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I really liked how this Win Some Cash task went with my Algebra 1 student!

Yesterday, we started graphing functions in Algebra 1 by making input/output tables.  I wanted to find a task to use with my students to introduce the concept without just jumping into a million practice problems.

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.

I modified the task wording slightly.  Here’s my take on the task.  It’s formatted to glue in my students’ interactive notebooks.

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.

When I did this task again in 2018, I realized a mistake I made before.

Last year, I had my students connect the dots to more easily see the shapes made by exponential, linear, and quadratic functions. This year, I highly emphasized discrete vs. continuous graphs and when it makes sense to connect the dots and when it doesn’t.

This is actually a discrete function, so we couldn’t connect the dots this year. With this in mind, I’d like to edit the activity a bit next year to bring out the general shapes of different types of functions more clearly.

Also, note to self: make the graph bigger. I made a note about that last year, and I forgot to fix it before printing it again for this year!