1. Using Algebra Tiles to Understand How to Solve Equations

2. During this chapter we will use Algebra Tiles to help us understand different ideas in Algebra. You will find a page of these tiles on my resource webpage that can be printed and cut out to work with at home, if you would like. You can also diagram any algebraic statement with a drawing. But with use of these tiles you will improve and eventually not need them.

3. This is a unit tile. A single unit tile represents 1. If seven unit tiles are grouped together, it is a model of the number 7. To make diagrams of a model for unit tile, we will use a dot. This is an x-bar or variable bar. A single bar is equal to x. If you group three bars together it is a model of 3x or three times x. Note the x-bar does have a value, but it is unknown. Many students think the x-bar is equal to 5 units, but this is not necessarily true. It could be equal to 120. We will use a line segment to represent an x-bar in our diagrams. This is an x-squared tile. A single x-squared tile equals x 2. The model for 2x 2 would be two x- squared tiles grouped together. Remember x 2 means x x. We will draw a square to model this tile in our diagrams. THERE ARE THREE DIFFERENT SIZES OF TILES

4. Example: 2 x 2 + 4x + 3 Model: Diagram: Algebra Tiles can model algebraic expressions. Here is an example.

5. Algebra Tiles can model equations. To do this you will have to know the goal and one rule… GOAL: To get one x alone on one side of the equation. RULE: Do the same thing to both side of the equation.

6. Lets model the equation… 2x + 1 = 7 Imagine a balance where the equal sign is the fulcrum. 2x + 1 = 7 Remember our goal is to get one x alone… Take one unit from each side Split the remaining tiles into two groups One x tile balances with three units X = 3

7. Example #2 4x + 7 = 2x + 11 X = 2

8. Example #3 5(x + 3) = 2(5x + 5)