Algebra with bracelets

Algebra involves working with numbers and variables. Working with variables can be confusing. This screen suggests a picture of algebra expressions with variables that may be helpful. Please remember: a picture of algebra is not algebra. Eventually you will have to work with algebra symbols alone.

How can you picture an algebra expression such as 2X + 3Y? Think about X and Y as colored circular stickers that can be combined to make bracelets. We will refer to these stickers as 'coins' because we will want to talk about the value of a bracelet.

The simplest bracelet is just a coin attached to a thin metal rod. We'll start with two kinds of coins: green and red (or any other colors you like). A green coin represents X and a red coin represents Y. Each link on the bracelet is shown as a gray bar.

Our two basic bracelets look like this: ___X___ and ___Y___ . Take a look at the figure at the right.

These are very simple bracelets. But any time you have two bracelets, you can link them together with a clasp, which will be shown as a plus sign. The new bracelets are named as the sum of the pieces, listed from left to right. In the figure at the right:

Line 1: X + X is the math name for ___X___+___X___.

Line 2: X + Y is the math name for ___X___+___Y___.

Line 3: X + X + Y + Y + Y is the math name for ___X___+___X___+___Y___+___Y___+___Y___.

Line 4 shows 2X + 3Y, a shorter name for the polynomial on line 3.

Line 5 shows the harder example: 4X2Y3Z + 77X3Y5Z2 - 2XYZ3. Can you figure out the idea?

Instructions

In the figure at the right, you can experiment by dragging the parts of the polynomial. When this screen is finished, you will be able to add and multiply polynomials by dragging variables, monomials, and terms.