Practical
Example- The fundraiser

Now let's make our expression do some real
world work for us. Suppose we match these numbers up with some objects in the
real world, and then use our shortcut. For example, let's suppose that we are
running a community fund raiser to raise money for the Inuksuk daycare and, at
the end of the fund raiser, we have stacks of loonies that have come in from
different people participating in the fund raiser.

Let's say that we
count the number of loonies in a number of these stacks, and find out that the
number of loonies in each stack happens to match perfectly with the numbers in
our expression version 1, from section 3.15. In other words, we find that
there is a stack of three loonies and a stack of four loonies and a stack of
five loonies and a stack of six loonies and a stack of one loonie (recall that
our expression, version 1, was 3 + 4 + 5 + 6 + 1).

Now suppose that we
want to know how much money the event has raised. One way to do this would be
to put all of the stacks together and count the number of loonies in the
resulting big pile of loonies. However, our mathematical knowledge will now
give us a short cut.

By matching numbers to the stacks of loonies
(the stack of three loonies with the number 3 and so on) and a mathematical
action (adding, +) to our real world action (putting the stacks together) we
can use our shortcut to determine how much money we've raised.

We
already know that our mathematical expression evaluates to 19. Since we've
matched our mathematical expression to our real world situation, we can quickly
say that we have 19 loonies without bothering to put all of the loonies in a
single pile and count them one by one. Our math knowledge has given us a short
cut.

Perhaps you have often used shortcuts similar to this. Now you
know that when you did you were, in fact, making and using a mathematical model
to come up with a real world answer.

Copyright Jen Schellinck, 2006