Transformations with
High School Pre-Calculus

submitted by: Ashley Butler
on Sun Sep 18 19:09:46 2005

Back to Math Tools
Course: PreCalculus
Topic: Transformations
Resource type: Tool
Catalogue entry:
Resource location:

I am a student at Utah State University in the Math Education Major. I used the transformations lesson, found on the eNLVM, as a lesson tool for a clinical I was to teach at Logan High School to a Pre-Calculus class. I was teaching the students about graph transformations, a concept that they had been taught already but were fairly new on.

I started the class with a warm-up activity to get their minds thinking along the lines that I wanted them to be thinking. This was a visual warm-up that I had created by using a big poster board, drawing a grid on it (with the coordinate plane centered on it) and collecting some bright colored push pins and red and yellow yarn. In the class, I wrote an equation on the board and asked the students to help me graph it. They told me where to stick the pins (plotted points along the equation graph) and then I connected the points (pins) with the red yarn. Then I made an alteration to the equation I wrote on the board. I asked them what would happen to each point on the graph and had a student come up and put some new pins at the new points and then we connected them with the yellow yarn. I repeated this activity several times with different alterations being made the first equation.

When I was convinced that they were freshened up on transforming graphs, I introduced the activity that we would be doing next. I demonstrated to the class on the overhead the steps they would take to log into the enlvm, find their class, and create a password. Then we came to a list of activities, staring with warm-up, and going through reflections, translations, dilations, and multiple transformations. The list finished with the practice quiz and the quiz. We went into each of the first activities on the list and did one from each activity. Since the students seemed (by their involvement and responses) that they knew what was going on and what to expect, so I sent them to the computers and had them begin with the warm-up.

As I observed them working, I noticed that a part of them were moving really fast, almost to the point of being bored, some were moving at a constant pace, but still stopping to think about things and discussing with neighbors what to do and what was going on (which I encourage of my students I work with) and some were really lost, maybe from lack of computer knowledge and maybe some because of the concept being covered in the activity. I think when I do this activity again, I will create some activities for students who go ahead and finish the activity to do that is a bit more challenging and would have them thinking more deeply about the concept so that they don't feel bored at the end. The students who lagged behind maybe should have been sat by one of the faster students so that they could collaborate and both would be benefiting from the experience.

The problems I found with this activity were that some of the students needed more of a challenge and some were behind simply because of computer skill and so did not benefit from the math activity as much as I would have like them to. Some students seem so computer shy that they were not relaxed enough to play with the program and observe the transformations. Some students were so eager to finish the assignment that they also didn't play with the activity and learn that way. I think given this opportunity again, I will pair students (given that I know my students better than when I just show up at a clinic and don't know any of them) so that they can discuss and play and work together, one benefiting from explaining the concepts, the other benefiting from understanding the computer enough to experiment with the concept. Also, I would create another place to put the quiz and practice quiz. It seemed that as soon as students saw this at the bottom of the activities, all attention was lost to the purpose of the activity, this being to have fun with math and play around with the program as they experiment with the equations and see what the graphs do.

I found the program to be beneficial to the students. As I walked around, I talked with several students who had questions about the questions being asked in the activity. Instead of just answering their questions, I worked on the activity with them and together we discovered the answer to the questions. After a while, I noticed students doing that with each other and I noticed students playing around on the program to answer confusing questions. Some even went on to create hard problems just to see what would happen. They relaxed and began to experiment and have fun. This is when the real learning can began, and I feel given another day with it, I could have taught them a whole lesson, from beginning to end without class discussion beforehand, and they would have had a more thorough understanding of transformations, then concluded with a class discussion.

Send comments to Ashley Butler at

[Privacy Policy] [Terms of Use]

Home || The Math Library || Quick Reference || Search || Help 

© 1994- The Math Forum at NCTM. All rights reserved.