In August, I know we will be introducing several parent functions to our Algebra 2 students. Our Algebra 2 curriculum is built around the study of functions, consistently analyzing how the values for a, h, and k affect the graph, how the equations are used in context, and learning to manipulate and interpret the equations.
I'm thinking that both last week and this week's problems can be used as illustrations for basic functions. (Although I'm still puzzled by last week's problem a bit. I read someone's comment that tire marks should be a function of speed, and I agree. It doesn't make as much sense to say speed depends on tire marks. It makes much more sense to say tire marks depend on speed ... which would make the equation some sort of quadratic, instead of a square root function!)
OK ... so this week's is definitely a step function. I know that my students will not have studied step functions in their Algebra 1 classes. So I am curious how they will graph the data. Here is the information presented from some textbook:
I would remove the term, "step graph," from the problem. Instead, I want to put the data out there and talk about how it might be graphed.
So ... after a brief discussion of the stamp, I would present data (I would add our current costs) and ask students to work in groups to graph the data. I'll ask them to explain if the data is continuous or discrete. I'll also ask them to identify the domain and range.
Each group will get an opportunity to share their graphs and explain why they graphed the data the way they did. I am hoping that there will be some differences in the graphs so that we can discuss their reasoning. I'd love to use "My Favorite No" strategy to discuss the positives and identify errors!
What would you do with this problem???