So it was really easy to see what 2(x+3) looks like in real form and when you actually make it with the tiles, one can easily see what the expanded form looks like and I think that could really help students who need some sort of visual to understand concepts.
So in the reverse, if you wanted to factor the expression, then in that case, you would be given the area of the tiles and you need to come up with the Length and Width that would form that pattern. So in order to do that, you first need to manipulate the tiles so that they make a square/rectangle shape once you have your square made, then its easy to see what you need to put in your x and y axis to make the square. Overtime you start to notice a pattern with these perfect squares where if you have x^2 and an equal number of x values, then you know how many small white tiles you need to fill up the remaining space.
What I also really liked was using the hanging number line to demonstrate to students how expressions would sit on a number line. So it is super easy to create, all V did was hang up 2 pieces of string one on top of the other. On the top string he put a paper marked 0, and on the bottom he put 0x.
From there he would show an expression, so for example 5x + 2. And he would ask us, where would you put this on the number line? We would answer, the bottom line because it has a variable in the expression, and then we would have to decide, does it go the right or left of the 0x. After that he would tell us that 12 corresponds to the expression and put the 12 directly above the expression on the number line without variables. From there he would hold up another piece of paper marked 5x and ask again where would we put this and why. From there, what would be the corresponding value for 5x and we would answer 10.
This demonstrates the number line
Hi Bonnie! Thank you for your post :) I really enjoy the discussion and lesson on algebra tiles as well. I had never heard of them until this class, not even in teachers college which I graduated from only two years ago. The article pointed out the benefits of using algebra tiles, but it was really helpful to see how they are used in person.
ReplyDeleteAt first, I was a little unsure about them, but once we continued to play and work with them, it became really clear how much of an impact this would have on student understanding of such an abstract subject as algebra. Leslie has mentioned that she would "never be scared of an x^2 again." I think that comment was quite interesting, because after all these years of not being able to grasp the concept of an x^2 something just clicked, which is something hopefully we can do for our students!
I enjoyed learning about this new manipulated that seems to never be mentioned, and bring it to life! Thanks for sharing :)