Year 6: Drawing a pie chart: the angles
Part of the Year 6 pie charts, line graphs and the mean chapter. Chapter overview · whole chapter on one page
Drawing a pie chart: the angles
To draw a pie chart from a table, you first need the angle of each sector. The table gives the number in each group, so the chart is in the same proportions as the table.
Follow these steps. First, find the total of all the numbers. Second, write each group as a fraction of the total. Third, multiply each fraction by 360 degrees. The angles of all the sectors must add up to 360. Then draw the sectors with a protractor, label each one and give the chart a title.
Key ideas
- Angle of a sector = fraction of the total × 360 degrees.
- The angles of all the sectors add up to 360 degrees.
- Check that the total of the sector numbers is the total in the table.
- Label every sector, so the reader knows what each one shows.
| Drink | Number |
|---|---|
| Water | 6 |
| Milk | 4 |
| Juice | 9 |
| Smoothie | 5 |
| Total | 24 |
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Find the fraction of the whole pie, then take that fraction of 360 degrees.
- Write the whole pie. A whole pie chart is a whole circle, and a whole circle is 360 degrees.whole pie = 360°
- Write the sector as a fraction of the total. Water is 6 out of 24, so divide 6 by 24.6 ÷ 24 = 1/4
- Multiply the fraction by 360 degrees. The fraction tells us the share of the whole circle.1/4 × 360 = 90
- Write the answer. The sector is this many degrees.90
Check. All the sector angles in a pie chart add up to 360 degrees. ✓
Watch out. Use 360 degrees for the whole pie, not 100. The 100 is only for percentages.
| Type of book | Number |
|---|---|
| Fiction | 15 |
| Non-fiction | 9 |
| Poetry | 6 |
| Total | 30 |
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Find the fraction of the whole pie, then take that fraction of 360 degrees.
- Write the whole pie. A whole pie chart is a whole circle, and a whole circle is 360 degrees.whole pie = 360°
- Write the sector as a fraction of the total. Fiction is 15 out of 30, so divide 15 by 30.15 ÷ 30 = 1/2
- Multiply the fraction by 360 degrees. The fraction tells us the share of the whole circle.1/2 × 360 = 180
- Write the answer. The sector is this many degrees.180
Check. All the sector angles in a pie chart add up to 360 degrees. ✓
Watch out. Use 360 degrees for the whole pie, not 100. The 100 is only for percentages.
| Drink | Number |
|---|---|
| Water | 6 |
| Milk | 4 |
| Juice | 9 |
| Smoothie | 5 |
| Total | 24 |
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Add the angles of all the sectors. They must make a whole pie.
- Work out the angle of each sector. Each angle is its share of the total, times 360 degrees.Water 90°; Milk 60°; Juice 135°; Smoothie 75°
- Add the angles. The angles of a whole pie add up to 360 degrees.90 + 60 + 135 + 75 = 360
- Write the answer. The angles make a whole turn, so the chart is correct.360
Check. 360 degrees is a whole turn. ✓
Watch out. If the total is not 360, one of the angles is wrong. Find it before you draw the chart.
Watch out
Common mistake: dividing the number by 360 instead of multiplying the fraction by 360. Write the fraction first, then multiply it by 360. For a sector of 6 out of 24, the fraction is 1/4, so the angle is 90 degrees, not 6 ÷ 360.
Exercise 12C Practice: working out the angles for a pie chart
Non-calculator| Drink | Number |
|---|---|
| Water | 6 |
| Milk | 4 |
| Juice | 9 |
| Smoothie | 5 |
| Total | 24 |
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Find the fraction of the whole pie, then take that fraction of 360 degrees.
- Write the whole pie. A whole pie chart is a whole circle, and a whole circle is 360 degrees.whole pie = 360°
- Write the sector as a fraction of the total. Water is 6 out of 24, so divide 6 by 24.6 ÷ 24 = 1/4
- Multiply the fraction by 360 degrees. The fraction tells us the share of the whole circle.1/4 × 360 = 90
- Write the answer. The sector is this many degrees.90
Check. All the sector angles in a pie chart add up to 360 degrees. ✓
Watch out. Use 360 degrees for the whole pie, not 100. The 100 is only for percentages.
| Drink | Number |
|---|---|
| Water | 6 |
| Milk | 4 |
| Juice | 9 |
| Smoothie | 5 |
| Total | 24 |
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Find the fraction of the whole pie, then take that fraction of 360 degrees.
