Algebra Tiles

What are Algebra Tiles and how do you use them?

Standards. CA & NY 6.EE.2 - Write, read, and evaluate expressions in which letters stand for numbers.

Mathematical practices: 1. Make sense of problems and persevere in solving them; 4. Model with mathematics; 5. Use appropriate tools strategically; 6. Attend to precision.

In our readings for last week, I came across something I had not heard of before: algebra blocks (aka algebra tiles). I wanted to know what these manipulatives were and how to use them. I found this virtual manipulative on the NCTM website: Algebra Tiles

At first glance, it was not apparent to me how these were meant to be used, but I played around with them for a while and I think I can explain the basics.

The board shown in this version of algebra tiles has a vertical line down the center which represents the equal sign. Everything to the left of the equal sign in your equation should be represented on the left side of the board and everything to the right on the right. 

Small square yellow tiles have a value of 1 and long green tiles have a value of x. (Large square blue tiles represent x squared but I’m not going to get into that function here.) The red versions of each of those tiles represent -1 and -x.

The object is to simplify the equation to the point where you have only one “x” on one side and the correct number of ones on the other. Here is a video to help explain: What are algebra tiles?

Step 1: Build your equation.

The app will give you an equation at the top that you are meant to build using the tiles. I’ve started with a simple one: x + 3 = 4.

I need to place tiles representing the x and 3 ones on the left and 4 ones on the right.

Step 2: Verify your equation.

Click the check to verify that the equation has been set up correctly. If it is, the top of the board will show (x = __) to let me know I can go ahead and solve for x. 

Step 3: Solving for x. 

The idea is to simplify the equation by ‘zeroing out’ everything but x and the number of ones that represent its value.

First I will add 3 negative ones to each side. 

Then I can delete the zero pairs.

And I’m left with an x on the left and a one on the right which means that x = 1.

Step 4: Verify your solution.

Enter “1” in the white box and click the check.

 

Of course, they do get more complicated. Take look at these screenshots from 2 - 3x = -2 - 2x.

Step 1. Step 2.

Step 3.

 

Step 4.

Overall, I think this is a good tool for beginners because it gives students the opportunity to actually balance an equation by adding and subtracting from each side. It also encourages students to see “x” as an actual entity with value instead of just a confusing letter thrown in with all the numbers. 

I still don’t fully understand this app, though - because I reached a point with one equation where I had no idea what to do next. The goal is to simplify the equation so you have only one x on one side and the value of x (in ones) on the other. The program doesn’t allow you to divide, or at least, I couldn’t figure out how to make it divide. In the example below I am left with 4x = 4 but the program won’t let me enter x = 1 until I’ve reduced the equation down to one x. If someone can figure this out please let me know!