Algebra Tiles

Algebra can sometimes feel like a puzzle of letters and numbers. Algebra Tiles turn those symbols into physical objects you can see, touch, and move!

2x − 3 = 5

The Tiles

Here's a template of the tiles:

or
,
cut out the tiles, and let's get started!

Each tile represents a different part of an expression. Use the labels to help you identify them:

Small Blue Square: +1
Small Red Square: −1
Green Rectangle: +x
Orange Rectangle: −x
Large Green Square: +x²
Large Orange Square: −x²

Notice the size: If you put some small unit squares in a row, they won't quite match the length of the x tile. This reminds us that x can be any value!

For the Black and White version you can color your tiles Positive (+) on one side and Negative (−) on the other, and use any colors you want!

Activity 1: The "Zero Pair" Magic

Before we do math, we need to know the most important rule: The Zero Pair.

If you have one positive tile and one negative tile of the same size, they cancel each other out. It's like taking one step forward and one step back, you end up at zero!

Your Turn! Lay out 5 positive unit squares and 3 negative unit squares. Remove the "Zero Pairs." What's left? (Answer: +2)

Activity 2: Building Polynomials

Try to "build" these expressions on your desk using the tiles:

2x + 3
x² + 4x − 2
−2x² − x + 5

Activity 3: Adding and Subtracting

To Add, simply put both sets of tiles together and remove any Zero Pairs.

To Subtract, start with your first set of tiles. If you need to "take away" tiles you don't have, add Zero Pairs until you do!

Example: (2x + 2) − (x + 3)

Start with 2 "x" rectangles and 2 small squares
It is easy to take away 1 "x" rectangle, but how do we take away 3 small squares? We only have 2
Let's add one Zero Pair (a +1 and a −1). Now we have three +1 tiles to take away
Remove the x and the three +1s, for −(x+3)
Result: We are left with x − 1