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graphical representations

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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: graphical representations

Duration: 50 minutes

Starter Activity (5 minutes)

Quick Recall

Write down everything you already know about graphical representations. Then check against the key terms: key terms from graphical representations. 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 graphical representations.
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: graphical representations. 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 graphical representations

Plenary (5 minutes)

Check Out

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

Lesson 2: Core Concepts: graphical representations

Duration: 50 minutes

Starter Activity (5 minutes)

Review Previous Lesson

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

Main Content (35 minutes)

Key Fact: A bar chart uses rectangular bars to represent frequencies; the height of each bar is proportional to the frequency of the category.
Key Fact: A dual (comparative) bar chart shows two datasets side by side for each category, allowing direct comparison between groups.
Key Fact: A compound (stacked) bar chart stacks sub-categories within each bar; the total bar height shows the overall total for each category.
Key Fact: Bar charts are used for discrete or qualitative data; the bars should have equal width and gaps between them.
Key Fact: A line graph plots data points and joins them with straight line segments; it is used to show trends over time for continuous data.
Key Fact: A scatter graph plots two variables against each other to display the relationship or correlation between them.

Practice (10 minutes)

Q: explain the key ideas of graphical representations

Answer:

Plenary (5 minutes)

Explain Back

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

Lesson 3: Application: graphical representations

Duration: 50 minutes

Starter Activity (5 minutes)

Quick Recall

Recall the key terms: key terms from graphical representations. 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: graphical representations

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 The grouped frequency table shows the marks of 40 students in a test. Draw a cumulative frequency curve and use it to find the median and interquartile range. 0–20: 4, 20–40: 8, 40–60: 16, 60–80: 8, 80–100: 4 <div class="

Plot cumulative frequencies at upper class boundaries: 20: 4, 40: 12, 60: 28, 80: 36, 100: 40 Draw a smooth S-shaped curve through the points. Median at cumulative frequency = 40 ÷ 2 = 20: Read from 20 on the y-axis → approximately 50 on the x-axis. Lower quartile at cumulative frequency = 40 ÷ 4 = 10: Read from 10 → approximately 35. Upper quartile at cumulative frequency = 3 × 40 ÷ 4 = 30: Read from 30 → approximately 65. Interquartile range = 65 – 35 = 30 marks.

Exam Tips: When drawing a cumulative frequency curve, always plot at the upper class boundary, not the midpoint. | In scatter graph questions, always comment on the type and strength of correlation, and identify any outliers by name or coordinates. | For frequency polygons, always close the polygon by joining the first point to the x-axis at the previous midpoint and the last point similarly. | When reading values from an ogive, use a ruler to draw a horizontal line from the cumulative frequency axis to the curve, then a vertical line down to the data axis. | Label all axes clearly and include units where appropriate — missing labels cost marks.
Common Errors: ✗ Plotting cumulative frequency at the midpoint of each class ✓ Cumulative frequency must be plotted at the upper class boundary, since it represents the running total up to and including that boundary value. ✗ Joining scatter graph points with lines ✓ Scatter graphs should show individual plotted points only; joining them implies a sequential relationship that does not exist between the two variables. ✗ Using a bar chart for continuous data without converting to a histogram ✓ Bar charts are for discrete or categorical data; continuous data should be displayed using a histogram (no gaps between bars) or frequency polygon. ✗ Reading the median from an ogive at half the x-axis range instead of
Stretch & Challenge (Grade 8-9):
  • Synoptic links: explain how graphical representations connects to another Statistics topic you have studied
  • Real-world: research one real-world use or example of graphical representations
  • Critical: "What are the limitations of the models used in graphical representations?"

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)