Year 6 Maths reasoning (SATs): Pie charts
Part of the Year 6 Maths reasoning (SATs) statistics and data chapter. Chapter overview · whole chapter on one page
Pie charts
Rule
A pie chart is a circle split into sectors. The whole circle is 360 degrees.
Angle of a sector = (number in the group / total) x 360. Number in the group = (angle / 360) x total.
Key ideas
- The whole pie is 360 degrees.
- Sector angle = share of the total x 360.
- The sector angles add up to 360 degrees.
Method. Find the fraction of the total, then multiply by 360.
- Share of the total. Bus is 18 out of 72.18 / 72
- Work out the angle. A whole pie is 360 degrees, so multiply the share by 360.18 / 72 x 360 = 90
- Write the answer. 90
Check. 90 / 360 = 18 / 72. ✓
Watch out. Make sure all the sector angles add up to 360.
Method. Find the fraction of the whole pie, then multiply by the total.
- Share of the pie. The sector is 120 of the 360 degrees.120 / 360
- Multiply by the total. Multiply the share by the total of 60.120 / 360 x 60 = 20
- Write the answer. 20
Check. 20 / 60 = 120 / 360. ✓
Method. Find the fraction of the whole pie, then multiply by the total.
- Share of the pie. The sector is 135 of the 360 degrees.135 / 360
- Multiply by the total. Multiply the share by the total of 40.135 / 360 x 40 = 15
- Write the answer. 15
Check. 15 / 40 = 135 / 360. ✓
Watch out
Watch out. A sector of 180 degrees is half the pie, not a quarter. A quarter is 90 degrees.
Exam tip
Practice guide. Work out the fraction first, then multiply by 360 or by the total.
Exercise 8B Practice: pie charts
Non-calculatorMethod. Find the fraction of the total, then multiply by 360.
- Share of the total. Football is 15 out of 60.15 / 60
- Work out the angle. A whole pie is 360 degrees, so multiply the share by 360.15 / 60 x 360 = 90
- Write the answer. 90
Check. 90 / 360 = 15 / 60. ✓
Watch out. Make sure all the sector angles add up to 360.
Method. Find the fraction of the total, then multiply by 360.
- Share of the total. Swimming is 10 out of 60.10 / 60
- Work out the angle. A whole pie is 360 degrees, so multiply the share by 360.10 / 60 x 360 = 60
- Write the answer. 60
Check. 60 / 360 = 10 / 60. ✓
Watch out. Make sure all the sector angles add up to 360.
Method. Find the fraction of the total, then multiply by 360.
- Share of the total. Art is 6 out of 36.6 / 36
- Work out the angle. A whole pie is 360 degrees, so multiply the share by 360.6 / 36 x 360 = 60
- Write the answer. 60
Check. 60 / 360 = 6 / 36. ✓
Watch out. Make sure all the sector angles add up to 360.
Method. Find the fraction of the whole pie, then multiply by the total.
- Share of the pie. The sector is 72 of the 360 degrees.72 / 360
- Multiply by the total. Multiply the share by the total of 40.72 / 360 x 40 = 8
- Write the answer. 8
Check. 8 / 40 = 72 / 360. ✓
Method. Find the fraction of the whole pie, then multiply by the total.
- Share of the pie. The sector is 180 of the 360 degrees.180 / 360
- Multiply by the total. Multiply the share by the total of 50.180 / 360 x 50 = 25
- Write the answer. 25
Check. 25 / 50 = 180 / 360. ✓
Method. Find the fraction of the whole pie, then multiply by the total.
- Share of the pie. The sector is 45 of the 360 degrees.45 / 360
- Multiply by the total. Multiply the share by the total of 80.45 / 360 x 80 = 10
- Write the answer. 10
Check. 10 / 80 = 45 / 360. ✓
Method. Find the angle left for Gardening, then work out the number of pupils.
- Angle left. 360 - 120 - 90 - 60 = 90 degrees.90
- Pupils. 90 / 360 x 72 = 18 pupils.18
- Write the answer. 18
Check. 120 + 90 + 60 + 90 = 360, and 18 is a quarter of 72. ✓
Method. Test each choice against the question.
- Read what the question asks. Decide what the answer must do or show.
- Test the choice. 180 is half of 360, so it shows half of the pupils.a half fits
- Reject the other choices. A quarter would be 90 degrees and a third would be 120 degrees.a quarter and a third do not fit
- Write the answer. a half
Check. a half is the one that fits. ✓
Method. Test each option.
- Check each option. Test each one against the rule or the calculation.
- Tick the true ones. The whole pie is 360 degrees, and each sector shows its share of the total.The sector angles add up to 360 degrees, Each sector angle is a fraction of the total
- Leave the others unticked. These do not match.A bigger sector always means fewer people, Each sector can be bigger than 360 degrees are not ticked
- Write the answer. The sector angles add up to 360 degrees, Each sector angle is a fraction of the total
Check. Each ticked option is true. ✓
Watch out. A bigger sector means more people, not fewer.
Method. Compare the angle with the whole pie.
- Share of the whole. 90 / 360 = 1/4.1/4
- Conclude. So the sector shows a quarter of the pupils.a quarter
- Write the answer. Because 90 is a quarter of 360, so the sector is a quarter of the whole pie.
Check. 90 / 360 = 1/4. ✓
Method. Find the fraction of the total, then multiply by 360.
- Share of the total. Music is 20 out of 80.20 / 80
- Work out the angle. A whole pie is 360 degrees, so multiply the share by 360.20 / 80 x 360 = 90
- Write the answer. 90
Check. 90 / 360 = 20 / 80. ✓
Watch out. Make sure all the sector angles add up to 360.
Method. Find the fraction of the whole pie, then multiply by the total.
- Share of the pie. The sector is 72 of the 360 degrees.72 / 360
- Multiply by the total. Multiply the share by the total of 90.72 / 360 x 90 = 18
- Write the answer. 18
Check. 18 / 90 = 72 / 360. ✓