Week 10 · Pie charts: reading and drawing with central angles · 3 lessons
2
Drawing a pie chart: central angle = share of the total × 360°
Mathematics Prep 1 Term 1, Unit 3, Lesson 3
GoalCalculate the central angles and draw a pie chart with a compass and a protractor.
New words
central angle · value ÷ total × 360°compass · a tool for drawing a circleprotractor · a tool for measuring and drawing anglesrounding · changing an angle to the nearest degree
Explanation
Why does the angle equal the share times 360°? The whole circle is 360° and stands for the whole total, so a category with a fraction of the total gets the same fraction of 360°. Angle = value ÷ total × 360°. If the data are percents, angle = percent × 3.6°, because 360° ÷ 100 = 3.6°. Steps: find the total, work out every angle, check that the angles add up to 360°, draw a circle with a compass, draw one radius, then measure each angle with the protractor one after another in the same direction, and label each sector. Rounding to whole degrees may make the sum 359° or 361°: then adjust one angle.
ƒFormula
angle = value ÷ total × 360°
From percents: angle = percent × 3.6°.
Worked examples
Club
Pupils
Angle = pupils ÷ 40 × 360°
Art
4
36°
Football
16
144°
Reading
8
72°
Chess
12
108°
Total
40
360°
Clubs of 40 pupils: art 4, football 16, reading 8, chess 12. Angles: 4/40 × 360 = 36°, 16/40 × 360 = 144°, 8/40 × 360 = 72°, 12/40 × 360 = 108°. Check: 36 + 144 + 72 + 108 = 360°. The football sector measures 144°.
Data as percents. Three categories are 25%, 15% and 60%. Angles: 25 × 3.6 = 90°, 15 × 3.6 = 54°, 60 × 3.6 = 216°. Check: 90 + 54 + 216 = 360°. Here is the 144° football angle on a protractor.
Rounding. Seven friends choose a drink: tea 2, juice 2, water 3. One friend is 360° ÷ 7 ≈ 51.43°. Tea: 2 × 51.43 ≈ 103°. Juice: 103°. Water: 3 × 51.43 ≈ 154°. Check: 103 + 103 + 154 = 360°.
Class activity
Draw it yourself. With a grown-up, ask 12 people their favourite fruit among three fruits. Work out the angles (each person is 30°). Draw the pie chart with a compass and protractor and label it.
Practice
1
Find the angle for 15 out of 60.
15/60 × 360° = 90°.
2
Find the angles for 20%, 30% and 50%.
72°, 108° and 180°. Check: 72 + 108 + 180 = 360.
3
Thirty pupils have pets: cats 10, dogs 8, birds 12. Find the three angles.
