Introducing Algebra

Years 7 - 8

Tony Wright, Bellarine Secondary College

Preparation

If students have had sufficient experience with Protons & Anti-Protons they will be comfortable with a blue-up plug representing ⁺1 and a yellow-up plug representing ^-1. They will also be familiar with ideas such as:

Any positive or negative number can be represented by an infinite number of collections, eg:
Each of these is worth 3 Protons (or ⁺3)

Adding a negative gives the same answer as subtracting a positive.

Algebraic Expressions

If the yellow and blue plugs can be used to represent any integer, then what shall the red plugs represent? How about x?
If you want to get really sophisticated perhaps a sticker could be put on one side of the red counter to represent ^-x.

Now we can make all sorts of expression to factorise and expand. For example:

Make the collection 6x - 12 and sort it into equal groups. You can make:

6(x - 2)

3(2x - 4)

2(3x - 6)

That's what factorising is all about.

Expanding is asking the reverse question, for example:

We have 5 groups of (x plus 1), ie: 5(x + 1), what is the total collection?

Plenty of practice may be required, but it is more meaningful than drill and kill exercises from the text book.

Linear Equations

Suppose we assign a value to a particular collection. We know the amount each yellow or blue plug contributes to the total value. The remaining amount must come from the red plugs - the x.

So, what is the value of x if 5x - 6 = 4?

Use the concept of the = sign being a balance...

Keep the balance level by doing the same thing to both sides...

Then each step parallels the 'standard' algorithm for solving a linear equation...

And we get the answer x = 2...

Now substitute that value back into the original collection to check that it works.

What happens if there are x plugs on both sides, eg:

3x - 6 = 4 - 2x?

Calculating Changes ... is a division of ... Mathematics Centre