Mathematics • Year 8 • Unit 4 • Lesson 5
Bar Charts and Pie Charts
Build fluency calculating pie-chart sector angles, reading bar charts, and applying the rules of each display. One worked example, one guided example with blanks, then eight independent problems.
1. I do — fully worked example
Read every line. Each step has a short reason so you can see why we do it, not just what we do.
Problem. 120 students were surveyed about how they get to school: Walk 30, Bus 48, Car 24, Cycle 12, Train 6. Calculate the pie-chart sector angle for each category and verify the sum is 360°.
Step 1 — Confirm the total n.
n = 30 + 48 + 24 + 12 + 6 = 120 ✓
Reason: always verify the total before calculating angles.
Step 2 — Apply Angle = (f ÷ n) × 360° to each category.
Walk: (30 ÷ 120) × 360 = 90° Bus: (48 ÷ 120) × 360 = 144° Car: (24 ÷ 120) × 360 = 72° Cycle: (12 ÷ 120) × 360 = 36° Train: (6 ÷ 120) × 360 = 18°
Reason: each angle is proportional to that category's share of the total.
Step 3 — Check the angles sum to 360°.
90 + 144 + 72 + 36 + 18 = 360° ✓
Answer: Walk 90°, Bus 144°, Car 72°, Cycle 36°, Train 18°.
2. We do — fill in the missing steps
Same shape as Section 1, but with the working faded. Fill in each blank. 4 marks
Problem. 40 students chose a favourite subject: Maths 10, English 8, Science 12, Art 6, PE 4. Find each pie-chart angle and verify the sum is 360°.
Step 1 — Confirm the total n:
n = 10 + 8 + 12 + 6 + 4 = ______
Step 2 — Apply Angle = (f ÷ n) × 360° to each category:
Maths: (10 ÷ ____) × 360 = ____° English: ____° Science: ____° Art: ____° PE: ____°
Step 3 — Check the angles sum to 360°:
____ + ____ + ____ + ____ + ____ = ____°
3. You do — independent practice
Show your working in the space under each problem. The first four are foundation. The middle two are standard. The last two are extension.
Foundation — quick recall
3.1 In a survey of 40 students, 10 prefer Drama. What is the pie-chart angle for Drama? 1 mark
3.2 A pie-chart sector is 72°. The total sample was 150. How many people does that sector represent? 1 mark
3.3 Name THREE features that must appear on a correctly drawn bar chart. 1 mark
3.4 A pie chart of 100 students has Walk = 25. What is the angle for Walk? 1 mark
Standard — two-step problems
3.5 60 students chose: Football 24, Tennis 18, Hockey 12, Other 6. Calculate all four sector angles and verify the sum is 360°. 2 marks
3.6 A bar chart shows 4 bars: Apples 12, Bananas 8, Grapes 15, Oranges 5. (a) Find the total frequency. (b) Find the relative frequency of Grapes (as a decimal and a percentage). (c) State the modal category. 2 marks
Extension — choose and reason
3.7 A researcher wants to show what share of national energy comes from solar, coal, gas, and hydro. Should they use a bar chart or pie chart? Justify in one sentence. 2 marks
3.8 A bar chart shows Category A with bar height 5 and Category B with bar height 4, but the y-axis starts at 3. (a) Why is this a misleading chart? (b) What should be done instead? 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (favourite subjects, n = 40)
Step 1: n = 40.
Step 2: Maths = (10÷40) × 360 = 90°; English = (8÷40) × 360 = 72°; Science = (12÷40) × 360 = 108°; Art = (6÷40) × 360 = 54°; PE = (4÷40) × 360 = 36°.
Step 3: 90 + 72 + 108 + 54 + 36 = 360° ✓.
3.1 — Drama angle
(10 ÷ 40) × 360 = (1/4) × 360 = 90°.
3.2 — Reverse pie chart
Proportion = 72 ÷ 360 = 0.2. Count = 0.2 × 150 = 30 people.
3.3 — Bar chart features
Any three from: descriptive title; labelled axes with units; even scale starting at 0; equal bar widths; gaps between bars; bars drawn to correct heights.
3.4 — Walk angle
(25 ÷ 100) × 360 = 90°.
3.5 — Sports pie chart
Football (24÷60) × 360 = 144°; Tennis (18÷60) × 360 = 108°; Hockey (12÷60) × 360 = 72°; Other (6÷60) × 360 = 36°. Check: 144 + 108 + 72 + 36 = 360° ✓.
3.6 — Fruit bar chart
(a) Total = 12 + 8 + 15 + 5 = 40.
(b) Grapes rel freq = 15 ÷ 40 = 0.375 = 37.5%.
(c) Modal category = Grapes (highest f = 15).
3.7 — Choose the chart
Pie chart — it shows parts of a whole (the four sources together make 100% of supply), and with only 4 categories it stays readable.
3.8 — Y-axis problem
(a) Starting the y-axis at 3 instead of 0 makes Category A's bar (height 5−3 = 2 units shown) look TWICE as tall as Category B's (height 4−3 = 1 unit), when really A is only 25% higher than B (5 vs 4).
(b) Redraw with the y-axis starting at 0 so the bar heights are proportional to the actual frequencies.