Made 4 Math #19 Parent Functions and Transformations
I'm really proud of myself for a couple of reasons that all pertain to the blogosphere. One is that I at least feel like I'm more on track this year based on what others are posting. It seems like every idea that comes up is either something I taught last week or something I'm planning for next week. That just makes my teacher heart happy.
Second, I took some ideas from other good bloggers and made two really good activities for my students. Teacher heart smiles again.
Third, my students really liked those activities. They said it forced them to read attention. They said they learned more than listening to me talk because they actually had to do all of the work themselves. They even said that students talked less because they were more engaged...they actually used the word engaged! Teacher heart passes out.
For my first activity, I shamelessly stole Pam Wilson's file Function Families Investigation. Her description reads: "modified through the years – this small group investigation allows students to learn how to enter different types of functions in graphing calculator; students group functions based on shapes of graph, then give a description of similarities in the functions’ equations."
With her permission I have modified it and will link to it here. The changes I made was to first type out very clear and very thorough directions on how to graph equations on the calculator because I knew my students would need it.
I also created a sheet of 16 graphs for students to sketch their answers on. I modified the equations so that there were 4 equations for the 4 parent functions I had in mind: linear, quadratic, exponential, and absolute value.
I basically used the same reflection questions at the end but I changed the graphs and added a couple of questions to the end.
Last but not least, I added a foldable at the end of the document. It lists the name and equation of the parent function as well as a description of what the graph should like. The space below gives room to glue 2 of the 4 graphs from each group. It works best to glue above and below the type. Then I had students fold the bottom up until it hits just below the parent function name. Then we cut the bottom half so that we have a 4 window foldable with tabs. I did not pass these out until students had completed the investigation and reflection questions.
The activity was awesome and very few people screwed it up. Here are some things to look out for: students graphed exponential functions as linear functions because they either ignored or didn't realize that the x was an exponent. Also, some students ignored the absolute value bars or thought that they were 1's. This resulted in students having 12 graphs with straight lines and 4 with parabolas...which made the sorting and analyzing next to impossible.
Also, students can't read. They would ask a question that was literally answered in the next sentence. Some just sat there waiting for me to tell them what to do. I warned them from the beginning that I was going to be a jerk and answer almost every question with "Read the directions". Then I proceeded to do so.
I made up a slide of the right answers but it just wasn't needed. And since students were working at their own pace, there was never an appropriate time to show it without ruining it for another student. Once they finally caught on...it was beautiful.
And so I proudly present:
Function Families Investigation
The foldable was printed separately on colored paper and made for a really nice transition into the next lesson...Function Transformations.
I planned this lesson to be an individual activity as well. You read the feedback from my students at the beginning of this post and that encouraged me to continue in that vein.
For transformations, I looked at several different bloggers' post but ultimately still created my own. I created a set of 8 transformation cards for the 4 parent functions with 6 sets to a page. The eight transformations were left, right, up, down, skinny/steeper, wider/flatter, flip, and then more than one combination of those.
For linear, I couldn't figure out if there was a transformation for left and right so I just didn't include those. Therefore, each student should have 30 transformation cards. I labeled them Transformation 1, Transformation 2, etc so that I wouldn't give away what the transformations were and I printed each transformation on a different color of card stock which greatly helped in the sorting.
From there students used their foldable to write in the parent function names and equations on all 32 graphs...which they hated and a lot of them skipped. I thought maybe I should just type them in but since I wasn't lecturing at all, I think this was an easy way for the students to commit those four function names and equations to memory.
They then sorted and found the cards for Transformation 1 and matched them to the correct graph shape (again reinforcing what they analyzed the day before). They wrote this new equation in the 'new equation' box and graphed it on their calculator. I plan to have students go back with a highlighter and highlight the part of the 'new equation' that is different from the original.
Next they graphed the new equation on their calculator and sketched it with a colored pencil on the graph. Now the parent graph is already on there and I did that on purpose so they could easily see what happens to their colored graph.
Therefore, the next step was for them to finish by answering the question "What happened to the graph?" This process is repeated throughout all 8 transformations.
And that ladies and gentlemen is Function Transformations:
The whole class hasn't finished yet but after they do we will go back and use the foldable to write down the transformations and the equation with the part that is causing the transformation to happen written in colored pencil.
My plan after that is to do a review game where I give students the equation and have them sketch the graph without a calculator and maybe vice versa where they have a picture and must write the equation. More to come on that...
My one annoyance is this...what do you do with the students who get done before everyone else? Oh wait, that's the same problem I always have. Maybe the real question is how do we get everyone else to speed up?