What does it mean?
A pie chart represents one complete total as a circle. Each sector shows a fraction of that total. A half-circle means half the observations, not necessarily a count of 180 people. The angle is measured in degrees; the number of observations comes from the named total.
A pie chart represents one complete total as a circle. Each sector shows a fraction of that total. A half-circle means half the observations, not necessarily a count of 180 people. The angle is measured in degrees; the number of observations comes from the named total.
Learning goal: Graphs and charts. The grade is a suggested starting point; school sequences vary. Use the first worked example to check readiness, and Grade 6 data handling: tally marks and bar graph questions if an earlier idea needs revisiting.
See the idea
Read each diagram with its labels, then follow the worked examples. Practice questions include their own measurements and information.
Enlarge diagram to read the labels
Swipe across the enlarged diagram to read every label.
Choose a method and explain why it works
Read the chart title, labels and total first. To turn a share into a count, multiply the share by the total. If a chart of 24 pupils assigns one quarter to tennis, 24 ÷ 4 = 6 pupils chose tennis. To find a missing share, subtract all named shares from one whole. The sectors must account for the same population.
Notation: title; labels; scale; values
Key rule and when to use it
Sector share = sector angle ÷ 360°. Category count = share × chart total. All sectors together represent one complete total.
Worked examples, step by step
Example 1: A pie chart of 24 pupils shows one quarter choosing tennis. How many choose tennis?
- The whole represents 24 pupils.
- One quarter of 24 is 24 ÷ 4 = 6.
Answer: 6 pupils
Example 2: A pie chart shows one half choosing football, one quarter tennis and the rest swimming. What fraction choose swimming?
- Named shares total 1/2 + 1/4 = 3/4.
- The remaining share is 1 − 3/4 = 1/4.
Answer: 1/4
Example 3: A chart of 40 pupils shows 1/2 choosing football, 1/4 swimming and the rest cycling. How many choose cycling?
- Football and swimming use 1/2 + 1/4 = 3/4 of the circle.
- Cycling is the remaining 1/4.
- 1/4 of 40 = 10 pupils. Check 20 + 10 + 10 = 40.
Common mistakes and important boundaries
Two equally sized sectors on charts with different totals can represent different counts. Half of 20 is 10, while half of 40 is 20. If angles are given, a sector’s share is its angle divided by 360°. Do not confuse a pie chart’s whole-circle meaning with a bar graph’s vertical scale.
A point to explain
The scale value, not the number of grid spaces, gives the data value.
Compare an uncertain attempt with the closest worked example. Look at the meaning of each operation, unit and label before repeating the arithmetic.
Reading Pie Charts: Shares and Totals — practice
Work on paper first. Open each answer afterwards and compare the reasoning. Print the questions with or without the separate answer key; no account is required.
Name: ____________________ Date: __________
A chart of 20 pupils has a half-circle sector for football. How many pupils is that?
Answer and a way to check
10
1/2 × 20 = 10.
A chart of 32 pupils has one quarter choosing tennis. Find the count.
Answer and a way to check
8
32 ÷ 4 = 8.
A sector is 90°. What fraction of a complete circle is it?
Answer and a way to check
1/4
90/360 = 1/4.
Shares are 1/2, 1/3 and a remaining category. Find the remaining fraction.
Answer and a way to check
1/6
1/2 + 1/3 = 5/6, leaving 1/6.
A chart represents 40 pupils. Fifteen choose cycling. What fraction of the chart is cycling?
Answer and a way to check
3/8
15/40 simplifies by 5 to 3/8.
Half of chart A represents 10 pupils. Half of chart B represents 20. What are the two total counts?
Answer and a way to check
20 and 40 pupils
Each whole is twice its half.
The largest category is 40%. Is that a majority?
Answer and a way to check
No.
A majority is more than 50%; largest category and majority are different.
A 120° sector represents 12 pupils. Find the whole chart’s total.
Answer and a way to check
36 pupils
120/360 = 1/3, so the whole is 3 × 12 = 36.
Reading Pie Charts: Shares and Totals — answer key
10 1/2 × 20 = 10.
8 32 ÷ 4 = 8.
1/4 90/360 = 1/4.
1/6 1/2 + 1/3 = 5/6, leaving 1/6.
3/8 15/40 simplifies by 5 to 3/8.
20 and 40 pupils Each whole is twice its half.
No. A majority is more than 50%; largest category and majority are different.
36 pupils 120/360 = 1/3, so the whole is 3 × 12 = 36.
Questions students and parents ask
Can a pie chart include overlapping categories?
Its sectors must divide one total without double-counting. If a pupil can choose both football and tennis, first define non-overlapping categories or use another chart suitable for multiple responses.
Does the biggest sector show the majority?
It shows the largest category, but a majority means more than half of the whole. A largest sector of 40% is not a majority.
Is this a complete set of textbook exercise solutions?
No. This guide adapts BananaLearn’s own teaching examples and practice. It is not official NCERT material or a promise of the exact chapter sequence in a particular board, country or textbook edition.
What if the examples are still difficult?
Revisit Grade 6 data handling: tally marks and bar graph questions. Try the first example with its model, then attempt one fresh question independently. A correct copied answer is not evidence that the method can be used without support.
Help at home
Ask “What is the whole circle counting?” before calculating a sector. Compare two circles with different totals to test whether that meaning is secure.
Keep one example of the learner’s own working. A repeated difficulty across fresh questions can guide a discussion with their teacher; one short practice sheet does not establish a diagnosis or a full mastery profile.
Connect this idea to the next skill
About this guide
Based on BananaLearn’s Grade 5 course lesson “Graphs and charts”. The explanations have been adapted for independent reading; course diagrams are reused where they fit the idea, and missing classroom givens are made explicit in questions.
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