When looking at the blogger prompts for week 2 of the blogger initiative, I initially thought there was no way I would share anything. As I looked over the prompts more and more, I did realize there were two things I would like to share, if for nothing else, feedback on how to make them better. That is part of what I want to get out of doing this blog. Blogging is for me, it is going to be a reminder of things I have done and continue to do. It is a way for me to reflect on what I am doing as a teacher so I can get better. Hopefully, along the way, I will get input from others on how to do “it” better.

I read through some of the new bloggers with the NBI, and I saw a post, I Still Suck at Teaching (and how I am going to fix that). This year I have felt this way more than ever and with all of the changes in our state (Louisiana), I am not 100% sure how I am going to fix it this year, but I am working on it. This post struck me though that I need to be finding more investigative activities for my students to engage in, from Geometry through Calculus. I am the only gifted math teacher at my school and teach Geometry, Algebra II, Advanced Math, Pre Calculus, and Calculus. So, time is tough. But, I thought, I have nothing good to even share, I have to not “suck at teaching” and get it together!

Coming back to the prompt I decided on, it was important for me to find a few things I have put together myself to help my students with investigative practices or constructing their own reasoning. Yes, there are things in Algebra II that students just have to do more “rotely” such as simplify rational expressions. But, there are things that can be more investigative. That is what I am challenging myself with this year, finding those things and creating meaningful tasks for them.

When thinking through my documents, I remembered that I had created a hands-on approach to teaching piecewise functions. When I would stand up in front of the room and teach piecewise functions in PreCalculus, it seemed like it was just a mystery to most students. I would even say, “Imagine cutting the function off at the endpoints given to you.” Then, a few years ago, I thought, why don’t I have the students literally cut out the graphs. So, I created an investigation for piecewise functions. Most people are probably thinking, DUH! Why wouldn’t I have done this before now, but at least I have it now.

This is what I came up with:

I realize it isn’t perfect, but it seems to work. After doing this, almost every one of my students understand how to graph piecewise functions.

I realized I had another project, which I am sure many of you do, but I still thought I would share it. It is my culminating project for PreCalculus. I have had many great projects through the years. I need to take pictures of my projects from last year. I check them by putting the functions into the N-Spire teacher software on my computer. This is what I give to the students:

I know I have a ton to learn and hope to have things to share through the school year, so I “don’t suck” and work on getting better everyday!

Cindy W

Aug 27, 2012@ 00:00:19Oooh! I just teach Algebra and Math 8, but I’ve got great ideas about how to modify the first activity for my Algebra students. Piece-wise defined functions are a part of Common Core for Algebra 1! Love the “cutting it up” concept.

I have done the “Math Art” project in the past with high school students. Some of the stuff I got was AMAZING! Those who did the best job really worked at their transformations to make everything “fit” the way they wanted it to!

I might try something similar with just linear functions in Math 8 this year. By the end of the year, maybe my Algebra students could use quite a variety of functions – we’ll see 🙂

pitoinfinity

Aug 27, 2012@ 00:09:23You are right, with CCSS, everything is moving down which means piece-wise defined functions as well. I “teach” them when we do absolute value functions in Algebra II, but really get into them a lot in PreCalculus. We not only graph them, but I have them understand them by finding things like f(2) so they have to understand what the notation really means. It would really help them to understand them a bit better if we did them in Algebra I. It is great that there are ways you can take this and modify for Algebra I or even Math 8th.

I need to take pictures of my projects from last year. I do have some on my computer at school, but sadly, I didn’t back it up since I save almost everything to my dropbox. When I turned my computer on a few weeks before school started, it just died. Motherboard = DEAD. So, I don’t have the ones we put in the computer N-Spire software, but it was neat because I could see all of the pieces and everything.

I would love to hear what you do in your class this year. I don’t know where you are teaching, but I am in Louisiana. I am excited for the change to CCSS because we are behind in our state standards from where I find other states at. 🙂

Cindy W

Aug 27, 2012@ 00:01:25Aaack! Delete my first comment. I fixed a typo and then it posted the whole thing again. Sorry 😦

pitoinfinity

Aug 27, 2012@ 00:11:13Done 🙂 and not a problem at all! I would never have known.

Rebecka Peterson

Sep 05, 2012@ 00:43:31This is awesome. I love the step-by-step instructions for (at least) two reasons: (1) The STUDENTS are doing the work! (2) The students are READING! Wohoo for literacy! Love this. I’m bummed we’ve already covered piece-wise functions in Pre-Calc this year. Maybe I’ll modify this activity for Test 1’s review later this week…

pitoinfinity

Sep 05, 2012@ 05:45:04Thank you! When I would teach it, I would say every time, imagine you were cutting up functions and putting it on one graph together. So, one day a few years ago, I finally said we are just going to do it. I am trying to find more things in the curriculum where students can do more inquiry. Hope you enjoy! Let me know how it turns out if you do it for review!

Rebecka Peterson

Sep 13, 2012@ 21:28:21Worked great!! Wrote about it here: http://www.epsilon-delta.org/2012/09/week-4-writing-piece-wise-functions.html