Factoring trinomials has been the bane of my existence as an Algebra 1 teacher. It's not that I don't like it... actually, that's exactly it. I'm not a fan. Don't get me wrong, as a math teacher, I completely see the usefulness of seeing the roots to a polynomial function laid bare before me. However, for the amount of time and effort we put into teaching Algebra 1 students factoring quadratic functions when the a-value isn't one, I don't see a lot of payoff. Plus, most of my students just see it as shuffling numbers around until someone tells them to stop. Kind of like musical chairs with factors. Not helpful.
Rather than continuing to use an obviously losing strategy, I let desperation lead me to something else this past February. I convinced my school to buy me a classroom set of Algebra Tiles off Amazon. I also found a great set of online Algebra Tiles. This is my first year ever using these things. I'm still figuring it out.
I started using them as soon as we started the chapter. We started out with multiplying binomials. Normally, I would just use the area model and the distributive property. Here, I forced students to use algebra tiles. Forced. They moaned and complained. I persevered because I knew what came next: factoring. Now that we were attempting to find the factors of a trinomial, we used algebra tiles to create the area model and find the side lengths. I did zero teaching on this at first. Instead, I used the introductory lab at the start of my book's lesson. I had to do some serious reformatting and added a couple of questions but it went really well. Much better than I expected. Here is a link to the file if your interested: MS Word, PDF.
Once students figured out how to create the rectangles everything started to click. We were even able build rectangles with side lengths (x-3) and (x+4) which require adding zero pairs to the initial tiles. Very cool. At the end, I asked them to try and generalize our findings. How do you know a trinomial is factorable? You can create a rectangle out of it. The side lengths of the rectangle are the factors of the trinomial!
We were even able to extend this to when the a-value isn't equal to one. That's the biggy. I forced students to use algebra tiles all the time. This is the first time students started making the connections without me having to be explicit about it. After a couple of days, they were begging for a better way. Algebra tiles were great and all but they were too much work and when the numbers got big you needed to pile all the individual sets together to do it. Students begging for generalization in Algebra 1? That's a win.
Rather than continuing to use an obviously losing strategy, I let desperation lead me to something else this past February. I convinced my school to buy me a classroom set of Algebra Tiles off Amazon. I also found a great set of online Algebra Tiles. This is my first year ever using these things. I'm still figuring it out.
I started using them as soon as we started the chapter. We started out with multiplying binomials. Normally, I would just use the area model and the distributive property. Here, I forced students to use algebra tiles. Forced. They moaned and complained. I persevered because I knew what came next: factoring. Now that we were attempting to find the factors of a trinomial, we used algebra tiles to create the area model and find the side lengths. I did zero teaching on this at first. Instead, I used the introductory lab at the start of my book's lesson. I had to do some serious reformatting and added a couple of questions but it went really well. Much better than I expected. Here is a link to the file if your interested: MS Word, PDF.
Once students figured out how to create the rectangles everything started to click. We were even able build rectangles with side lengths (x-3) and (x+4) which require adding zero pairs to the initial tiles. Very cool. At the end, I asked them to try and generalize our findings. How do you know a trinomial is factorable? You can create a rectangle out of it. The side lengths of the rectangle are the factors of the trinomial!
We were even able to extend this to when the a-value isn't equal to one. That's the biggy. I forced students to use algebra tiles all the time. This is the first time students started making the connections without me having to be explicit about it. After a couple of days, they were begging for a better way. Algebra tiles were great and all but they were too much work and when the numbers got big you needed to pile all the individual sets together to do it. Students begging for generalization in Algebra 1? That's a win.
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