1. Equations with Algebra Tiles
Section 2.2 introduction — an exploration into:
Equations with Algebra Tiles

2. Equations with Algebra Tiles
Exploration
2.2
Equations with Algebra Tiles
You can use red and blue tiles to represent math equations. =
Equations show that two things are “balanced,” and you’re not allowed to do anything that might make them unbalanced.
This means you can add or remove tiles, as long as you do the same to both sides.

3. Remove 2 squares from both sides.
Exploration
2.2
Equations with Algebra Tiles
You can use tiles to represent equations. These tiles show that x + 2 = 5. =
When you have an equation, you can add or remove tiles — as long as you add or remove exactly the same tiles on both sides. =
Remove 2 squares from both sides.
If you can get x by itself, you can find its value.
Here, x = 3.

4. Remove 3 squares from both sides.
Exploration
2.2
Equations with Algebra Tiles
Example
Show the expression x + 3 = 5 with algebra tiles, and then find the value of x.
Solution
The equation x + 3 = 5 looks like the picture on the right. =
Remove 3 squares from both sides to get x by itself.
Remove 3 squares from both sides. =
This tells you that x = 2.
Solution follows…

5. Equations with Algebra Tiles
Exploration
2.2
Equations with Algebra Tiles
For some equations, you need to use zero pairs before you can get x by itself.
1 + (–1) = 0
Remember, a zero pair is one blue tile and one red tile that together have a total value of zero.

6. Equations with Algebra Tiles
Exploration
2.2
Equations with Algebra Tiles
Example
Show x – 4 = 7 with tiles, and find the value of x.
Solution =
The equation x – 4 = 7 looks like this.
Add 4 tiles to both sides,
and then remove zero pairs.
This leaves x on one side of the equation, and 11 blue tiles on the other side. So x = 11.
Solution follows…

7. Equations with Algebra Tiles
Exploration
2.2
Equations with Algebra Tiles
Example
Show 3x = –15 with tiles, and find the value of x.
Solution
3x = –15 looks like the picture on the right. Put the x’s in a line, and then put the same number of tiles next to every x. =
For every x, there are 5 red tiles. This tells you that x = –5.
Solution follows…

8. Equations with Algebra Tiles
Exploration
2.2
Equations with Algebra Tiles
Exercises
1. Use algebra tiles to model each of these equations, and then find the value of x: c. d. e. b. a. =
Add 3 blues to both sides
Remove zero pairs
x = 11 =
x = 3
Remove 6 tiles from both sides
x = –7 =
Add 2 reds to both sides
Remove zero pairs =
x = 5 =
x = –4
a. x + 6 = 9
b. x – 3 = 8
c. x + 2 = –5
d. 2x = 10
e. 3x = –12
Solution follows…

9. Equations with Algebra Tiles
Exploration
2.2
Equations with Algebra Tiles
Exercises
2. Write the equation that is represented by these tiles. Then solve the equation to find the value of x. =
This is x – 4 = –5 =
Remove 4 tiles from each side =
x = –1
Solution follows…

10. Equations with Algebra Tiles
Exploration
2.2
Equations with Algebra Tiles
Round Up
Keeping equations balanced by doing the same to both sides is one of the most important things you’ll ever learn in math.
There will be a lot more about this in the next section.