Pizza Slices
Introduction
In the last lesson, we came across some vocabulary to do with circles. But there are more words that you will need to learn. Click here to find out what they are. You may wish to play these games to help you memorise these terms.
Now that you know how to find the circumference of a circle, can you come up with a formula to find the area?
For this activity you will need colours, scissors, glue, paper and these pizza slices (PRINT ME) and investigate.
Start with the 4 slice pizza. Colour one half in one colour and the other half in a contrasting colour.
Cut up the 4 slice pizza and arrange with the slices alternating (see the diagram on the right) and stick them on a piece of paper.
Now repeat steps 1 and with each of the 8, 16 and 32 slice pizzas.
Questions:
What is the same about the four diagrams? What is different about them?
What can you tell me about the area of the shapes you have made compared to the area of the original pizza?
What does the shape start to resemble as there are more slices? Use this animation to help you cut up to 200 slices!
How do you calculate the area of this shape?
What are the dimensions in terms of the original circle?
Hence can you come up with a formula for calculating the area of a circle? Check and see if you got the right answer here.
Further Practice
In today's investigation, you should have discovered how to find the area of a circle. Here is the Circle Song to help you memorise the formula (and this is a version from two self-proclaimed "natural-born Math-a-magicians" who would like to encourage all Islanders to "choreograph dances in Math"). After you have learnt it, it's time to apply it. Practise the relevant skills on DrFrostMaths, CorbettMaths, MyiMaths and Eedi.
Transum
Circles - try this self-marked exercise. There are altogether 6 levels.
Areas of Composite Shapes - try this self-marked exercise. There are altogether 5 levels.
Area and Perimeter - try this self-marked exercise. Name the shapes then find formulas to calculate the area and perimeters from the given lengths.
Circle Video - this is a comprehensive video to teach you how to solve different problems related to circles.
For more goodies on cicrles on transum, click on the hyperlink.
Area and Circumference of Circles
Ken Stafford: Past Paper Qs : Solutions
Dr Frost : Questions (Ans. inc.)
For some textbook practice, see below, answers are here:
10 Ticks - Circle Area Problems.pdf10 Ticks - Circle Mixed Problems.pdfExtension
nRich
Here is a collection of activities to do with "area - circles, sectors and segments". In particular, you may want to look the Running Race problem taken from UKMT maths challenge. For a similar but easier problem, try Track Design.
Don Steward
These activities based on circles may also interest you.
Finally, try these:
Can you use what you have learnt to calculate the perimeter and area of the Island School logo? What measurements do you absolutely need?