We had a fun day in Accelerated Algebra 2 and all the kids were working hard. We are learning all about rational functions now. I explained to them that as a teacher it can be challenging to come up with just the right problem to put on a quiz. Maybe I want them to graph a rational function that has 2 asymptotes and a hole. I need the equation to work out nicely, so I have to play with it a bit.
I told them today they were going to be the teacher and create 4 rational functions to graph. I had grand plans that we didn't get all the way through, but they did the meat of the lesson. Originally I created a teacher answer key for them as the teacher to complete. They had to write 4 rational equation in factored form and graph them on www.desmos.com/ Then, they had to write them in standard form, fill in all the properties, and sketch the graph - essentially, creating an answer key. This was as far as we got and I collected them because I didn't want them to get lost over vacation.
I intended for them to then write the standard form of each on a student form and trade with another student. They complete all 4 problems and give it back to their "teacher" who checks it with their answer key. But, alas, no time.
However, the conversation was rich and wonderful. Even I was learning and that is super for the day before vacation. I originally asked them to create a rational function with 1 vertical asymptote, 1 horizontal asymptote, and 1 slant asymptote. Ah, but you can't. Why not? It was a good thinking question. There were more questions to come - what's the difference between a reciprocal equation and a rational equation? How do I "create" a hole? How do I know the x-intercepts? the range? All good. Next year, I hope to have 2 days to complete this and actually get to the student part.
Here is the lesson: Graphing Rational Activity
Here is a picture of the class working hard: