## Introduction: Algebra Tiles

Algebra Tiles are a new way of teaching algebra to students who are just beginning to learn the basic concepts.

This instructable will show you how to use an Epilog laser cutter to make a set of the useful tiles. If you do not have a laser cutter, you can use Ponoko or similar laser cutting services to make yours.

## Step 1: Supplies

The supply list for this project is:

Sheets of Acrylic (32 dollars for a 24x34 inch piece from Tap Plastics)

A Laser Cutter

The template that is attached

I included 2 templates, one for 1 set and one for a set of 39. They can be edited in corel draw or a similar program.

## Step 2: Laser Cut the Acrylic

My laser cutting settings were as follows:

Engraving: 400 dpi Speed: 100 Power: 40

Cutting: 400 dpi Speed: 10 Power: 100 Frequency: 5000

I removed the paper off the acrylic as to help the engraving, with the paper on you'll have to change your settings.

## Step 3: Finished Tiles

Once you laser cut them, use a toothpick to poke out the extra plastic. Then you are left with the pretty tiles.

## Step 4: How to Use the Tiles

The tiles are used to show kids how perfect square trinomials work. There are three main tiles in this set:

x^{2} Tile which has side x

x Tile which as an x and a 1 side

and the 1 Tile that has a 1x1 sides

Each tile has a positive side (denoted by the lines) and a negative side (smooth side)

In our picture example we see the trinomial:

x^{2} + 2x + 1

When the tiles are fitted together we see it makes a perfect square, and looking at each side we can see that each side makes up x+1

Therefore the prime factor of the trinomial is (x+1)^{2}

## Step 5: Final Thoughts

For teachers looking for a more visual way to introduce algebra concepts to students algebra tiles are perfect. If you have access to a laser cutter or willing to use ponoko you can get a set of these tiles pretty easily.

I hope to present more concepts on how to use algebra tiles in the future, if you use these tiles in your classroom please comment and tell me how you use these neat tiles!

thanks. emlak

I agree these are a great tool to teach/learn algebra -- I hated them :) -- I was a very paper math person, so I could just visualize the problems and the plastic bits just confused me. Lots of my classmates raved about them. Knowing they are an educational product, the teacher warned us not to lose any because each set was ridiculously expensive (in the $50/student range for a small box of pieces.) Perhaps it would be cool to include just the dimensions of the pieces for those of us who are condemned to using a lowly 'saw' to cut pieces :D

Talking of ridiculously expensive stuff in my chemistry class we used some sticks and round balls with holes to demonstrate the bonding angles of atoms and my teacher said they were like $200 a box. I think we got most of them from college students who didn't need them anymore though. But back on topic I've never used these and glad I didn't. I would probably get confused also. I like pen, paper, and plenty of sleep in my math classes. I've seen these in math books before though and they were intriguing, but I have never had a problem understanding math. Maybe that is because my teacher is amazing though.

someone made 3d printable versions on thingiverse

I was a very brain math person. The paper only had question numbers and answers.

> the dimensions of the pieces

. Just pick a number. The 1 piece is that many pick-your-unit-of-measure on each side. The x piece is that many pick-your-unit-of-measure on one side and twice that many pick-your-unit-of-measure on the other side. X

^{2}is twice that many pick-your-unit-of-measure on each side.the x piece is 'unit x about 2.5*unit' -- not just twice as long. Otherwise, it can be easy to confuse and say x = 1+1 etc.

. So it actually takes ALL the pieces to make X

^{2}(not just the piece labeled X^{2})?it means you can have something like x^2 + 2x + 1 makes a perfect square...x2 is the larger square. All I was saying is the x pieces are not just a 2:1 rectangle, or it would be easy to say 2x = x^2 = 1+1+1+1

. Oops! I guess I should have paid more attention to Step 4. Thanks for splainin' it to me.

Thank you emlak

Isn't x=.125 similarly confusing for the observant student? Maybe different colors can be used for variables and constants. Very nicely made.

Use different shapes and colors. If I where a student looking at this I would think that since the X is twice the size of 1, X = 2, and since X ^ 2 is equal to four 1's, X^2 is 4. If you are teaching math, make sure that your students understand that these props just represent abstract ideas. If you don't, students will assign imaginary significant to objects and this will harm them later on.