# Circles

**Labeling a Circle**

A nice activity for the pupils to move points about and identify the different parts of a circle. A slightly different activity from the normal worksheet with gaps!

**Circumference Investigation**

Find lots of circular objects. At least 5 from around the house. You will also need a ruler, pencil and a piece of string. Wrap the piece of string around your circular objects

Fill out the table below, you will need to measure the circumference of each object by wrapping the piece of string around your circular objects and the diameter of each object and fill these values into you table. Do this for your objects. Then have a look at the data and see if you can find a connection between the radius and the circumference

Can you find a number that connects the circumference with the diameter?

**Pi discussion points**

Look at the statements made by these characters from Brave. They are really good starting points for discussions in class

**Circumference of Circles**

Drag the green point to appropriate position to measure the diameter of the circle. What is its diameter? Drag the red point P to straighten the circumference. Divide the scale of the ruler to measure its length to **two decimal places**. Use the Zoom In, Zoom Out and Move tools if necessary. Change the diameter of the circle to 2 cm, 3cm, or any other diameters. Calculate the value of: circumference ÷ diameter. What do you observe?

**Area of a circle**

A lovely activity that shows how to find the area of a circle by cutting it into multiple sectors and rearrange into a rectangle. Discussions around what happens to the accuracy if you cut it into smaller sectors.

**Connect Thoughts!**

To play you must answer the question in each of the rectangles. If you get that question correct you can place your sticker over that square with the answer on it. The winner is the first person to get four questions correctly answered in a row **vertically or diagonally**. One person in each group will act as the referee and will check that the answer given is correct.

**Area of Circles**

What is the area of a circle? Explore with the following applet.

**Length of a paperclip**

Using what we have learnt about circumference of a circle, can you find the length of of the paperclip.

**Area and Circumference of a circle**

Can you fill in all the gaps in the table to work out the area and circumference of sectors as well as finding the radius and diameter given the circumference

**Penny Farthing**

Boris Biker entered the Tour de Transylvania with an unusual bicycle whose back wheel is larger than the front. The radius of the back wheel is 40cm, and the radius of the front wheel is 30cm.

On the first stage of the race the smaller wheel made 120,000 revolutions. How many revolutions did the larger wheel make?

**Growing Grass**

The lawn needs re turfing, so that you don’t buy too much turf you need to find the exact area of the lawn?

**Six Circles**

Each of the corners of the small rectangle is the centre of one of the large circles.

The perimeter of the small rectangle is 60cm.

What is the perimeter of the large rectangle?

**Contact Circles**

Four touching circles all have radius 1 and their centres are at the corners of a square.

What is the radius of the circle through the points of contact *X*,*Y*,*Z* and *T*?

## Further Ideas

**A brief History of Pi**

This video goes through the history of pi, it takes us from the Middle East through Europe. This is good to give pupils an idea of where Pi has come from and how it has changed over time.

**Penny Farthing**

**Answer**: 90 000

**Six Circles**

The small rectangle consists of 12 of the radii of the circles, each connecting a point of contact to the centre of the relevant circle. These are shown in green and orange in the diagram on the right.

Since this has a total length of 60cm, each radius is of length 60cm÷12=5cm.

The large rectangle can also be broken down into segments of this length. These are shown in blue and red on the diagram. There are 20 of these, so the perimeter of the large rectangle is 5cm×20=100cm=1m.

**Contact Circles**

The square whose vertices are the centres of the original four circles has side of length 2 units and this distance is equal to the diameter of the circle through *X*,*Y*,*Z* and *T*.

Therefore the radius is 1 unit long.