D. Data · Data Literacy and Probability

Making Circle Graphs

D1.3 D1.2About 55 minutes

Learning goals

I can change percentages or fractions of a data set into central angles.
I can draw a circle graph with a protractor.
I can give my circle graph a title, labels or a legend, percentages and a source.
I can check that my angles add to 360° and my percentages add to 100%.

Words to know

central angle
The angle of a sector at the centre of the circle.

protractor
A tool for measuring and drawing angles in degrees.

compass
A tool for drawing circles. You can also trace around a round lid.

legend
A key that tells what each sector stands for.

source
Where the data came from, such as "Survey of 40 Grade 7 students, Pine Hill P.S."

Remember from Grade 5

You measured and drew angles in degrees with a protractor. Place the centre of the protractor on the vertex, line up 0° with one arm, and read the scale that starts at 0. You will use that skill to draw circle graphs.

From a table to a circle graph

In Lesson 2, the student council found the favourite winter activities of 40 students: skating 35%, tobogganing 25%, skiing 15%, snow forts 15%, snowshoeing 10%. Let's turn this table into a circle graph.

Each sector's central angle is its share of 360°:

Central angle = percentage × 3.6 or Central angle = (count ÷ total) × 360

Round to the nearest degree if you need to. Then check that the angles add to 360°.

Worked example

Example 1: Angles from percentages

Find the central angle for each winter activity: skating 35%, tobogganing 25%, skiing 15%, snow forts 15%, snowshoeing 10%.

Skating: 35 × 3.6 = 126°.
Tobogganing: 25 × 3.6 = 90°.
Skiing: 15 × 3.6 = 54°.
Snow forts: 15 × 3.6 = 54°.
Snowshoeing: 10 × 3.6 = 36°.
Check: 126 + 90 + 54 + 54 + 36 = 360°. ✓

126°, 90°, 54°, 54° and 36°.

Drawing it

Draw a circle with a compass, or trace around a round lid. Mark the centre. (With a lid, trace a second circle, cut it out with scissors and fold it in half twice; the folds cross at the centre. Lay it on your drawn circle and poke a pencil point through the centre to mark it.)
Draw a start line (a radius) from the centre straight up to the circle.
Put your protractor's centre on the circle's centre and its 0° line on the start line. Mark the first angle (126°) and draw a radius there.
Use the new line as the 0° line for the next angle (90°). Keep going around the circle.
The last sector should end exactly at your start line. If it is a degree or two off, that is just measuring wobble.
Label each sector (or use a legend) with the category and percentage. Add a title and a source.

It helps to draw the sectors from largest to smallest, going clockwise.

The first sector, 126° for skating, measured clockwise from a start line at the top.

The finished circle graph. Skating 35% (126°), tobogganing 25% (90°), skiing 15% (54°), snow forts 15% (54°), snowshoeing 10% (36°).

Worked example

Example 2: Angles straight from counts

A class of 24 students voted for a juice at the year-end picnic: grape 10, orange 8, apple 6. Find the central angles and percentages.

Each student is 1/24 of the circle. 360 ÷ 24 = 15° per student.
Grape: 10 × 15 = 150°. Orange: 8 × 15 = 120°. Apple: 6 × 15 = 90°.
Check: 150 + 120 + 90 = 360°. ✓
Percentages: grape 10 ÷ 24 ≈ 41.7%, orange 8 ÷ 24 ≈ 33.3%, apple 6 ÷ 24 = 25%.

Grape 150° (about 41.7%), orange 120° (about 33.3%), apple 90° (25%).

Grape 150°, orange 120°, apple 90°. The percentages are rounded to one decimal place.

Worked example

Example 3: A day in your life

Noor tracked one school day (24 hours): sleep 9 h, school 6 h, meals 2 h, homework and reading 2 h, sports and free time 5 h. Find the central angles.

