Mathematics • Year 7 • Unit 4 • Lesson 5
Pie Charts — Mixed Challenge
Bring together angle = (f ÷ n) × 360°, the reverse f = (angle ÷ 360°) × n, and percentage = (angle ÷ 360°) × 100. Spot a sector-angle mistake and design your own pie chart from a frequency table you choose.
1. Mixed problems
Show working. 2 marks each
1.1 A pie chart has 4 equal sectors. What is the angle of each sector, and what percentage does each represent?
1.2 Of 50 students, 35 prefer summer. Calculate the sector angle for summer.
1.3 A pie chart shows three sectors of 90°, 150° and 120°. Do these angles fit a valid pie chart? Justify in one sentence.
1.4 A pie chart of 90 students has a "Walking" sector of 80°. How many students walk to school?
1.5 Convert these proportions to sector angles: 25%, 33⅓%, 12.5%.
1.6 A pie chart shows 5 categories. Two of them are 60° and 90°. The remaining three sectors are EQUAL. What is the angle of each of those three?
2. Find the mistake
A Year 7 student has calculated sector angles for a class survey of 60 students about screen time per day. Exactly one line contains a clear mistake. Spot it, explain, then rewrite. 3 marks
Student's working (n = 60):
Line 1: Under 1 hour: f = 5. Angle = (5 ÷ 60) × 360 = 30°.
Line 2: 1–2 hours: f = 15. Angle = (15 ÷ 60) × 360 = 90°.
Line 3: 2–3 hours: f = 25. Angle = (25 ÷ 60) × 360 = 150°.
Line 4: 3+ hours: f = 15. Angle = (15 ÷ 60) × 100 = 25°.
Line 5: Total: 30 + 90 + 150 + 25 = 295°. (Student says "must be a rounding error.")
(a) Which line contains the mistake?
(b) Explain in one or two sentences why that line is wrong.
(c) Write the corrected working, including the corrected line and the new total.
Stuck? Look at the multiplier. The formula is × 360° (degrees), not × 100 (percent).3. Open-ended challenge — design your own pie chart
This question has many correct answers. Show your work clearly. 4 marks
3.1 Imagine you surveyed 40 Year 7 students about their favourite weekend activity. Choose exactly five categories (e.g. sport, screen time, music, family time, outdoor adventure), and choose realistic frequencies for each that add to 40.
(i) Write your frequency table. Confirm the total is 40.
(ii) For each category, calculate the sector angle to the nearest whole degree and the percentage to 1 d.p.
(iii) Confirm that your five sector angles add to exactly 360° (or 359°/361° — explain how rounding could cause this and how you'd fix it).
(iv) Sketch the pie chart in the box below, with each sector clearly labelled with the category and its angle.
Bonus: identify the smallest sector and state in one sentence whether a pie chart or a bar chart would communicate your data more clearly.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — 4 equal sectors
Each sector = 360 ÷ 4 = 90°. Each = 100% ÷ 4 = 25%.
1.2 — Summer sector (n = 50)
angle = (35 ÷ 50) × 360 = 0.7 × 360 = 252°.
1.3 — Three sectors check
90 + 150 + 120 = 360°. Yes, these three angles fit a valid pie chart because they sum to exactly 360°.
1.4 — Walking sector backwards
f = (angle ÷ 360°) × n = (80 ÷ 360) × 90 = 20 students.
1.5 — Percentage to angle
25% → (25 ÷ 100) × 360 = 90°.
33⅓% → (1/3) × 360 = 120°.
12.5% → (12.5 ÷ 100) × 360 = 45°.
1.6 — Three equal sectors
Remaining for three sectors: 360 − 60 − 90 = 210°. Each equal sector = 210 ÷ 3 = 70°.
2 — Find the mistake
(a) The mistake is on Line 4.
(b) The student multiplied by 100 instead of 360. The pie-chart formula is angle = (f ÷ n) × 360°, not × 100 (× 100 would give a percentage, not a degree value).
(c) Corrected Line 4: 3+ hours: f = 15. Angle = (15 ÷ 60) × 360 = 90°. New total: 30 + 90 + 150 + 90 = 360° ✓. The "rounding error" guess was wrong — it was a formula error.
3 — Design your own pie chart (sample)
(i) Sample frequency table (n = 40 total): Sport 12, Screen time 10, Music 8, Family time 6, Outdoor adventure 4. Check: 12 + 10 + 8 + 6 + 4 = 40 ✓.
(ii) Sport: (12 ÷ 40) × 360 = 108° (30.0%). Screen: (10 ÷ 40) × 360 = 90° (25.0%). Music: (8 ÷ 40) × 360 = 72° (20.0%). Family: (6 ÷ 40) × 360 = 54° (15.0%). Outdoor: (4 ÷ 40) × 360 = 36° (10.0%).
(iii) Check: 108 + 90 + 72 + 54 + 36 = 360° ✓. (Rounding could cause a small mismatch when n doesn't divide 360 evenly; if so, adjust the LAST sector by 1° to make the total exact.)
(iv) Pie chart sketch: largest sector Sport (108°) starting at 12 o'clock, then Screen (90°), Music (72°), Family (54°), Outdoor (36°), each labelled with category and angle.
Bonus: Smallest sector is Outdoor adventure (36°). With 5 reasonably-sized sectors and clear differences, a pie chart works well here. A bar chart would also be fine and might make exact comparisons easier (e.g. seeing that Sport is 2 more than Screen).
Marking: 1 for valid frequency table summing to 40; 1 for correct sector angle calculations; 1 for total checked at 360°; 1 for clearly-labelled sketch. Bonus for any reasonable comment on pie vs bar choice.