A4A project from the Portage Public Schools team on modeling data with exponential functions.
Modeling data with exponential functions
A3.2, A2.1, A2.3, A2.4
I plan to use this lesson. Currently I plan to introduce exponential functions by using the single-elimination tournaments, i.e. how the number of teams decrease after each round. (The guys should really like this since "March Madness" is going on now.)
I like the hands-on activity and it provides a visual for the concept. Students will be able to observe how actual data differs from theoretical data.
I plan to use pebbles instead of popcorn since we have a critter problem in our school. Plus I can reuse the pebbles. I also after the students graph the data, I would like students to represent this function using a real scenario and determining the equation. I will use the exponential regression model on the graphing calculator.
I like the pebble idea. We have a critter roblem in our school also, but it is the scent of burnt popcorn that makes me not ever want to smell it.
I like this model. I would recommend that you include in your students' directions when dropping the popcorn that they drop the popcorn directly over the point where the dividing lines intersect.
I liked your "what comes next" suggestion of changing the number of sections. I think that after doing the experiment with the plate divided into 4ths to be sure everyone has the method down and is able to figure out the equations, I think dividing the class into groups and assigning different fractional amounts on the plates would make a good study into the meaning of the different variables in the equation.
This is a great activity. I like the interaction and the hands-on activity. Often times, students enjoy participating in "experiments", like this so they can see what happens. You mention creating an equation for their data. Do you have them do this just on the graphing calculator or do you talk about what the data looks like and then try to match it to an exponential function without the use of the calculator arriving at the equation for the students? I do like how the tables were incorporated. I would love to see extensions upon this concept because I could envision much dialogue going along with this.
Thanks for sharing and providing a wonderful resource!