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

index numbers & population estimation

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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: index numbers & population estimation

Duration: 50 minutes

Starter Activity (5 minutes)

Quick Recall

Write down everything you already know about index numbers & population estimation. Then check against the key terms: key terms from index numbers & population estimation. Use a mini-whiteboard or paper.

Main Content (35 minutes)

Parent/Teacher Guide:
Before lesson: Read the script below. Pre-teach key vocab: key terms from index numbers & population estimation.
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: index numbers & population estimation. By the end you will be able to answer exam questions on it unaided. It connects to the rest of Statistics 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: explain the key ideas of index numbers & population estimation

Plenary (5 minutes)

Check Out

Your student states one thing they learned and one question they still have about index numbers & population estimation.

Lesson 2: Core Concepts: index numbers & population estimation

Duration: 50 minutes

Starter Activity (5 minutes)

Review Previous Lesson

Quick recap: write 3 key points from Lesson 1 on index numbers & population estimation. Check them against the notes below.

Main Content (35 minutes)

Key Fact: An index number measures how a quantity changes relative to a base period; the base value is always 100
Key Fact: Index number = (current value ÷ base value) × 100; an index of 120 means a 20% increase from the base period
Key Fact: RPI (Retail Prices Index) measures the change in cost of a basket of goods and services including mortgage interest payments
Key Fact: CPI (Consumer Prices Index) is similar to RPI but excludes mortgage interest and housing costs; CPI is used for the government’s inflation target
Key Fact: GDP (Gross Domestic Product) measures the total value of goods and services produced in a country; GDP per capita = GDP ÷ population
Key Fact: A price relative = (current price ÷ base price) × 100; it shows the change in price for a single item

Practice (10 minutes)

Q: explain the key ideas of index numbers & population estimation

Answer:

Plenary (5 minutes)

Explain Back

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

Lesson 3: Application: index numbers & population estimation

Duration: 50 minutes

Starter Activity (5 minutes)

Quick Recall

Recall the key terms: key terms from index numbers & population estimation. 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.

Work through the practice questions on the revision notes page for this topic.

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: index numbers & population estimation

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: Full-Mark Response A health researcher compares two towns. Town X has a crude death rate of 14 per 1000. Town Y has a crude death rate of 9 per 1000. After standardising for age, Town X has a standardised rate of 10 per 1000 and Town Y has a standardised rate of 11 per 1000. Explain these results. <div class="

The crude rates suggest Town X has a higher death rate (14 vs 9 per 1000), which might lead to the conclusion that Town X is less healthy. However, after standardising for age, Town Y actually has the higher standardised death rate (11 vs 10 per 1000). This reversal happens because Town X likely has a larger proportion of older residents. Older people are more likely to die, so Town X’s crude rate is inflated by its age structure. Once we adjust for this by applying the same standard age distribution to both towns, the true picture emerges: Town Y has slightly worse health outcomes when age is accounted for. This demonstrates why standardised rates are essential for fair comparisons between populations with different age structures.

Exam Tips: Always state the base year when giving an index number, and show the calculation as (current/base) × 100 | For weighted index questions, set out a clear table with columns for item, price relative, and weight before calculating | When discussing RPI vs CPI, mention that CPI excludes mortgage interest payments and is the government’s preferred measure | In capture-recapture questions, list the assumptions and explain how violating each one would affect the estimate | For crude vs standardised rate questions, always explain that crude rates can be misleading due to different population structures
Common Errors: ✗ Saying an index of 130 means prices are 130% higher ✓ An index of 130 means a 30% increase from the base period (index of 100) ✗ Using a simple average instead of a weighted average when items have different importance ✓ Multiply each price relative by its weight, sum, then divide by the sum of weights ✗ Forgetting to check capture-recapture assumptions before calculating ✓ Always state assumptions: closed population, no lost marks, equal chance of capture ✗ Confusing CPI and RPI ✓ CPI excludes housing costs like mortgage interest; RPI includes them. CPI is used for the inflation target.
Stretch & Challenge (Grade 8-9):
  • Synoptic links: explain how index numbers &amp; population estimation connects to another Statistics topic you have studied
  • Real-world: research one real-world use or example of index numbers &amp; population estimation
  • Critical: "What are the limitations of the models used in index numbers &amp; population estimation?"

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)