I am kind of excited about this (bonus) test question I used today . . .
My advanced algebra 2 students just finished studying a few of the basic parent functions and their transformations. Today, they took a test.
First there was a standard paper/pencil part of the test. Nothing unusual here.
Next, they picked up one of these cards containing the description of a parent function and a transformation.
The cards were color-coded according to difficulty level. Students were free to choose. Every card is different, so you won't be working on the same graph as your neighbor. Students were to pick up an iPad and use Desmos.com to create the function described.
Green Cards: Create a graph using a given parent function and animate one given transformation.
Purple cards: Animate two given transformations.
When finished, students bring me the iPad. I check that the graph matches the description, stamp the card, and clear out the graphs for the next person.
I was really pleased with the results. Almost everyone was successful in creating their graph. I don't feel like this needs to be a bonus question next time. It might even become a regular part of test-taking in my classroom.
Now I am thinking about the possibilities. My head is already spinning with ways I can use this question format for other topics:
Quadratics/Polynomials: Create a function with given vertex or given zeroes. Can you keep the vertex in place while animating the zeroes? Can you keep one zero in place and animate the other(s)? Create a function with given end behavior.
Systems: Create a system with one solution, no solution, or infinite solutions. Create a system with a given solution.
Rational function: Create a function with given vertical and/or horizontal asymptotes. Animate one or both asymptotes.
P.S. If you are wondering what we did in class BEFORE this assessment, here is a quick summary:
1. We spent several days sketching parent functions and transformations the old fashioned way, using paper and pencil. Students completed tables and plotted points, sketched graphs, looked for patterns, and generalized their discoveries.
2. Once students had mastered the basic functions and their transformations, I spent one class period introducing Desmos.com. I reserved our math department's shared iPad cart. I showed students how to enter equations, create sliders, and click play to ANIMATE (<3). They were as enamored as I was when I saw this a month ago at TMC13! Then I just let them play.
3. Finally, I started giving them a few challenges. Try to make an x^2 that moves vertically while stretching. Can you keep it from turning upside down? Can you restrict its movement to the second quadrant? Can you make it move horizontally along the line y = 2?