lesson
The whole circle represents the total
1 · Learn
A pie chart represents a whole using sectors. Sector angles correspond to proportions: a half is 180°, a quarter 90° and a tenth 36°. State the total before turning a proportion into a count.
Two charts with equal-looking sectors may represent different numbers if their totals differ. A sector label or reliable angle is needed; guessing from an imprecise drawing can mislead.
Here is a complete invented dataset for drawing: A has 10 votes, B has 20 and C has 10, a total of 40. Each vote represents 360 divided by 40 = 9 degrees. Draw sectors of 90, 180 and 90 degrees. Label all three sectors and the total. Their angles add to 360 degrees and their counts to 40.
2 · Worked example
In a group of 40, a 90° sector represents one quarter, so it represents 10 people. The same sector in a group of 80 represents 20 people.
3 · Your turn
A pie chart represents 60 votes. How many votes does a 120° sector represent?
Check your answer
120/360 = 1/3 of the whole, so it represents 20 votes.
4 · Apply your learning
Draw sectors for a supplied simple dataset using a protractor, checking that counts and angles both add to their totals.
Adult guidance and safety
Ask the learner to explain the method and check it using a different representation. Supply place-value grids, fraction strips, accurate diagrams and measuring tools where needed. These examples need varied practice; a short correct answer alone does not establish fluency.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
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