Wednesday, March 27, 2013

Factoring Trinomials (A not 1) - The Unconventional Way

My Algebra 2's today were dealing with factoring (4 different ways). This is typically an Algebra 1 skill but we place it in Algebra 2. We deal with GCF, Difference of Squares, and the two types of Trinomials. Last semester, I found a really funky way of factoring trinomials and this semester, I finally put a story behind the method.

The story goes as follows. We start by always looking for a greatest common factor as he gets carried on to the final answer. (He doesn't deal with the shenanigans that are to follow). Then, the evil King Trin kidnaps the new A coefficient and hides him away in the C value. This has now disguised our trinomial as a trinomial where A is 1. This is then easy to factor by looking for a value that multiplies to be C but adds to be B. After this trinomial has been factored, we come to the rescue with the A being placed back next to his x. However, there is an impostor in our midst. To find the impostor, we take the GCF of each parentheses. The impostor is then revealed and he is banished from the kingdom. The leftover factors then rejoice and rejoin with their original GCF. They then live happily every after <3.

The kids had some fun with this story as I was told all day long that it was not nice to kidnap values and then make them go poof. When the impostors are banished, a few kids claim that they are stabbed but I just say they are forced to go away.

This can be a fun method and an easy one too especially if the original A value is not so nice :)

Friday, March 1, 2013

Real World Matrix Stations & Gallery Walk

Nearing spring break! Nearing spring break! I'm one week away from being on spring break! But before I get to fly away, I have to finish my second unit with the kiddos. The second unit has to do with systems and matrices and I for one, LOVE MATRICES! I'm not sure why but for some reason, I love that there is a pattern. For the most part, the kids so far seemingly enjoy them as well. But today, I of course needed to give them a context, some real world applications so we embarked on the word problems.

Last semester, I tried doing stations where kids had to go around the room to answer the various questions and they hated it. They got overwhelmed and just wanted to call it quits. So this semester, I decided to change it up a bit. I still love the idea of stations, getting my kids moving, but I decided that because this topic can be difficult, it'd help if they had partners to help them.

I started off the lesson by doing an example with my kiddos and asking them for thoughts on what I should do and how I could solve this using matrices. I took their thoughts and asked question where they explained why they were doing these actions and finally came to our conclusions. We talked about what made this problem difficult was the fact that we had to decide how to set up our matrix equations. This of course, is the issue with these types of problems, How do I set it up so that I get the results I want?

So I split the kids into groups and each group got a question to answer together. Then, they were to create a display illustrating their work and explaining how they know their answer was correct. The kids who are in my class again decided that they liked this way much more which was quite reassuring. Plus, the kids loved that they were able to create some "art" in their math class. Great way to end the week.

After the kids created their poster, we hung them up on the wall. Once the class was done, we selected a representative of the poster to defend their work and explain their work to the gallery attendees. The rest of the class then walked around the room and attempted the problems and asked questions about how students set their problems up.

The best part was the fact the kids came up with different ways to solve the problems throughout the day so I got to encourage each group to find another way to set up the problem. After the lesson, we talked about how they felt and for the most part, kids thought they learned a lot more and could handle these types of problems.

Oh, of course my last class of the day didn't get to the gallery walk so I started giving groups the other problems when they were waiting on other groups to finish. Stupid Friday Funk....

Another thing, something I would change would be to create more structure with the gallery walk. Perhaps a "passport" with spaces for the kids to take notes at each station that way we can guarantee that they've made the journey to that station.

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