Mathematics • Year 7 • Unit 4 • Lesson 5

Pie Charts — Real World

Apply the formula angle = (f ÷ n) × 360° to real settings: a household budget, an election result, a nutritional label, a sports club roster, and reading a pie chart backwards (angle → frequency).

Apply · Real-World Maths

1. Word problems

Show working — answers without working only earn half marks.

1.1 — Household budget. A family spends $2400 per month broken down as: Rent $1200, Food $600, Transport $300, Entertainment $180, Savings $120.

(a) Calculate the sector angle for each category.
(b) Check that the four angles add to 360°. 3 marks

Stuck? Total = $2400 (use as n). Rent is half the budget, so the rent angle is half of 360° = 180°.

1.2 — Class election. 45 students voted in a class captain election. Maya 18 votes, Liam 15, Aisha 9, Jay 3.

(a) Calculate the sector angle for each candidate.
(b) Without measuring, which candidate's sector should be the largest, and why?
(c) Express each candidate's votes as a percentage of the total. 4 marks

Stuck on (b)? The candidate with the most votes has the largest sector.

1.3 — Nutritional label. A 200 g muesli bar contains 100 g carbs, 50 g protein, 30 g fat and 20 g other.

(a) Calculate the sector angle for each macronutrient.
(b) Confirm the four angles sum to 360°.
(c) What percentage of the bar is fat? 3 marks

Stuck on (c)? Percentage = (mass ÷ total mass) × 100.

1.4 — Sports club roster. A school has 120 students who play a sport. Their breakdown: Soccer 50, Netball 30, AFL 24, Cricket 16.

(a) Calculate each sector angle.
(b) The school wants to use a pie chart in the newsletter. Suggest one reason a pie chart suits this data, AND one reason a bar chart might suit it better. 4 marks

Stuck on (b)? Pie charts are good for showing "share of the whole"; bar charts make exact comparisons of frequencies easier.

1.5 — Reading a pie chart backwards. A pie chart shows how 80 students travel to school. The given sector angles are: Walk 144°, Bus 108°, Car 72°, Bike 36°.

(a) Confirm that the four angles sum to 360°.
(b) Calculate the NUMBER of students in each category using f = (angle ÷ 360°) × n. 3 marks

Stuck? Rearrange the lesson formula: f = (angle ÷ 360°) × n.

2. Explain your thinking

Communication matters. Use full sentences. 4 marks

2.1 A Year 7 student is given a frequency table with 8 different categories and is told to draw a pie chart. In your own words, explain (i) why drawing a pie chart with 8 sectors is usually a BAD idea for readability, (ii) what other graph type would work better for many categories and why, and (iii) one situation when a pie chart with that many sectors might still be OK (e.g. if a few categories dominate and most are tiny).

Stuck? Revisit lesson § "Spot the Trap" — pie charts struggle with more than 6–7 thin slices.

How did this worksheet feel?

Got it Partly Lost

What I'll revisit before next class:

Answers — Do not peek before attempting

1.1 — Household budget

(a) Rent: (1200 ÷ 2400) × 360 = 180°. Food: (600 ÷ 2400) × 360 = 90°. Transport: (300 ÷ 2400) × 360 = 45°. Entertainment: (180 ÷ 2400) × 360 = 27°. Savings: (120 ÷ 2400) × 360 = 18°.
(b) Check: 180 + 90 + 45 + 27 + 18 = 360° ✓.

1.2 — Class election (n = 45)

(a) Maya: (18 ÷ 45) × 360 = 144°. Liam: (15 ÷ 45) × 360 = 120°. Aisha: (9 ÷ 45) × 360 = 72°. Jay: (3 ÷ 45) × 360 = 24°.
Check: 144 + 120 + 72 + 24 = 360° ✓.
(b) Maya — she has the most votes (18), so her angle is the largest.
(c) Maya: 18/45 = 40.0%. Liam: 15/45 ≈ 33.3%. Aisha: 9/45 = 20.0%. Jay: 3/45 ≈ 6.7%. Check: 40 + 33.3 + 20 + 6.7 = 100% ✓.

1.3 — Nutritional label (n = 200 g)

(a) Carbs: (100 ÷ 200) × 360 = 180°. Protein: (50 ÷ 200) × 360 = 90°. Fat: (30 ÷ 200) × 360 = 54°. Other: (20 ÷ 200) × 360 = 36°.
(b) 180 + 90 + 54 + 36 = 360° ✓.
(c) Fat = (30 ÷ 200) × 100 = 15%.

1.4 — Sports club (n = 120)

(a) Soccer: (50 ÷ 120) × 360 = 150°. Netball: (30 ÷ 120) × 360 = 90°. AFL: (24 ÷ 120) × 360 = 72°. Cricket: (16 ÷ 120) × 360 = 48°.
Check: 150 + 90 + 72 + 48 = 360° ✓.
(b) Pie chart suits because it instantly shows that Soccer is nearly half (150° out of 360°) — the "share of the whole" message is the headline.
Bar chart might suit better when readers want to compare exact numbers (e.g. is the difference between Netball and AFL really only 6 students?). Bar heights make small differences easier to read than thin pie slices.

1.5 — Reading a pie chart backwards (n = 80)

(a) 144 + 108 + 72 + 36 = 360° ✓.
(b) Walk: (144 ÷ 360) × 80 = 0.4 × 80 = 32 students. Bus: (108 ÷ 360) × 80 = 0.3 × 80 = 24 students. Car: (72 ÷ 360) × 80 = 0.2 × 80 = 16 students. Bike: (36 ÷ 360) × 80 = 0.1 × 80 = 8 students.
Check: 32 + 24 + 16 + 8 = 80 ✓.

2.1 — Explain your thinking (sample response)

A pie chart with 8 sectors is usually a bad idea because each sector ends up thin and hard to compare visually — the human eye is much better at comparing the heights of bars than the angles of narrow slices. A bar chart (or column graph) works better for many categories because each bar has a clear height that can be read against a numerical scale, and the bars can be sorted from largest to smallest to make the most-popular category obvious. A pie chart with 8 sectors might still be acceptable when one or two categories dominate the data and the rest are very small — for example, if 70% of the data is in one category and the remaining 7 are tiny, the pie chart's headline message ("most of it is X") still comes through clearly even with many slices. In that situation, the small slices can also be grouped into a single "Other" sector to keep the chart readable.

Marking: 1 for explaining the readability problem with many slices; 1 for naming bar chart and giving a clear reason; 1 for a sensible exception or fix (grouping into "Other"); 1 for clear sentences.