Context

• Unit: Mastering Algebraic Concepts
• Lesson: 9 of 10
• Duration: 30 minutes
• Class size: 1 student
• Age group: Year 11 (15–16 years old)
• Curriculum reference:
  • National Curriculum for England, Mathematics - Key Stage 4
  • Algebra: Use and interpret algebraic notation, including inequalities (NC 2014, KS4 references: Number and algebra, A1.1, A1.3)

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Learning Objectives

By the end of this lesson, the student will be able to:

• Understand the concept of inequalities and how they differ from equations.
• Solve simple linear inequalities in one variable.
• Represent inequalities graphically on a number line.
• Interpret and write inequalities from real-life contexts.

Success Criteria

• The student can correctly solve at least three inequalities involving linear expressions.
• The student accurately graphs the solution sets of these inequalities on a number line.
• The student can explain the key differences between an equation and an inequality.

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Resources Needed

• Whiteboard or notebook and pen
• Graph paper or number line printed sheet
• Markers or coloured pencils
• Pre-prepared inequality problem cards (3 examples)
• Calculator (optional)

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Lesson Outline

1. Starter (5 minutes)

Focus: Engage the student by revising equations vs inequalities

• Begin with a quick recap question: "What is an equation? Can you give me an example?"
• Present two statements and ask the student to identify which is an equation and which is an inequality:
  • ( 3x + 5 = 11 )
  • ( 3x + 5 > 11 )
• Discuss briefly the concept of equality vs inequality symbols (<, >, ≤, ≥, ≠).
• Highlight that inequalities represent a range of solutions, not a fixed point.

National Curriculum reference: Recognise and use inequality symbols (NC KS4, A1.1)

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2. Main Teaching Activity (15 minutes)

Focus: Solving and graphing inequalities

Explanation (5 minutes)

• Introduce how to solve inequalities similarly to equations by performing inverse operations, but with a key difference when multiplying or dividing by negative numbers — the inequality sign reverses.
• Use a worked example on the board:
  • Solve ( 2x - 4 < 6 )
  • Step 1: Add 4 to both sides: ( 2x < 10 )
  • Step 2: Divide both sides by 2: ( x < 5 )
• Demonstrate how to graph ( x < 5 ) on a number line: open circle at 5, shaded to the left.

Assessment: Ask the student to explain back the steps in their own words.

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Guided Practice (10 minutes)

• Provide 3 inequalities for the student to solve and graph:
  1. ( 3x + 2 \geq 11 )
  2. ( -x + 5 < 2 )
  3. ( 4x - 3 \leq 13 )
• Student solves each, then graphs the solution on their number line.
• Teacher guides and prompts as needed, ensuring conceptual understanding, especially the rule about reversing inequality signs when multiplying or dividing by negative numbers.

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3. Plenary / Review (5 minutes)

Focus: Consolidate learning and self-assessment

• Revisit success criteria.
• Ask the student to summarise what inequalities are and how they differ from equations.
• Prompt the student to reflect on challenges faced in solving inequalities and graphing solutions.
• Pose a challenge question: "If ( x \geq 3 ) and ( x < 7 ), how would you represent this combined inequality on a number line?"
• Discuss intersecting solution sets briefly as a teaser for next lesson.

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Differentiation / Personalisation

• As the class size is 1, the lesson can be personalised in real-time:
  • Adjust difficulty by increasing complexity of inequalities if student is confident.
  • Use real-life examples the student relates to (e.g., budgeting, temperature ranges) for contextual understanding.
  • Scaffold through step-by-step questioning where necessary.

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Assessment for Learning (AfL)

• Ongoing questioning and explanation from student to check understanding.
• Review of completed inequality problems and graphs to evaluate accuracy.
• Use of verbal summarisation for formative feedback.

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Cross-curricular Links

• Use inequalities in real-world contexts relevant to Science (temperature thresholds, chemical concentrations) or Geography (population growth models).

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Teacher’s Reflection Notes (Post-Lesson)

• Note the student’s fluency with negative number operations and symbol manipulation; use this info to tailor final unit lesson.
• Consider introducing compound inequalities or simultaneous inequalities next.

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This concise and focused 30-minute plan balances explanation, practice, and assessment tailored precisely to meet national standards for Year 11 algebra work on inequalities. It makes the most of 1:1 teaching with adaptive, personalised scaffolding and real-time formative assessment.