Thankfully, I saved a bunch of math tasks this summer and attempted to categorize them for future reference. One of these tasks turned out to be the perfect introduction!
I found this task on the Riverpoint Advanced Mathematics Partnership - Algebra (RAMP-A) website.
Here's the original task:
|Task Source: https://sites.ewu.edu/jcoomes/math-tasks/|
Your math teacher has recently come into a large inheritance. She announces that during one period of the day she is going to give one lucky student in the school some money. The money she will pay the winner will be determined by one of the functions below, where x is the period of the day in which the money is awarded.
A(x) = 2^x - 1
B(x) = 2x
C(x) = 2x^2
She hasn't decided which period of the day she will give the money away, but she has decided that the student who is chosen will immediately have to choose which function they would prefer to be paid by. Assuming you are the winner, how should you choose?
After reading the task, students were full of ideas and opinions. I tried to help them focus their ideas a bit by asking them to consider which function they would choose if their math teacher deemed them the winner 4th period.
It was fun to watch the students' opinions change as we worked out the values for each function. In their words "B is trash!"
After working out all of the function values, we graphed each function on the coordinate plane. We had a good conversation about how to label our axes. In retrospect, I should have made the graph a bit larger because counting by 5's on the y-axis only got us to 120 when our highest value was 127. Some of my students suggested counting by 10's, but that would put us at 240 with almost half of the graph not being used. We decided to count by 5's and have one of our points slightly off the graph. Of course, a few students suggested we count by 7's or 9's.
As we graphed each function, I had students label the function type. This was my students' first experience with the terms linear, quadratic, and exponential. The conversations surrounding why each function was labeled its appropriate name was so refreshing to hear in my classroom!
We summed up the task by writing how we would choose the function if we were the winner. This was definitely a worthwhile way to spend the majority of a class period.
I've uploaded my version of the task here.