Pie Graphs With Purpose

Overview

Students investigate categorical data, then construct and analyse a pie graph using frequencies, fractions, percentages and angles. The lesson develops statistical thinking by connecting a data display to a question and requiring students to justify what the graph shows and does not show.

Learning intentions

• WALT identify when a pie graph is an appropriate display for data.
• WALT convert frequencies into proportions, percentages and sector angles.
• WALT construct an accurate, clearly labelled pie graph.
• WALT analyse a pie graph and communicate evidence-based conclusions.

Success criteria

• I can explain why a pie graph is suitable for categorical data showing parts of a whole.
• I can calculate sector angles using the total frequency.
• I can construct and label a pie graph accurately, including a title and key or labels.
• I can make a comparison or conclusion using data from the graph and identify a limitation.

Curriculum links

• Mathematics and Statistics — statistical investigation, data displays and interpretation.
• Mathematics and Statistics — proportional reasoning, percentages, fractions and angles.
• Mathematics and Statistics — communicating findings and justifying mathematical decisions.
• Mathsteasers — higher-order thinking and challenge through non-routine analysis.

Lesson structure (60 minutes)

1. 0–7 min · Hook and prior knowledge. Teacher opens the pie graph hook and lesson sequence with the question, “If our class had one shared celebration budget, how could we show everyone’s preferences fairly?” Students silently estimate which category would be largest, then discuss what a pie graph can show and recall that a complete circle represents 360°.

2. 7–15 min · Choosing a graph. Teacher displays a small data set showing students’ preferred after-school activities and asks when a pie graph is useful and when a bar graph may be better; hand out the graph choice decision tree for pairs to consult. Students classify the data as categorical or numerical, identify the whole, and justify the most suitable graph using the sentence frame: “A pie graph is/is not suitable because…”

3. 15–27 min · Explicit teaching and modelling. Teacher uses the pie graph calculation and modelling slides to model the data: sport 12, music 8, gaming 6, reading 4; total 30. Model frequency ÷ total, percentage, and angle: sport (12/30 \times 360=144°), then demonstrate using a protractor, checking that all angles total 360°. Students complete the calculation table with the teacher and explain why rounding can cause a total slightly different from 100% or 360°.

4. 27–45 min · Create and analyse. Teacher distributes the pie graph construction and analysis worksheet and reminds students to work carefully with a ruler, compass and protractor; circulate to check totals before sectors are drawn. Students calculate the remaining angles, construct and label the pie graph, add a title and key, then answer questions such as “Which category is most common?”, “How many more students chose sport than reading?”, and “What conclusion can you make about the class?”

5. 45–54 min · Statistical discussion. Teacher returns to the comparison and discussion prompts and presents two pie graphs: one with clear labels and one with a misleading or incomplete presentation. Students compare accuracy, readability and purpose, then discuss why a pie graph cannot easily show change over time and why a sample of 30 students may not represent all Year 9 students.

6. 54–60 min · Exit assessment and reflection. Teacher displays the plenary and exit questions. Students complete the final worksheet questions: “A category has 9 out of 36 responses. What percentage and angle should its sector represent?” and “State one conclusion and one limitation of this graph.” Invite two students to explain their reasoning before collecting responses.

Resources

• the pie graph hook and lesson sequence
• the pie graph construction and analysis worksheet
• the graph choice decision tree
• Compass, ruler and protractor for each pair
• Coloured pencils or highlighters
• Calculators, optional for checking calculations
• Whiteboard and markers
• Projector or interactive display

Assessment

• During modelling, check that students can identify the total and explain why each sector angle is calculated from 360°.
• During construction, inspect calculation tables and require students to check that frequencies, percentages and angles represent the same proportions.
• Use the completed exit questions to assess calculation accuracy, graph interpretation, conclusion-writing and awareness of limitations.

Differentiation

• Support learners with a partially completed calculation table, a displayed formula ( \text{angle}=\frac{\text{frequency{\text{total\times360° ), a worked example and a teacher check after each sector. Pair students strategically and allow calculators for checking rather than replacing reasoning.
• Provide dyslexia-friendly copies of the worksheet: clear sans-serif font, larger spacing, uncluttered layout, bold headings, short numbered instructions and no unnecessary decorative text. Read instructions aloud and allow students to explain answers verbally before writing.
• Support EAL learners with visual examples and sentence starters: “The largest sector represents…”, “This is shown by…”, and “A limitation is…”. Pre-teach whole, category, frequency, proportion, sector and representative.
• Extension learners create a second pie graph from a new data set, compare it with a bar graph, and evaluate which display communicates the findings more effectively. They may also design a data set that produces three equal sectors and justify their choice.