introduce visual representation of inequalities.

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2. Main Teaching Input (15 minutes)

Focus: Algebraic manipulation of inequalities

• Explicitly teach solving linear inequalities (e.g., 3x - 4 > 2, 5x + 7 ≤ 22).
• Emphasise changing direction of inequalities when multiplying/dividing by negative numbers with worked examples.
• Demonstrate correctly representing solutions on number lines (solid dot for ≥ or ≤, open dot for > or <).
• Use on-screen worked examples and annotate them live.

Key Concept: Understanding the link between algebraic and graphical representation.

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3. Guided Practice (15 minutes)

Activity: Problem Card Challenges

• Distribute cards with inequalities based on real-life situations (e.g., budget constraints, speed limits, class attendance).
• Students solve inequalities in pairs and illustrate solutions on mini whiteboards.
• Circulate to provide rapid formative feedback.
• Ask select pairs to present their solutions, encouraging peer evaluation.

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4. Independent Practice (10 minutes)

Activity: Inequality Word Problems

• Students individually solve 3-4 inequality word problems in their books.
• Problems require forming inequalities first, then solving and interpreting the solutions (e.g., "You must score at least 40 marks to pass").
• Encourage students to underline key phrases indicating inequality types.

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5. Plenary Assessment (10 minutes)

Activity: Mini Quiz & Reflection

• Quick 5-question quiz covering notation, solving and representing inequalities, and interpreting context.
• Example questions:
  • Solve and represent: 2x - 5 ≤ 9
  • Write inequality for: "Height must be more than 150 cm"
  • If x > 3 and x < 7, show the range on a number line.
• Students self-assess confidence on a 1–5 scale.
• Teacher to collect quiz for assessment, providing immediate whole-class feedback.

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Assessment Methods

• Formative: Observation during matching and paired work, peer presentations.
• Summative: Mini-plenary quiz and individual solution accuracy.
• Self-assessment of confidence at plenary fosters metacognition and identifies misconceptions.

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Extension Ideas (For faster learners or homework)

• Explore double inequalities and compound statements (e.g., 2 < x + 3 ≤ 7).
• Investigate contextual problems involving inequalities in geometry (e.g., perimeter constraints).
• Introduce basic quadratic inequalities if confident.

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Differentiation

• Provide scaffolded problem cards with hints for lower ability students.
• Challenge higher ability students with inequalities involving fractions or negative coefficients.
• Use mixed-ability pairing for peer support.

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Teacher’s Notes

• Reinforce precise mathematical language and notation throughout.
• Use real-life contexts to increase engagement and relevance.
• Monitor common errors such as forgetting to flip inequality direction or incorrect graph shading.

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This lesson plan offers a structured, engaging, and curriculum-aligned approach to inequalities, blending visual, collaborative, and independent methods to develop both fluency and reasoning in Year 10 Maths.