- Write the whole pie. A whole pie chart is a whole circle, and a whole circle is 360 degrees.whole pie = 360°
- Write the sector as a fraction of the total. Juice is 9 out of 24, so divide 9 by 24.9 ÷ 24 = 3/8
- Multiply the fraction by 360 degrees. The fraction tells us the share of the whole circle.3/8 × 360 = 135
- Write the answer. The sector is this many degrees.135
Check. All the sector angles in a pie chart add up to 360 degrees. ✓
Watch out. Use 360 degrees for the whole pie, not 100. The 100 is only for percentages.
| Drink | Number |
|---|---|
| Water | 6 |
| Milk | 4 |
| Juice | 9 |
| Smoothie | 5 |
| Total | 24 |
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Find the fraction of the whole pie, then take that fraction of 360 degrees.
- Write the whole pie. A whole pie chart is a whole circle, and a whole circle is 360 degrees.whole pie = 360°
- Write the sector as a fraction of the total. Smoothie is 5 out of 24, so divide 5 by 24.5 ÷ 24 = 5/24
- Multiply the fraction by 360 degrees. The fraction tells us the share of the whole circle.5/24 × 360 = 75
- Write the answer. The sector is this many degrees.75
Check. All the sector angles in a pie chart add up to 360 degrees. ✓
Watch out. Use 360 degrees for the whole pie, not 100. The 100 is only for percentages.
| Type of book | Number |
|---|---|
| Fiction | 15 |
| Non-fiction | 9 |
| Poetry | 6 |
| Total | 30 |
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Find the fraction of the whole pie, then take that fraction of 360 degrees.
- Write the whole pie. A whole pie chart is a whole circle, and a whole circle is 360 degrees.whole pie = 360°
- Write the sector as a fraction of the total. Fiction is 15 out of 30, so divide 15 by 30.15 ÷ 30 = 1/2
- Multiply the fraction by 360 degrees. The fraction tells us the share of the whole circle.1/2 × 360 = 180
- Write the answer. The sector is this many degrees.180
Check. All the sector angles in a pie chart add up to 360 degrees. ✓
Watch out. Use 360 degrees for the whole pie, not 100. The 100 is only for percentages.
| Type of book | Number |
|---|---|
| Fiction | 15 |
| Non-fiction | 9 |
| Poetry | 6 |
| Total | 30 |
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Find the fraction of the whole pie, then take that fraction of 360 degrees.
- Write the whole pie. A whole pie chart is a whole circle, and a whole circle is 360 degrees.whole pie = 360°
- Write the sector as a fraction of the total. Poetry is 6 out of 30, so divide 6 by 30.6 ÷ 30 = 1/5
- Multiply the fraction by 360 degrees. The fraction tells us the share of the whole circle.1/5 × 360 = 72
- Write the answer. The sector is this many degrees.72
Check. All the sector angles in a pie chart add up to 360 degrees. ✓
Watch out. Use 360 degrees for the whole pie, not 100. The 100 is only for percentages.
| Pet | Number |
|---|---|
| Rabbit | 15 |
| Hamster | 20 |
| Guinea pig | 10 |
| Fish | 15 |
| Total | 60 |
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Find the fraction of the whole pie, then take that fraction of 360 degrees.
- Write the whole pie. A whole pie chart is a whole circle, and a whole circle is 360 degrees.whole pie = 360°
- Write the sector as a fraction of the total. Hamster is 20 out of 60, so divide 20 by 60.20 ÷ 60 = 1/3
- Multiply the fraction by 360 degrees. The fraction tells us the share of the whole circle.1/3 × 360 = 120
- Write the answer. The sector is this many degrees.120
Check. All the sector angles in a pie chart add up to 360 degrees. ✓
Watch out. Use 360 degrees for the whole pie, not 100. The 100 is only for percentages.
| Lunch | Number |
|---|---|
| Sandwich | 16 |
| Jacket | 10 |
| Pasta | 8 |
| Salad | 6 |
| Total | 40 |
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Find the fraction of the whole pie, then take that fraction of 360 degrees.
