Teacher’s name
Juliet Chappell.
Lesson title
Learning Pi with Pie!
Subject area
Key Stage Three Mathematics.
Pupils’ ages
11 and 13, though this is more dependent on ability.
Lesson length
1 - 1 ½ hours.
Lesson aims and objectives
To introduce the concept of π and teach the formulae concerned with calculating the
circumference and area of a circle, whilst having some fun through a more practical
approach!
Necessary preparation
Check with the children’s parent(s) and the children themselves that they are allowed
to eat fruit pie and make sure you know what they like.
Buy a good sized, circular pie with a pastry top (this is less messy).
Take the following worksheet, a calculator, some clean string, a clean ruler long
enough to measure your pie’s diameter and the pie itself to the lesson.
Plan
Work through the attached worksheet with the children, explaining anything they are
unsure of along the way. Alternate tasks (such as reading the worksheet, the practical
measuring and writing down the calculations) with the children throughout to maintain
variety and aid understanding. Finish by eating some pie!
Experience with the lesson and its success
This lesson was received especially well by the children. Mathematics is a subject
which they are not normally overly interested in and it is also challenging to find new
ways to make complicated areas appealing and accessible, but this lesson had them
enthralled. The apparatus and tactic involved cannot and would not be employed in
the classroom with a large number of students so it is ideal for a home tutor and one or
two pupils to have fun with.
In terms of the subject material, I have found it is sometimes hard for children to grasp
the use of a new formula and how it relates to a calculation in practical terms,
particularly where π is involved. By actually demonstrating the use of π and the
means of working out a circle’s circumference and area with a real object as opposed
to merely paper drawings, I found that the children were able to understand effectively
how the formulae itself were constructed.
As well as successfully teaching Mathematics, this lesson was ideal for developing my
relationship with the children’s family because inevitably it attracted a lot of attention
from their siblings and mother. And of course it was lovely to share the pie with
everyone!
Learning Pi with Pie!
Today we are going to learn about the number pi and how it can help us in Maths.
We write the number with a symbol (π) and we pronounce it just the same as
how we say ‘pie’. The number is named after a letter of the Greek alphabet.
But what exactly is pi and why is it so special? Pi is a number which never ends.
This means we call it an infinite number. Normally we round it up to two decimal
places, so we say π = 3.14, but this is what the start of pi looks like if we
continue it on for much longer:
3.1415926535897932384626433832795……
So although pi is really only a small number, just a bit bigger than 3, it is still
complicated! Pi is special because we use this number in lots of Mathematics,
especially formulae for circles. Have a look at these formulae:
C= πd
A= πr2
As you can see, the π symbol is used just like any other letter is in a formula.
This means it does not need to have a multiplication symbol between it and the
letter. Instead of π x d it is πd and instead of π x r2 it is πr2.
Now it is pie time! Have a look at your pie and see the top of it is circular. We
want to find out the perimeter of our pie. We could do this by taking the piece
of string, wrapping it around the top of the pie and then measuring how much
string we needed with a ruler. But sometimes we don’t have string, so we would
have to use π and the first formula from above.
For a circle the perimeter is called the circumference, but it is still the distance
around the edge of the circle. In our formula the circumference is shown by the
capital letter C.
The distance all the way across the circle in a straight line (its width) is called
the diameter and this is shown by the small letter d. We can use the ruler to
measure the diameter of our pie.
This is the formula we use to work out the pie’s circumference:
Circumference = pi x diameter
C= πd
Now we have the formula sorted let’s work out the circumference of our pie!
We can use a calculator to do the actual working out, but first we must
substitute the letters in the formula for numbers. An example is below:
C= πd
π= 3.14
d= 12cm
C= 3.14 x 12
C= 37.68cm
Follow this method and see if you can work out the circumference of our pie
below:
Now we can use the string and ruler to check that the answer is right. The
answers should be very similar though they won’t be exactly the same because
we have only used pi to two decimal places, remember.
So we now know the circumference and diameter of our pie, but what about the
area? We can work this out with a formula as well.
First we need to learn what the radius of a circle is. The radius is the distance
from the middle of the circle to the edge. It is the line you cut when you are
slicing a pie. It is also half of the diameter because slicing the diameter would
be cutting a line across the entire pie. In the formula the radius is shown by the
small letter r.
The formula we use to work out the pie’s area is:
Area = pi x radius x radius
A= πr2
This formula is a bit more complicated than the first one we did so let’s look at
it in more detail. Because part of it is ‘radius x radius’ we say ‘radius squared’,
just like we do with any number which is multiplied by itself. We write ‘squared’
as a small number 2 in the air (2) instead of putting two ‘r’s next to each other.
Remember that the radius is half of the diameter, so to find a circle’s radius we
must divide the diameter by 2.
Now we have the formula sorted let’s work out the area of our pie! We can still
use a calculator to do the actual working out, but first we must substitute the
letters in the formula for numbers. An example is below, using the same pie as
before:
A= πr2
π= 3.14
r= d ÷ 2
r= 12 ÷ 2
r= 6cm
A= 3.14 x 62
A= 3.14 x 6 x 6
A= 113.04cm2
Remember areas are always in a measurement squared. Here it is cm squared,
which we write cm2.
Follow this method and see if you can work out the area of our pie below and on
the next page:
Now we know the circumference and area of our pie!
Remember you can use the rules and the formulae we have learnt today to work
out the circumference and area of any circle, so long as you know the diameter
and the magic number which is pi.
Try doing these calculations for lots of other circular objects around the house.
See if you can remember what all these words mean as you do it:
Pi
Infinite
Perimeter
Circumference
Diameter
Area
Radius
Squared
Substitute
Well that’s enough Maths for one day - let’s eat some pie!!