I started planning for Algebra Support this weekend, specifically related to their lessons on Algebra Tiles – what they are and how to use them. I needed to start by sketching out what I wanted their notes to look like by the time the lesson is over. I wrote out 5 pages of notes (in a composition notebook) – 1 page each on the following:
- What each type of tile usually represents and how to create expressions with them
- What the Zero Principle is and how it works with the tiles
- How to show adding and subtracting polynomials with the tiles
- How to show multiplying polynomials with the tiles and a product mat
- How to show dividing polynomials with the tiles and a product mat
(Writing out the notes like this gives me the added bonus of having a master copy that I can tell students to copy into their own notebooks when they are absent. This has always seemed like such a great idea to me that I never really get around to implementing effectively.)
When I say “dividing polynomials”, I don’t mean polynomial long division. I’m using it as a sort of intro to factoring – if I give you the multiplied expression and one of the factors, use the tiles to find the other factor. I’m hoping that this will help the students make the connection to factoring – when you have to find both factors. Since I’m planning on getting to this concept before one of the Algebra 1 teachers gets to factoring, I’m hoping it will help the students understand what they’re doing when they get to that point. (I don’t know what order the other Algebra 1 teacher is using for all the quadratics skills we are teaching in January, so I’m going to have to find out this week and adjust to figure out how to assist those students.)
Ok, now for some pictures of the pages I’ve put together.
First, intro to Algebra Tiles and how to use them to represent terms and expressions:
I changed my mind on this page – I’ll be using a 6-door foldable on the top half of the page for the different tiles instead of just writing them. I’ll try to remember to update this post when I have the final version of the page.
Next topic: Zero Property
The first page is all examples that will be copied during class. The second page is the practice problems that the students will do and record in their notes for reference.
Next topic: Adding and Subtracting Polynomials
This topic is actually two pages long because I put subtracting on the second page. There are two problems on each page – I’m planning to do the first one as an example and have kids do the second as practice.
Quick note – in the subtraction section, I’m using the terminology we’ve already introduced when the kids learned to subtract polynomials in December. I didn’t use the tiles then (which I’m sort of regretting now but I didn’t have time), so we taught them to “distribute” the negative sign and then just combine all the like terms. When we do this with tiles, I’m going to keep the same terminology and we’ll do that by flipping all the tiles over to their opposite side.
Next topic: Multiplying Polynomials
Yeah, I never got around to coloring these pages.
We’re going to start with what they know – using an array to multiply 3*5 – then see how to expand that to variables. I’ve already exposed them to this idea because we’ve used “the box” to multiply polynomials already. I want them to make the explicit connection to the tiles.
Last Topic: Dividing Polynomials
The practice problems on the second page are for the kids to do in class. (Notice the second one is actual factoring!)
When we actually learn about factoring, my intention is to continue using the tiles but also emphasize the notation on paper, because the kids need to be able to factor
quickly in less than an eternity in their Algebra 1 classes. Involving negative signs in the process also complicates things a lot when you use the tiles, so I’ll have to handle that very carefully. (I haven’t planned the factoring unit yet, so this is a bridge I’ll cross when I come to it.)
We’ll see how this goes. I am hoping to keep up with my goal of posting at least once per week this semester better than last semester, so hopefully I will be able to update any curious readers about the effectiveness of my approach.