The whole circle is 24 hours. 360 ÷ 24 = 15° per hour.
Sleep 9 × 15 = 135°. School 6 × 15 = 90°. Meals 2 × 15 = 30°. Homework and reading 2 × 15 = 30°. Sports and free time 5 × 15 = 75°.
Check: 135 + 90 + 30 + 30 + 75 = 360°. ✓

135°, 90°, 30°, 30°, 75°. As percentages: sleep 37.5%, school 25%, meals and homework about 8.3% each, sports and free time about 20.8%.

Good circle graph checklist

A clear title that says what and who.
Every sector labelled (or a legend) with the category and percentage.
The total number and the source.
Angles add to 360°, percentages to about 100%.
Not too many sectors. With more than about 6, small slivers are hard to read; you can group small categories as "other".

Just for fun

Why does the protractor get invited to every party?

It always knows the right angles!

Hands-on activity

Graph your own day

You need: paper, a pencil, a ruler, a protractor, scissors, a round lid (or a compass, with a grown-up nearby because of the sharp point) and a calculator.

Think about yesterday. How many hours did you spend sleeping, at school, eating, doing homework, playing, using screens, and so on? Make sure the hours add to 24.
Multiply each number of hours by 15°.
Check that the angles add to 360°.
Draw the circle graph with your protractor. Give it a title, labels with percentages, and a source ("My log, one school day").
Ask a family member to make one for their day. Compare: who sleeps the greatest percentage of the day?

Math talk: "Which sector was hardest to draw accurately? How could you make your graph more exact?"

Your turn

What is the central angle for 20%?

What is the central angle for 45%?

A survey of 30 people: 12 chose fish, 9 chose chicken and 9 chose vegetarian. Find the central angles.

Find the percentages for the survey of 30 people above.

Sam's angles are 100°, 120°, 80° and 50°. Can they be a circle graph? Why or why not?

Lucy slept 8 hours in one day. What is the central angle for sleep in a circle graph of her day?

What should every circle graph have besides the sectors?

More practice: warm-up

Central angle for 50%?

Central angle for 10%?

Central angle for 5%?

In a class of 20, how many degrees is each student worth?

How many degrees is one hour in a circle graph of a 24-hour day?

More practice: on your own

A survey of 60 people: hockey 24, soccer 15, basketball 12, other 9. Find the percentages and central angles.

Find the central angle for 12.5% and for 37.5%.

A family's monthly budget: housing 30%, food 20%, transportation 15%, savings 10%, everything else 25%. Find the central angles.

In a survey of 7 people, 3 chose cats. What is the central angle, to the nearest degree?

Why do we draw each new angle from the last line we drew, instead of always from the start line?

Challenge

Survey of 36 students: maple taffy 15, hot chocolate 12, bannock 9. (Bannock is a bread made and shared in many First Nations and Métis communities.) Find the angles and percentages, to one decimal place.

Rounded to the nearest degree, a student's angles are 67°, 101°, 79° and 112°. Do they add to 360°? What should the student do?

A circle graph has 5 sectors of equal size. What is each central angle and each percentage? What if there were 8 equal sectors?

Check your understanding

Quiz

What is the central angle for 30%?

In a survey of 40 people, how many degrees does each person get?

10 of 24 students chose grape juice. What is the central angle?

After you draw the first sector, where do you measure the next angle from?

Which set of angles can make a circle graph?

Which is not needed on a good circle graph?

For parents and teachers

Big idea: Grade 7 students display data in circle graphs with proper sources, titles and labels (D1.3), using percentages from organized data (D1.2). The key calculation is percentage × 3.6 (or count ÷ total × 360). Measuring with a protractor reuses Grade 5 skills.

Common difficulties:

Measuring every angle from the start line instead of from the last line drawn.
Reading the wrong protractor scale (the inner versus outer numbers). Remind them to start from 0 on the line they are measuring from.
Angles that don't add to 360° because of a calculation slip or rounding.
Leaving out the title, percentages or source.

How to help: A round lid and a protractor are all you need. Make a "my day" circle graph together (15° per hour). If the drawing is fiddly, praise careful measuring and checking. Safety: a compass has a sharp point, so stay nearby, or trace a lid instead.