Primary 6 Maths | Pie Charts: Reading Sectors, Percentages and 3.6 Degrees

2026-11-08

Tutor lesson-prep guides · Primary maths

Pupils read a pie chart by comparing which slice looks bigger, then stop dead when asked how many people that slice means. Angle, percentage and number of pupils are three different things stacked on one drawing. This lesson fixes the order: percentage first, angle second, people last.

Objectives — Pupils can: (1) convert between percentages and sector angles using a full circle of 360 degrees and 1% = 3.6 degrees; (2) work back from a sector angle and a total to a number of pupils; (3) explain why the same looking sector in two charts does not mean the same number of people.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Meaning of percentage	25% is what fraction	One quarter
Using a protractor	What the protractor centre must sit on	The vertex, with the 0 line on one arm
Finding a part	25% of 40 pupils	10 pupils

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-5 min	Opening question	Show two pie charts and ask which chart shows more bus passengers, watching whether pupils compare slices	State what they based the answer on
5-15 min	360 degrees and 100%	A full circle is 360 degrees and 100 parts, so 1% is 3.6 degrees	Work out 3.6 themselves, then 25%
15-25 min	Percentage to angle	Convert 25%, 10%, 35%, 30% one by one with the multiplication shown	Convert 35% (126 degrees) and check with a protractor
25-34 min	Angle to people	72 degrees divided by 360 gives 20%, then 20% of 50 gives 10 pupils	Run the same step in reverse
34-41 min	Two-chart trap	Different totals: the same slice size is not the same number of people	Compute once with 40 pupils and once with 200
41-45 min	Exit check	Collect two answers and mark at once, naming the error type	Work independently

03 Teaching script (read it out)

Scene 1: Act 1: A full circle is 360 degrees and 100%

Draw a circle and write two numbers inside it: 360 and 100%. Say: “The same circle is 360 degrees if you measure angles, and 100 parts if you measure shares.” So 1% is 360 / 100 = 3.6 degrees. Pupils must compute that 3.6 themselves; do not write it on the board for them.
Then show three anchors: 25% is 3.6 x 25 = 90 degrees, a quarter of the circle; 10% is 36 degrees; 50% is 180 degrees. Ask pupils to shade the 90 degree sector, then check it with a protractor so that “one quarter” and “90 degrees” meet in their hands.

Say this: “Do not memorise that 90 degrees is 25%. Keep 360 and 100, multiply once, and you will never get it backwards.”

Scene 2: Act 2: Three conversions, in a fixed order

Write the steps as a staircase: (1) percentage to angle, multiply by 3.6; (2) angle to percentage, divide by 360 then multiply by 100; (3) percentage to people, multiply the percentage by the total. Work one full example: 40 pupils, 35% take the bus. Angle 35 x 3.6 = 126 degrees; number 40 x 35% = 14 pupils. Always give both, because the question may ask either.
Then run it backwards: a sector of 72 degrees with a total of 50 pupils. 72 / 360 = 0.2, so 20%, and 50 x 20% = 10 pupils. Require pupils to name which conversion each line is doing, so an error points straight at one layer.

Pupil task: work the 108 degree sector with a total of 200 pupils: 30% and 60 pupils.

Scene 3: Act 3: A pie chart shows shares, not amounts

Show two charts: chart A has 40 pupils, chart B has 200, and both show 25% walking. Ask which chart has more walkers. Looking at the drawing, pupils answer “the same”, because the slices are identical. The answers are 10 pupils and 50 pupils.
So the rule is: inside one chart, slice sizes can be compared; between two charts with different totals, slice sizes cannot be compared as numbers of people. To get people you must find the total and multiply. Write that rule in the notes and ask “what is the total?” before every statistics question.

Say this: “A slice tells you the share, not the amount. A share has to be multiplied by the total before it becomes people.”

