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.