Circles
In this topic you will
- Find the centre of a circle using folding.
- Use folded circles to determine angles and turns.
Key Words
- centre
- distance
Show Definitions
- centre: The point in the middle of a circle that is the same distance from every point on the edge.
- distance: The length between two points, measured in a straight line.
A circle is a round $2$D shape.
All points on the edge of the circle are the same distance to the centre.
Ask your teacher for a paper circle.
Fold it in half exactly, then open it out.
Turn the circle a little bit then fold it again.
Open it out.
The centre of the circle is where the two folds meet.
Any line that is drawn from one edge to the other and through the centre of the circle makes a line of symmetry.
Circles are all over the world: in art, nature, buildings, and in our homes.
EXERCISES
$1$. An angle is the amount of turn between two lines that meet each other.
Use your folded paper circle to draw the lines that show:
a. a quarter turn clockwise
b. a quarter turn anticlockwise
c. a half turn clockwise
d. a half turn anticlockwise
e. a full turn
How many of your lines made a right angle at the centre of the circle?
👀 Show answer
$2$. Use your folded paper circles to help you draw the lines that show:
a. $2$ right angles
b. a half turn
c. a quarter turn anticlockwise
👀 Show answer
a. $2$ right angles is the same as a half turn, so draw a straight line through the centre from one side of the circle to the opposite side.
b. A half turn is also a straight line through the centre joining opposite points on the circle.
c. A quarter turn anticlockwise is a right angle, so draw two lines from the centre that meet at $90^\circ$ in the anticlockwise direction.
Think like a Mathematician
Investigation: Next time you see a bike, look at the wheels. As they turn, the shape of the wheels stays the same.
Look carefully at the two wheels shown below. What is the same about them? What is different?
Task:
- Draw $2$ different car wheels.
- Write $2$ things that are the same about your wheels.
- Write $2$ things that are different about your wheels.
Follow-up Questions:
Show Answers
- 1: A wheel stays the same shape because it is a circle, and rotating a circle does not change its size or shape.
- 2: All wheels are circular, have a centre point, and have all points on the edge the same distance from the centre.
- 3: The centre allows the wheel to turn evenly around one fixed point, keeping the motion smooth and balanced.