# 187. Clever circles

Here is a quick, multi-function resource for you: a set of overlapping circles for angles, pie-charts and fractions/percentages.

Equipment
Card
Scissors
Pencil
Straight edge or ruler
Pair of compasses
A 360 degree protractor printed on paper (or a tracing paper protractor cut out)

Construction
1. Cut out three identical circles and the paper protractor.

2. Stack them on top of each other and put the pointy end of the compasses (or a drawing pin) through the middle. Wiggle it around to make a bigger hole – please don’t stab yourself.

3. Draw a radius on the circles.

4. Cut down each radius on the circles and the 0 degree line on the protractor.
5. All done!

Activity 1: Angle Estimation
Slot two circles together:

Estimate the orange angle.
What could the blue angle be?
Show me an acute angle.
Show me a blue 170 degree angle.

Activity 2: Reading a protractor scale
Slot the protractor into a circle:

How big is the blue angle?
Show me an 80 degree angle.

Activity 3: Pie-charts
Slot the three circles together:

What could this pie-chart represent?
Show me a pie chart with two equal sections

Activity 4: Fractions and percentages
Use three circles again:

Estimate what percentage is purple.
What fraction could the blue section represent?

# 2. Human pie chart

The main problem students have with drawing pie charts is working out the angles. Barcharts are easy, but as soon as protractors are involved the shutters go down.

How about using the whole class to turn a barchart into a pie chart using nothing more than a playground and a piece of chalk?

1. Pick a topic eg How did you get to school today?
2. Get pupils to move into the correct groups eg Automobile (car), Bus, Walk, Cycle
3. Create a human barchart eg
AAAAAA
BBBB
WW
CCC
4. Move the bars in order into a line
AAAAAABBBBWWCC
5. Move the bars into a circle
(You’ve just turned a barchart into a circle)
6. Mark the centre of the circle, mark in the lines between each section (4 sectors)
7. Ask how many degrees one person represents.
8. Ask how many degrees each sector is worth.
Note: If you have a low ability group or no calculators you may wish to edit the number involved to be a factor of 360. Extra pupils can be keeping notes on a mini whiteboard.
9. To consolidate this you can repeat this with a different question.
10. To extend this task you can split up the class into two groups and ask a different question. They must create two pie charts and compare the data.

This activity is a great task as it makes for a memorable lesson and good discussion point. If you take pictures for a wall display it can make a nice revision prompt.