Scene 4: Act 4: The three-total check

Give a question: sectors of 144, 108 and 108 degrees with a total of 200 pupils. First check the angles: 144 + 108 + 108 = 360, so the reading is consistent. Then convert each: 144 / 360 = 40% (80 pupils), 108 / 360 = 30% (60 pupils), and 60 pupils again. The percentages must total 100% and the pupils must total 200. Those two sums are the best self-check available.
If the angles do not total 360, stop and find the misread sector rather than pushing on. It is usually the outer protractor scale or a forgotten “other” slice.

Pupil task: finish the three sectors, then say all three totals aloud: 360 degrees, 100%, 200 pupils.

04 Question types and worked steps

Type	Example	Steps	Answer
Percentage to angle	35%	Multiply by 3.6	126 degrees
Angle to percentage	72 degrees with total 50	72 / 360 x 100 = 20%, then x 50	20%, 10 pupils
Percentage to people	25% of 40 pupils	Total x percentage	10 pupils
Three-sector check	144, 108, 108 degrees, total 200	Angles 360, percentages 100, pupils 200	40/30/30% = 80/60/60 pupils

Sanity check (teach this): After every question run three sums: the angles must total 360 degrees, the percentages must total 100%, and the parts must total the whole. If any sum is off, the data was misread or a slice was missed, so do not continue calculating. Example: 144 + 108 + 108 = 360, then 40% + 30% + 30% = 100%, then 80 + 60 + 60 = 200.

05 Independent practice (3 questions)

Question	Answer	What to watch
40 pupils: 25% walk, 35% bus, 30% train, 10% other. How many take the bus, and what is the sector angle?	14 pupils; 126 degrees	Do they answer both parts
A sector of 72 degrees out of 50 pupils: what percentage, and how many pupils?	20%; 10 pupils	Did they multiply by 100 after dividing
Sectors of 144, 108 and 108 degrees with 200 pupils: give percentages and numbers.	40% / 80, 30% / 60, 30% / 60	Did they run the three sums

06 Common mistakes and what to say

Mistake	Student writes	Say this
Thinking 100% is 100 degrees	35% written as 35 degrees	A full circle is 360 degrees, not 100. Multiply 35 by 3.6 to get 126
Reading an angle as people	126 degrees answered as 126 pupils	An angle is a share. Multiply by the total: 35% of 40 is 14 pupils
Comparing slices across charts	Equal slices answered as equal numbers	The totals differ: 25% of 40 is 10, but 25% of 200 is 50
Using the wrong protractor scale	90 degrees read as 270	Centre on the vertex, 0 on one arm, and read the same ring you started on

07 Homework (paper, section and question numbers)

Independent practice in this chapter (questions 1-3 above) — Q1 give both the number and the angle; Q2 work back from the angle; Q3 include the three sums
Primary maths test papers (statistics items) — Do three statistics questions, writing the total, then the percentage, then the number
Primary maths chapter index (same level) — Revise the P6 averages and line graphs chapter and compare what each chart can answer

08 Exit check (last 5 minutes)

Question	Answer	Decision
How many degrees and how many percent in a full circle?	360 degrees and 100%	Cannot say: back to Act 1
How many degrees is 1%?	3.6 degrees	Answering 1 degree means 360 and 100 are not linked
Sector angle for 35%?	126 degrees	Answering 35 degrees: back to Act 2
Two charts with different totals: do equal slices mean equal numbers?	No, multiply by each total	Saying yes: reteach Act 3

09 Tutor FAQ

Why memorise 3.6?

Because 360 / 100 = 3.6, which is the bridge between degrees and percentages. Pupils who know where it comes from will not treat 100% as 100 degrees. If they forget, ask them to rebuild it from 360 and 100.

When should a pie chart be used instead of a bar chart?

A pie chart answers “what share of the whole”; a bar chart answers “which is more, and by how much”. If two groups have different totals, a pie chart misleads and a bar chart is far clearer.

Pupils keep misreading the protractor. What helps?

Fix one sentence: “Centre on the vertex, 0 on one arm, read the same ring you started on.” Then ask whether they read the inner or outer ring; pupils who can say it usually read it correctly.

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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.