Mathematics • Year 7 • Unit 4 • Lesson 5
Pie Charts
Build fluency with the single formula angle = (frequency ÷ total) × 360°. The full circle is 360° (= 100% of the data); each category becomes a sector whose angle is proportional to its frequency. If all the angles add to exactly 360°, you've done it right.
1. I do — fully worked example
Read every line. Each step shows the formula in action with a short reason.
Problem. 30 students chose a favourite sport: Swimming 10, Football 8, Basketball 7, Tennis 5. Calculate each sector angle and check the total.
Step 1 — Confirm the total.
n = 10 + 8 + 7 + 5 = 30 students ✓ (matches given)
Reason: the formula divides by n, so n must be correct first.
Step 2 — Apply the formula angle = (f ÷ n) × 360° to each sport.
Swimming: (10 ÷ 30) × 360 = 120°
Football: (8 ÷ 30) × 360 = 96°
Basketball: (7 ÷ 30) × 360 = 84°
Tennis: (5 ÷ 30) × 360 = 60°
Reason: f ÷ n is the proportion; multiplying by 360 turns proportion into degrees.
Step 3 — Check the total = 360°.
120 + 96 + 84 + 60 = 360° ✓
Reason: the four sectors must fill the whole circle exactly.
Step 4 — Sketch the pie chart and label each sector.
Use a protractor; start from "12 o'clock"; mark off 120° for Swimming, then 96°, then 84°, then 60°.
Reason: the largest sector (Swimming, 120°) is the most common; the smallest (Tennis, 60°) is the least common.
Answer: Swimming 120°, Football 96°, Basketball 84°, Tennis 60° (sum = 360°).
2. We do — fill in the missing values
20 students chose a favourite ice-cream: Chocolate 8, Vanilla 6, Strawberry 4, Mango 2. Fill in each blank. 4 marks
Step 1 — Total students: n = 8 + 6 + 4 + 2 = _____
Step 2 — Apply angle = (f ÷ n) × 360°.
Chocolate: (8 ÷ _____) × 360° = _____°
Vanilla: (6 ÷ _____) × 360° = _____°
Strawberry: (4 ÷ _____) × 360° = _____°
Mango: (2 ÷ _____) × 360° = _____°
Step 3 — Add the four angles. Total should be _____°.
Step 4 — Largest sector (most common): ______________
3. You do — independent practice
Show your working with the formula angle = (f ÷ n) × 360°. Always check the angles add to 360°.
Foundation — single sector angle
3.1 40 students were surveyed. 10 chose Maths as their favourite subject. What is the angle of the "Maths" sector? 1 mark
3.2 Out of 36 students, 9 chose Soccer. Find the angle for the Soccer sector. 1 mark
3.3 A category has a sector angle of 90°. What FRACTION of the pie is this? 1 mark
3.4 A category has a sector angle of 60°. What PERCENTAGE of the pie is this? 1 mark
Standard — full pie chart
3.5 A class of 24 students reported how they get to school: Walk 12, Bus 8, Car 4. Calculate each sector angle and confirm they sum to 360°. 2 marks
3.6 Of 60 students, 25 chose pizza, 20 chose pasta, 10 chose sushi, 5 chose sandwiches. Calculate each sector angle. Confirm the total is 360°. 2 marks
Extension — push your thinking
3.7 A pie chart has three sectors. The first is 144° and the second is 90°. What is the third sector's angle? If 40 students were surveyed in total, how many fall in the third sector? 3 marks
3.8 7 students were surveyed about their favourite season: Summer 3, Autumn 2, Winter 1, Spring 1. Calculate each sector angle to one decimal place. They will NOT add to exactly 360° due to rounding — how can you fix this? 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — Ice-cream (We do)
n = 20. Chocolate: (8 ÷ 20) × 360 = 144°. Vanilla: (6 ÷ 20) × 360 = 108°. Strawberry: (4 ÷ 20) × 360 = 72°. Mango: (2 ÷ 20) × 360 = 36°. Total: 144 + 108 + 72 + 36 = 360° ✓. Largest sector: Chocolate.
3.1 — Maths from 40
angle = (10 ÷ 40) × 360° = 0.25 × 360° = 90°.
3.2 — Soccer from 36
angle = (9 ÷ 36) × 360° = 0.25 × 360° = 90°.
3.3 — 90° is what fraction?
90° ÷ 360° = 1/4 (a quarter of the pie).
3.4 — 60° is what percentage?
60° ÷ 360° × 100% = 16.7% (or exactly 1/6).
3.5 — Transport (n = 24)
Walk: (12 ÷ 24) × 360 = 180°.
Bus: (8 ÷ 24) × 360 = 120°.
Car: (4 ÷ 24) × 360 = 60°.
Total: 180 + 120 + 60 = 360° ✓.
3.6 — Lunch (n = 60)
Pizza: (25 ÷ 60) × 360 = 150°.
Pasta: (20 ÷ 60) × 360 = 120°.
Sushi: (10 ÷ 60) × 360 = 60°.
Sandwich: (5 ÷ 60) × 360 = 30°.
Total: 150 + 120 + 60 + 30 = 360° ✓.
3.7 — Find third sector
Third sector = 360 − 144 − 90 = 126°.
Number of students: rearrange the formula to f = (angle ÷ 360) × n = (126 ÷ 360) × 40 = 0.35 × 40 = 14 students.
3.8 — Seasons (n = 7)
Summer: (3 ÷ 7) × 360 ≈ 154.3°.
Autumn: (2 ÷ 7) × 360 ≈ 102.9°.
Winter: (1 ÷ 7) × 360 ≈ 51.4°.
Spring: (1 ÷ 7) × 360 ≈ 51.4°.
Sum = 154.3 + 102.9 + 51.4 + 51.4 = 360.0° ✓ (or sometimes 359.9° due to rounding — adjust the LAST sector up by 0.1° to make the total exact). Lesson tip: with messy totals like 7, round to 1 d.p. and fix the last sector if needed.