Perimeter and Circumference - Getting Into It

Lesson 1: Perimeter and Circumference - Getting Into It

   Getting Into It

Here is what you will need for the following investigation:

• a circular plate and bowl
• paper and pencil
• calculator
• smarties (or dimes)

Task 1

1. Place the plate and bowl upside down on a hard, flat surface.


2. Place the smarties around each object. Be sure the smarties are touching each other and the outer edge of each object.


3. Carefully remove each object. Try not to disturb the smarties.


4. Place a line of smarties across the centre of each circle (create a diameter).


5. Count the number of smarties that go around and across each circle, and record the values.
   
   

   	around	across
   circle 1
   circle 2



6. Divide the number of smarties that went around each circle by the number that went across the same circle, and record each value.
   
   Example:
   13 around and 4 across
   13 ÷ 4 = 3.25
   
   

   	around ÷ across
   circle 1
   circle 2

   
   What do you notice about the calculated values?

   Points to Ponder

The number of smarties that went around each circle represents the circumference, as measured in the non-standard unit of smarties.

You may have noticed that the relationship between the number of smarties around and the number of smarties across each circle was about the same for each circle. You may also have noticed that when you divided the circumference (in smarties) by the diameter (in smarties) the result was close to Pi (π) which is 3.14159...

The formula for the circumference of a circle, if the diameter is known is:

Circumference = π x diameter
C = πd

Because smarties were used, the results were close to Pi, but not exact. Using standard units results in greater accuracy.


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