Homeschool Guide: These lesson plans are a guide for parents. Content may contain errors — always cross-reference with official exam board specifications.

inequalities

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4 detailed 50-minute lessons with teaching scripts, worked examples, parent guides, and assessment criteria.

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Lesson Overview

Total Lessons: 4
Tier: Foundation and Higher
Duration: 50 minutes per lesson (200 minutes total)
Exam Boards: AQA, Edexcel, OCR, Eduqas, CCEA

Learning Objectives

Prerequisites

Materials & Equipment

Lesson 1: Introduction: inequalities

Duration: 50 minutes

Starter Activity (5 minutes)

Quick Recall

Write down everything you already know about inequalities. Then check against the key terms: Key rule. Use a mini-whiteboard or paper.

Main Content (35 minutes)

Parent/Teacher Guide:
Before lesson: Read the script below. Pre-teach key vocab: Key rule.
If stuck: Re-read the revision notes (link above), then break the content into smaller steps.
Extension: See the Stretch & Challenge ideas in Lesson 4.
Teaching Script (35 mins):
Mins 0-5 - Hook: "Today: inequalities. By the end you will be able to answer exam questions on it unaided. It connects to the rest of Mathematics because the ideas here recur across the spec."
Mins 5-20 - Direct Instruction: Work through the core ideas below one at a time; after each, ask your student to explain it back in their own words.
Mins 20-30 - Guided Practice: Model the worked example together, then let your student attempt the first practice question with guidance.
Mins 30-35 - Independent Practice: 2-3 practice questions from Lesson 3 below, with immediate feedback.
First Look

Start with the revision notes summary, then attempt: Solve: 4x - 7 > 13

Plenary (5 minutes)

Check Out

Your student states one thing they learned and one question they still have about inequalities.

Lesson 2: Core Concepts: inequalities

Duration: 50 minutes

Starter Activity (5 minutes)

Review Previous Lesson

Quick recap: write 3 key points from Lesson 1 on inequalities. Check them against the notes below.

Main Content (35 minutes)

Key rule: Solve like equations, BUT when multiplying or dividing by a negative number, reverse the inequality sign.
ItemDetail
<Less than
>Greater than
≤Less than or equal to
≥Greater than or equal to

Practice (10 minutes)

Q: Solve: 4x - 7 > 13

Answer: x > 5

Plenary (5 minutes)

Explain Back

Your student teaches the key points back to you without looking. Fill any gaps immediately.

Lesson 3: Application: inequalities

Duration: 50 minutes

Starter Activity (5 minutes)

Quick Recall

Recall the key terms: Key rule. Define each in one sentence.

Main Content (35 minutes)

Parent/Teacher Guide: Let your student attempt each question alone first, then compare with the model answer. Award method marks for correct working even if the final answer is wrong.

Q1: Solve: 4x - 7 > 13

Answer: x > 5

Q2: Solve: 2x + 5 ≤ x + 8

Answer: x ≤ 3

Q3: Solve: -3x > 12

Answer: x < -4

Q4: List the integer values satisfying -3 < x ≤ 2

Answer: -2, -1, 0, 1, 2

Q5: Solve: x² - 9 > 0

Answer: x 3

Q6: Solve: x² + 5x + 6 < 0

Answer: -3 < x < -2

Plenary (5 minutes)

Error Review

Review any questions answered incorrectly. Identify whether the error was knowledge, method, or reading the question.

Lesson 4: Exam Practice: inequalities

Duration: 50 minutes

Starter Activity (5 minutes)

Command Words

Review what these command words require: state (one point), describe (say what happens), explain (say why), compare (both sides), evaluate (judgement).

Main Content (35 minutes)

Extended Answer

Extended question: Extended Answer 6 marks: A company's profit is P = -x² + 12x - 20 thousand pounds, where x is the price in pounds. (a) Find the prices that give zero profit. (b) Find the price range for positive profit. (c) What price maximises profit? <div class="

(a) -x² + 12x - 20 = 0 → x² - 12x + 20 = 0 → (x - 2)(x - 10) = 0 → x = 2 or x = 10 (b) Parabola opens downward (negative x²). Positive profit between roots: 2 < x < 10 (c) Maximum at midpoint of roots: x = 6. P = -36 + 72 - 20 = 16 thousand pounds (£16,000) Mark scheme: (a) 2 marks. (b) 2 marks for correct inequality with reasoning. (c) 2 marks.

Exam Tips: When multiplying/dividing by negative: flip the sign! | Open circle for < or >, filled for ≤ or ≥ | For quadratics: sketch the graph to see the solution region | Above x-axis = positive, below = negative | Check a value in each region to verify
Common Errors: Watch Out! 1. Wrong: Dividing -4x > 12 by -4 gives x > -3 Correct: When dividing by negative, FLIP the sign: x < -3 2. Wrong: Solving x² > 4 as x > 2 only Correct: x² > 4 means x > 2 OR x < -2 (both directions from zero) 3. Wrong: Writing -3 < x < 5 as {x: x < 5 and x > -3} Correct: Use proper set notation {x : -3 < x < 5} or separate inequalities connected by "and"
AO3 - Reasoning & Interpretation: Reasoning and Interpretation A theme park ride has a height restriction: riders must be at least 120 cm tall but under 200 cm. (a) Write this as an inequality using h for height. (b) A child is 1.3 m tall. Can they ride? (c) The park changes the rule: riders must be at least 140 cm OR accompanied by an adult. Explain why this changes the set of allowed riders. Answers: (a) 120 ≤ h
Stretch & Challenge (Grade 8-9):
  • Synoptic links: explain how inequalities connects to another Mathematics topic you have studied
  • Real-world: research one real-world use or example of inequalities
  • Critical: "What are the limitations of the models used in inequalities?"

Plenary (5 minutes)

Assessment Criteria
  • Got it: Confident explanation + correct worked examples
  • Getting there: Main points OK, needs support with detail
  • Not yet: Confused on key concepts - re-run Lesson 2

Homework & Consolidation

Recommended Resources

🎓 Smart Lesson (Guided)