My Algebra classes are learning to factor quadratics right now. I enjoy factoring, but I'm a nerdy math teacher. My students are going to need to be adept at factoring to tackle more complex problems in higher math classes, so I need to get a good deal of quality practice in for them this year.
We did a really successful exploration with Algebra tiles this week. I was able to build on prior knowledge from multiplying polynomials recently when we first used Algebra tiles. The students worked in groups of four to build models and analyze their work, building up to the observation that the factors of a trinomial with leading coefficient a=1 (ax^2 + bx + c) can be written using the numbers that add to b and multiply to c. If you use this activity, you'll find that students get held up at letter F because they first have to use a zero pair in that question. They will also struggle with G unless they again use zero pairs. Only about 10-20% of my students were able to find the relationship between b, c, and the factors without some additional scaffolded questioning from me. I asked them to go back to the standard form and the factors for each question and look for a pattern. Example C is especially useful for getting students to see the pattern.
You can download the Algebra tiles exploration here. It's meant to be attached to an interactive notebook when folded in half; that's why there's a blank area.
The exploration took three days, about 30 minutes per day, perhaps less on the final day. At the conclusion, we wrote down some extra examples of factoring quadratics with a leading coefficient of 1. Then, I did a scavenger hunt around the classroom. It's not typed up but I might work on that over the weekend if anyone is interested in it. Note to self and others: make sure you shuffle the cards really well. I shuffled them back to their original places in some bizarre mathematical anomaly and my students just ended up going in a circle à la stations. Ugh. I only heard a few (dozen) complaints from the kids about my goof.
Today, everyone had finished the tiles and the stations but I wanted to incorporate some fun practice, especially because one class had gotten ahead of the other and I wanted to even things back out. Does anyone else do this? I can't stand being 20 minutes apart from one section to the other, so I sometimes build in an activity that I know I can cut from the class that's behind. It helps me stay sane to have my classes doing the same lessons. I went to an activity that I used last year and it was well received by the kids.
Tic Tac Times is a game that nearly tricks kids into factoring. I learned my lesson from last year and taught students the winning strategy before they started. I showed them what would happen if I just randomly chose two factors (I'd end up somewhere random and possibly far away from my other squares) compared with how I could use factoring to select the factors that matched a box I wanted to claim. Most kids caught on quickly. One girl was ecstatic, "I actually did something right!" when she beat her partner in just a few moves. Another team decided to see if they could fill the board before either of them won. I told them that was fine; they would be doing more math. Only one pair out of 48 students asked, "What should we do when someone wins?" because everyone else just started right into a second round. I also explained the strategy of occupying a factor that your opponent needs to keep them from winning. Again, in order to do that, the student must factor squares that his opponent might want to mark.
It was a great day and I finished class with an exit pass of three questions. 48 of my 56 Algebra students were in school today. Of them, the scores were:
3/3 = 44 students
2.5/3= 2 students (one had a sign error, the other wrote a 3 instead of a 2 for no apparent reason; oddly two of my most solid performers)
2/3 = 1 student (thought one problem couldn't be factored when it could)
0/3 = 1 student (wrote no answers, only the questions; we're working on it)
How do you introduce factoring?