Exponential Funtions
Date | March 2006 | ||||||||||||||
Class | Advanced Math class | ||||||||||||||
Teacher | Becky Bruening | ||||||||||||||
Notes | Double Your Pleasure I used “Double Your Pleasure” activity in my Advanced Math class to show a model of exponential growth. We had just finished talking formally about exponential growth and how, while you don’t see much change at first, later there is an explosion! We had discussed compounded interest formulas, half-life and populations, but this was a simple activity that THEY generated an exponential curve instead of the book or me doing it. I did change the name of the activity to “M&M Reproduction” – generating a little more student interest and curiosity. I had them start with 4 M&M’s. We defined an M as a girl, and of course girls have babies. We rolled, put a “baby” in for each girl (m), counted and recorded. The original activity had them adding 2 for each m, but if I remember from last summer this took a LOT of M&M’s and got “big” even faster. Our experiment lasted for about 6 years up to 10 years with only about 50 candies per person. I liked this change, although I realize that the regression equation would be different. It might be interesting when we do regression to have different groups use different rules and look at the equations. (Although I fear I am quickly running out of days this year!) |
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Date | February 2006 | ||||||||||||||
Class | Algebra 2 (Grades 10-12) | ||||||||||||||
Teacher | Mary Beth Weier | ||||||||||||||
Notes | DOUBLE YOUR PLEASURE ACTIVITY Objectives: To collect data and analyze it to find the relationship between the “year” and the “population” of candies. |
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Date | February 2006 | ||||||||||||||
Class | Algebra | ||||||||||||||
Teacher | Patti Bailey | ||||||||||||||
Notes | For exponential growth I used M&Ms and had students add more for each one that was letter up. I then had them do it again with doubling the population. They made great exponential curves! I also had them do exponential decay with for their final graph. After the first class, I made modifications to the chart. I had them roll the M&Ms 8 times rather that just 5. It definitely gave them a better curve. After another class did the activity, I again made modifications to the chart. I will do this activity with an additional class next week. We’ll see if any more modifications are needed. It was a great to get students excited about class. They knew they were going to get to have the M&M activity! I will use this activity again! It is a great way to show growth! --->>> worksheet | ||||||||||||||
Date | January 2006 | ||||||||||||||
Class | Calculus & Pre-Calculus classes | ||||||||||||||
Teacher | Stephanie Reynolds | ||||||||||||||
Notes | M&M lab – Double Your Pleasure |
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Date | November 30, 2005 | ||||||||||||||
Class | precalculus classes | ||||||||||||||
Teacher | Ray Weier | ||||||||||||||
Notes | In my precalculus classes, we were beginning to work on exponential functions. We had just finished looking at some application problems on growth and decay, so I decided to try to do the Double Your Pleasure activity with them. This activity involves using M&M’s to simulate a population model. It requires that the students do some data collection and then try to fit regression equations to this data.
Using their tables, the students were told to use their calculators to StatPlot their data points and then were asked to try to estimate an exponential (growth) function for their data. They then used their calculators to fit both a linear regression equation and an exponential regression equation to their data to see which gave them a better fit. Note: The worksheet for this activity |
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For exponential growth I used M&Ms and had my algebra students add more for each one that was letter up. I then had them do this again with doubling the population. They made great exponential curves! I also had them do exponential decay with for their final graph. After the first class, I made modifications to the chart. I had them roll the M&Ms 8 times rather that just 5. It definitely gave them a better curve. After the second class did the activity, I again made modifications to the chart. I will do this activity with the third class next week. We’ll see if any more modifications are needed. It was a great way to get the kids excited to come to class. They knew they were going to get to have the M&M activity! I will use this activity again! It is a great way to show growth! |