A4A project from the Portage Public Schools team on modeling data with exponential functions.

 

Authors:

Laura Cleasby

Robert Eustice

Angie Kirschman

Betty Smith

 

Subject Area:

Algebra

 

Topic:

Modeling data with exponential functions

 

HSCE's:

A3.2, A2.1, A2.3, A2.4

Tags: exponential, exponential regression, geometric sequences, prediction, probability, regression

Views: 238

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This modeling activity looks great. I think that students would enjoy the activity because not only are they able to be active, but they are also going to see that exponential functions are able to be simulated physically. My only critique of this activity is the lack of relevance to reality for the student. If you're having the students physically simulate something, it would be wonderful if the data represented a real world scenario for the students. For example, you could say that the popcorn is being eaten, and the shaded portion represents how much you scoop each time you get a bite. Students like seeing the relevance of math in addition to hands on activities, in my opinion.

I would definitely use this lesson when introducing the application and graphing of exponential functions. Not only does this reinforce the use of tables, it would also be a great opportunity for students to practice regression with their graphing calculators.
This is a very easy, inexpensive and creative way to demonstate exponential functions. I am extremely greatful to all those people who take the time to post activities for those of us who are a little less creative.

I like that this experiment covers both growth and decay. I like that it is adaptable to use food. High School students love to eat and will be ready to get involved in this activity. I like the critical thinking questions and use of the graphing calculators.

Thanks again for taking the time to share!
Dawn Meacham .
I really like the way you have set up this activity. I plan on using it in my classroom when we get to the exponential functions section to introduce the topic to my students (although, I think I may use M&M's instead of popcorn). I think that this will give my students something tangible to help them grasp the idea instead of just lecturing. My only concern is that I hope my students will get some practical experience out of this activity. Having another example relating to something they really care about, such as money, would really hit home. I like the example that asks: “Would you rather have $1 million today, or $.01 today, double that tomorrow, double again the next day and so on for 30 days. I believe this could be a great way to really get their attention at the start of the lesson and be applicable to one of their true interests. Other than that, I think it is a great idea to introduce the exponential function topic. Thanks for sharing your work and I can’t wait to try it out!!!

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.

Monica

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!

I could also imagine different groups of students having plates shaded with different sectors.  Whole group conversation could draw upon the Shapes of Algebra experiences as they compare the similarities and differences between there reports.

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