D. Data · Data Literacy and Probability

Reading Circle Graphs

D1.3 D1.6About 45 minutes

Learning goals

I can explain that a circle graph shows the parts of one whole data set.
I can use benchmarks (half, quarter, eighth, tenth) to estimate the size of a sector.
I can connect percentages to angles: 100% is 360°, so 1% is 3.6°.
I can use the percentages and the total to find how many are in each category.

Words to know

circle graph
A graph that shows the parts of one whole as sectors of a circle. Also called a pie chart.

sector
A wedge-shaped part of a circle, between two radii (like a slice of pizza).

central angle
The angle of a sector at the centre of the circle. All the central angles add to 360°.

legend
A key that tells what each sector stands for.

benchmark
A familiar amount you can compare with, like a half or a quarter.

New in Grade 7

You know many graphs already: line plots, bar graphs, stem-and-leaf plots, multiple-bar and stacked-bar graphs, histograms and broken-line graphs. In Grade 7 you add the circle graph. It is made for showing parts of a whole, which is exactly what percentages describe.

A whole pizza of data

Imagine one pizza for the whole data set. Each category gets a slice. A bigger category gets a bigger slice. That is a circle graph.

The whole circle is the whole data set: 100% of the people or things.
Each sector (slice) is one category.
The size of a sector matches its percentage. 40% of the data gets 40% of the circle.
A legend or labels tell what each sector means.
Like every graph, it needs a title and a source, and it should say how many were surveyed.

Bus 40%, walk 25%, car 20%, bike 10%, other 5%. Each sector's central angle is its percentage of 360°: 144°, 90°, 72°, 36° and 18°.

Percentages and angles

A full turn around the centre is 360°. The whole data set is 100%. So:

100% ↔ 360°
1% ↔ 3.6° (because 360 ÷ 100 = 3.6)

To find the central angle of a sector: percentage × 3.6. The walk sector is 25% × 3.6 = 90°, a right angle, just like the corner of a sheet of paper.

Useful benchmarks help you estimate without measuring:

A circle split into a half (50%), a quarter (25%) and two eighths (12.5% each). Benchmarks: half = 180°, quarter = 90°, eighth = 45°, tenth = 36°.

Worked example

Example 1: How many in each category?

Use the graph How 200 Grade 7 Students Get to School. How many students are in each category?

Multiply each percentage by the total, 200. 1% of 200 is 2, so multiply each percentage by 2.
Bus: 40 × 2 = 80. Walk: 25 × 2 = 50. Car: 20 × 2 = 40. Bike: 10 × 2 = 20. Other: 5 × 2 = 10.
Check: 80 + 50 + 40 + 20 + 10 = 200. ✓

Bus 80, walk 50, car 40, bike 20, other 10.

Worked example

Example 2: From an angle to a percentage

In a circle graph about 150 people, the swimming sector has a central angle of 72°. What percentage chose swimming, and how many people is that?

The sector is 72 out of 360 degrees: 72 ÷ 360 = 0.2 = 20%.
20% of 150 = 0.2 × 150 = 30.

20%, which is 30 people.

Worked example

Example 3: Asking questions about the graph

What can we learn from the travel graph? Ask and answer some questions.

Which way is most common? The bus, at 40%. It is a bit less than half the circle.
What percent come by a motor vehicle (bus or car)? 40% + 20% = 60%, more than half.
What percent are active travellers (walk or bike)? 25% + 10% = 35%, about one third.
How many more ride the bus than walk? 80 − 50 = 30 students.

A circle graph is great for seeing how big each part is compared with the whole, and for combining parts.

Read the whole graph

Before answering questions, read the title, the legend, the source and the total. A circle graph shows percentages, so you need the total to find actual numbers. If the total isn't given, you can compare parts, but you can't say how many people are in each part.

Just for fun

Why do circle graphs make everyone hungry?

Because the data is always served in slices!

Hands-on activity

Percent circle from a paper plate

You need: a paper plate (or a circle traced from a plate onto paper and cut out with scissors), a pencil and a ruler.

Fold the circle in half and unfold it. Label each half 50%.
Fold it into quarters. Label the quarters 25%. Each quarter has a 90° corner at the centre.
Fold it once more into eighths. Each eighth is 12.5%, or 45°.
Hold your percent circle next to the circle graphs in this lesson. Cover the labels with your hand and estimate each sector's percentage. Then check.
Next time your family has a round pizza or pie cut into 8 equal slices, say what percentage each slice is (12.5%), and how much 3 slices is (37.5%).

Math talk: "Is the car sector more or less than a quarter? How do you know?"

Use this graph for the Your turn questions. Summer 45%, winter 30%, fall 15%, spring 10%.

Your turn

Look at Favourite Season of 120 Students. Which season is the most popular? Is it more or less than half?

How many students chose winter?

How many students chose spring?

What is the central angle of the summer sector?

What percentage chose fall or spring?

How many more students chose summer than winter?

Without the total of 120, could you still say how many chose summer? What could you still say?

More practice: warm-up

A sector is half the circle. What percentage is it?

A sector is a quarter of the circle. What is its central angle?

What do all the percentages in a circle graph add to?

What do all the central angles in a circle graph add to?

A sector is 10%. What is its central angle?

More practice: on your own

A sector has a central angle of 54°. What percentage is it?

A circle graph shows how 400 people voted. The yes sector is 65%. How many voted yes?

In a circle graph, the hockey sector is a little bigger than a quarter. Which percentage could it be: 18%, 28% or 48%? Explain.

A circle graph has 4 sectors. Three of them are 120°, 90° and 60°. What is the fourth angle, and what percentage is it?

In the travel graph (200 students), the bike sector is 10% and the bus sector is 40%. How many times as many students ride the bus as bike?

Challenge

A circle graph about lunch choices has a soup sector of 126°. 28 students chose soup. How many students were surveyed in total?

Two sectors in a circle graph together make a straight line through the centre. One is 30%. What is the other one?

Amir reads a circle graph and says, "The skiing sector is 90°, so 90 people chose skiing." Explain his mistake. If 240 people were surveyed, how many chose skiing?

Check your understanding

Quiz

What does the whole circle in a circle graph stand for?

A sector is 25% of a circle graph. What is its central angle?

A sector has a central angle of 36°. What percentage is it?

A circle graph about 300 students shows that 30% chose skating. How many students chose skating?

A sector is a little less than half of the circle. Which percentage fits best?

Which information do you need to find the number of people in a sector?

For parents and teachers

Big idea: Circle graphs are new in Grade 7 (D1.3, D1.6). Students learn that a circle graph shows the parts of one whole data set, that the percentages add to 100% and the central angles add to 360°, and that 1% matches 3.6°. Students reading graphs should always look for the title, the total and the source.

Common difficulties:

Thinking the angle is the number of people (90° means 90 people). Connect angles to percentages first, then to numbers.
Forgetting that the total is needed to find counts.
Estimating badly. Practise with benchmarks: half, quarter, eighth, tenth.

How to help: Use a pizza or pie cut into equal slices to talk about percentages and angles (8 slices: 12.5% and 45° each). Look for circle graphs in news, flyers or utility bills together and ask: "What is the whole? What is the biggest part? How many is that?"