Not like I’m opinionated or anything, but if you are teaching students younger students (or struggling students) algebra and you are not using Algebra Tiles, then you are missing the boat! Not that I can be too judgmental, I had them on my shelf and missed fabulous opportunities to use them all year.
I bought them solely for multiplying polynomials with my 7th graders. I only bought a few sets because I didn’t want to waste too much money if we all hated them. I have taught older students Algebra (Pre-Algebra, Algebra IA, Algebra IB, Alg II for seniors) many times in the past and never used them. With those classes the kids had seen Algebra before, sometimes many times, and I didn’t think it would benefit them very much. The tiles seem very elementary, not to mention a lot of trouble, and I was afraid it would be, “too little, too late”. So yeah, I was WRONG again.
I pretty much bought them for one purpose. I wanted to show 7th graders who had never multiplied x by x to SEE the difference between
x + x = 2x and x times x = x^2.
Plus, they are young (12-13) and thus more concrete thinkers so I felt it was a good tool to use for this age group. I wanted to explore taking them from the concrete to the abstract with Algebra Tiles. I was skeptical but hopeful. I’ll try anything once!
However, once I pulled these things out though there was no stopping us! For the first time ever, my students did not mix up 2x and x^2. W-O-W. If you’ve taught Algebra before, you know that is big. My students knew not only what it meant, but what it looked like. They knew why the 2x and x^2 were different. They did not ask me a gazillion times if it was 2x or x^2. And if they did, all I had to do was pull out three tiles and viola – instant understanding. I mean, HELLO – Look at them! They look nothing alike! You cannot ask for a better explanation than that!
One thing that I discovered that really helped my students is how you can represent negatives with the tiles. This was wonderfully helpful with multiplying a negative through a polynomial. My kids always stumble over that or even “forget” it. However, since we have been doing the tiles they can see what they are doing and are no longer forgetting it. Bonus!
I bought them to teach polynomials to 7th grade, but once I got them out, I have not put them away! The tiles put ACTION with the MATH. More great uses for the tiles:
- Illustrating the distributive property. As fun as “The Claw” is, seeing is really believing for my students.
3(x + 2) is just THREE sets of x and three 2’s. (Ahhh,… so THAT’s what we’ve been doing all year.)
- Negative Operations – The opposite of a positive number is it’s negative. For the tiles, to get the negative (or opposite), we flipped the tile over to the other side. (one side is yellow – positive, the other is red – negative). This can even illustrate basic concepts, like – (-4). What is the opposite of -4? Flip it over and see!
- Multiplying a negative + distributive property. – (x – 3) or -2(x – 4). When you see – (x – 3) you are taking the opposite of (flipping) everything inside of the parenthesis.
- Equation solving – I draw a line down the center of the paper and use the algebra tiles to solve equations. When kids tried to subtract 4 from 6x, I would take out 6 x-tiles and 4 constant tiles and say, “Now, how can I combine these?” The answer, “Oh you can’t, they aren’t like terms.”
- Equation solving – divide by a number. 3x = 6. Three x’s = 6, so one x must be 2. Then, I would split the x’s and line up the constants on the other side, dividing the x’s.
- Equation solving – FRACTIONS. x/2 = 3 . If HALF of an x = 3, then what does an entire x equal?
- Multi-step equation solving – This was especially helpful when I was teaching multi-step equations. With tons of tiles spread out all over the paper, the students could easily SEE that of course I needed to combine like terms before trying to get x alone on one side!
(I used Hands On Equations at the beginning of the year, but I think that the Algebra Tiles beat them “hands” down. They are just more intuitive, especially when it comes to the negatives.)
Of course I still do my crazy songs, dances and rhymes so that math will be stuck in their brains – FOREVER. (And yeah, I just LOVE to sing and dance!) But, I think that it is important for every student to know what they are doing, and not to just be following random steps! So, one day in the future, when they can’t get our annoying equation song out of their head, maybe they will also recall the Algebra Tiles, and remember WHY x times x = x^2 and NOT 2x.
Links:
Algebra Tiles Video
Interactive Online Algebra Tiles
I Speak Math 