- Write the whole pie. A whole pie chart is a whole circle, and a whole circle is 360 degrees.whole pie = 360°
- Write the sector as a fraction of the total. Sandwich is 16 out of 40, so divide 16 by 40.16 ÷ 40 = 2/5
- Multiply the fraction by 360 degrees. The fraction tells us the share of the whole circle.2/5 × 360 = 144
- Write the answer. The sector is this many degrees.144
Check. All the sector angles in a pie chart add up to 360 degrees. ✓
Watch out. Use 360 degrees for the whole pie, not 100. The 100 is only for percentages.
| Pet | Number |
|---|---|
| Rabbit | 15 |
| Hamster | 20 |
| Guinea pig | 10 |
| Fish | 15 |
| Total | 60 |
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Find the fraction of the whole pie, then take that fraction of 360 degrees.
- Write the whole pie. A whole pie chart is a whole circle, and a whole circle is 360 degrees.whole pie = 360°
- Write the sector as a fraction of the total. Guinea pig is 10 out of 60, so divide 10 by 60.10 ÷ 60 = 1/6
- Multiply the fraction by 360 degrees. The fraction tells us the share of the whole circle.1/6 × 360 = 60
- Write the answer. The sector is this many degrees.60
Check. All the sector angles in a pie chart add up to 360 degrees. ✓
Watch out. Use 360 degrees for the whole pie, not 100. The 100 is only for percentages.
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Find the fraction of the whole pie, then take that fraction of 360 degrees.
- Write the whole pie. A whole pie chart is a whole circle, and a whole circle is 360 degrees.whole pie = 360°
- Write the sector as a fraction of the total. Fish is 15 out of 60, so divide 15 by 60.15 ÷ 60 = 1/4
- Multiply the fraction by 360 degrees. The fraction tells us the share of the whole circle.1/4 × 360 = 90
- Write the answer. The sector is this many degrees.90
Check. All the sector angles in a pie chart add up to 360 degrees. ✓
Watch out. Use 360 degrees for the whole pie, not 100. The 100 is only for percentages.
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Find the fraction of the whole pie that the sector is, then use that fraction to find the whole.
- Find the fraction of the pie. A sector of 90 degrees is 90 out of 360 of the whole pie.90/360 = 1/4
- Work out the total from the sector. If one quarter of the pie shows 15 children, the whole pie shows 4 quarters.15 × 4 = 60
- Decide. So the whole chart does show 60 children, and Mia is right.Yes, Mia is right.
Check. 15 is a quarter of 60, because 15 + 15 + 15 + 15 = 60. ✓
Watch out. A quarter of the pie is 90 degrees. Multiply by 4 to find the whole.
| Lunch | Number |
|---|---|
| Sandwich | 16 |
| Jacket | 10 |
| Pasta | 8 |
| Salad | 6 |
| Total | 40 |
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Find the fraction of the whole pie, then take that fraction of 360 degrees.
- Write the whole pie. A whole pie chart is a whole circle, and a whole circle is 360 degrees.whole pie = 360°
- Write the sector as a fraction of the total. Jacket is 10 out of 40, so divide 10 by 40.10 ÷ 40 = 1/4
- Multiply the fraction by 360 degrees. The fraction tells us the share of the whole circle.1/4 × 360 = 90
- Write the answer. The sector is this many degrees.90
Check. All the sector angles in a pie chart add up to 360 degrees. ✓
Watch out. Use 360 degrees for the whole pie, not 100. The 100 is only for percentages.
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Find the angle for one pupil.
- Write the whole pie. The whole pie is 360 degrees.360 degrees
- Share it between the pupils. Each pupil is one of the 36 equal shares of the whole pie.360 ÷ 36 = 10
- Write the answer. One pupil needs 10 degrees, and every sector is a whole number of pupils.10
Check. 10 × 36 = 360. ✓
Watch out. Each pupil has the same angle. Divide 360 by the total number of pupils.
Watch out
Watch out: a sector for each group in the table needs its own angle. If you use the wrong total, every angle will be wrong. Check that the angles add up to 360 before you draw.
Exam tip
When you draw the chart with a protractor, start at the top, go clockwise, and draw the biggest sector first if you wish.