🎯 Learning Objectives
- calculate sector angles;
- construct pie charts;
- recover frequencies from angles;
- compare proportions;
- check that sectors total 360°.
Introduction
This lesson develops Pie Charts from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
Central Relationship
Sector angle = frequency ÷ total frequency × 360°
Frequency = sector angle ÷ 360° × total frequency
Worked Example
In a survey of 40 learners, 10 choose football. Sector angle=10÷40×360°=90°.
🥧 Build a Pie Chart
Change the frequencies. The total, percentages and sector angles update automatically.
Total
Largest sector
Practice Questions
- Find the sector angle for 15 out of 60 learners.
- A sector is 72° in a survey of 50 people. Find the frequency.
- Frequencies are 8, 12 and 20. Find all sector angles.
- How can you check a completed pie chart?
✅ Check Your Work
Show answers and working
- 15÷60×360=90°.
- 72÷360×50=10 people.
- Total=40. Angles: 72°, 108° and 180°.
- Add all sector angles; they must total 360°. Also compare sector sizes with the original proportions.
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Pie charts show proportions of a whole.
- Angles must total 360°.