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.