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

growth and decay

FoundationHigherAll Boards

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: growth and decay

Duration: 50 minutes

Starter Activity (5 minutes)

Quick Recall

Write down everything you already know about growth and decay. Then check against the key terms: Growth, Decay. Use a mini-whiteboard or paper.

Main Content (35 minutes)

Parent/Teacher Guide:
Before lesson: Read the script below. Pre-teach key vocab: Growth, Decay.
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: growth and decay. 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: £5000 at 4.5% compound interest for 8 years. Find the final amount.

Plenary (5 minutes)

Check Out

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

Lesson 2: Core Concepts: growth and decay

Duration: 50 minutes

Starter Activity (5 minutes)

Review Previous Lesson

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

Main Content (35 minutes)

Growth: When a quantity increases by a fixed percentage each time period (e.g., compound interest, population growth).
Decay: When a quantity decreases by a fixed percentage each time period (e.g., depreciation, radioactive decay).

Practice (10 minutes)

Q: £5000 at 4.5% compound interest for 8 years. Find the final amount.

Answer: £7109.62 (5000 × 1.045⁸)

Plenary (5 minutes)

Explain Back

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

Lesson 3: Application: growth and decay

Duration: 50 minutes

Starter Activity (5 minutes)

Quick Recall

Recall the key terms: Growth, Decay. 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: £5000 at 4.5% compound interest for 8 years. Find the final amount.

Answer: £7109.62 (5000 × 1.045⁸)

Q2: A laptop costs £1200 and depreciates at 20% per year. Find its value after 3 years.

Answer: £614.40 (1200 × 0.8³)

Q3: £3000 grows to £3646.52 at 5% compound interest. How many years?

Answer: 4 years

Q4: A population of 2000 grows by 3% each year. Find the population after 10 years.

Answer: Approximately 2688 (2000 × 1.03¹⁰)

Q5: A radioactive sample has half-life 5 years. Starting with 64g, how much after 20 years?

Answer: 4g (64 × 1/16 = 64 × 1/2⁴)

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: growth and decay

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 car is bought for £25,000. It depreciates at 15% per year. (a) Find its value after 5 years. (b) After how many years is it worth less than £5000? (c) The owner says "After 7 years it will be worthless." Show this is incorrect and find its actual value after 7 years. <div class="

(a) Value = 25,000 × 0.85⁵ = 25,000 × 0.44370 = £11,092.53. (b) 25,000 × 0.85^n 9.90. So after 10 years. (c) After 7 years: 25,000 × 0.85⁷ = 25,000 × 0.32058 = £8014.42. The car still has significant value. It is NOT worthless — exponential decay never reaches zero. Mark scheme: M1 decay formula, A1 £11,092.53, M1 inequality or logs, A1 10 years, M1 calculation for 7 years, A1 £8014.42, A1 explanation

Exam Tips: Multiplier = 1 + rate for growth, 1 - rate for decay | Use the formula: Final = Initial × multiplierⁿ | Compound interest uses powers, simple interest does not | For half-life: multiplier = 0.5, substitute number of half-lives | Check answers are sensible: growth should increase, decay should decrease
Common Errors: Watch Out! 1. Wrong: For compound interest at 5% for 3 years, adding 3 × 5% = 15% to the original Correct: Use (1.05)³ = 1.1576, so the total increase is 15.76%, not 15%. Compound interest gives MORE than simple interest. 2. Wrong: For decay, using (1 + r/100)^n instead of (1 − r/100)^n Correct: Decay means the quantity decreases, so use (1 − r/100)^n. E.g. 8% decay per year: multiply by 0.92 each year. 3. Wrong: Thinking that half-life means the quantity is zero after two half-lives Correct: After 1 half-life: ½ remains. After 2 half-lives: ¼ remains. After 3: ⅛. The quantity halves each time but never reaches zero.
AO3 - Reasoning & Interpretation: Reasoning and Interpretation A radioactive substance has a half-life of 8 years. The initial mass is 100 g. (a) How much remains after 24 years? (b) A scientist says "After 40 years, only 3.125 g will remain." Verify this claim. (c) Another scientist says "After 80 years (10 half-lives), the substance will be completely safe." Is this statement justified? Explain. Answers: (a) 24 years = 3 half-lives. Remaining = 100 × (½)³ = 100 × ⅛ = 12.5 g. (b) 40 years = 5 half-lives. Remaining = 100 × (½)⁵ = 100 × 1/32 = 3.125 g. The scientist is correct ✓ (c) After 10 half-lives: 100 × (½)¹⁰ = 100/1024 ≈ 0.098 g. There is still radioactive material present — it is NOT zero. Whether it is "safe" depends
Stretch & Challenge (Grade 8-9):
  • Synoptic links: explain how growth and decay connects to another Mathematics topic you have studied
  • Real-world: research one real-world use or example of growth and decay
  • Critical: "What are the limitations of the models used in growth and decay?"

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)