Lesson: M & M Hunting Activity (Intro to Exponential Functions) & Graphing
What is exponential growth and decay?
Can you look at an equation or graph and decide if it is growth or decay?
Can you graph exponential graphs (including their transformations)?
Can you discuss the relationship of domain and range of exponential functions and how it changes with transformations?
Large bags of M&Ms (Each group of 4 students needs about ½ a large bag.
Clean large pizza boxes (1 per group of 4 students)
Graphing calculator & graph paper for students.
Hands-on student activities
Teacher lead instruction
Vocabulary for a Word Wall:
Exponential Growth, Exponential Decay
Prior Knowledge/ Possible Warm-up Activities:
Graphing lines & quadratic equations
One 80 minute class or Two traditional class periods
1) Put students in groups of 4. Each group gets a M & M activity worksheet, and a clean large pizza box which I fill with about 1/3 of a large bag of M&M's.
2) After reading the introduction on the activity sheet out to the students, have them predict how many trials it will take until the M&M's are gone (or there are less than 5). Students are supposed to count the total M&M's in the box, shake the pizza box, then open it and remove any M & M with the "M" showing, count how many M&M's were removed, record the number, then repeat the process. I tell the students that they cannot eat any M&M's until they are removed from the box.
3) Students graph the results from the table that they filled out and try to predict the equation that would fit the points on the graph. After predicting a graph, students can enter the data points in their graphing calculators and see what equation is provided. This is a perfect opportunity to introduce the exponential graph (including decay).
4) Once students have received some teacher-lead information on the exponential function and its basic graph (domain/range), I like to have the students explore the exponential graph and its basic transformations. My purpose is for students to see that the same transformations that occur to the graphs of linear and quadratic functions are the same for exponential functions.
5) Pass out the exponential graphing worksheet. Students use their graphing calculators to draw sketches and answer the questions on the worksheet.
6) I close the exploration with a discussion on the patterns that are developed examining the graphs. My purpose is for students to see that whenever you add a number to function that the graph moves up/down on the y-axis according to that number, adding/subtracting a number within the x value of the function moves the graph left/right opposite of the number added, multiplying/dividing by a number moves the graph closer to the x/y axis, and multiplying by a negative reflects the graph over the x-axis.
Assessment (Acceptable Evidence):
Question #9 on the exponential graphing worksheet. Students may need more samples to show synthesis of the patterns developed in the previous examples.
Census.gov (world and U.S. population clocks)
Cautionary notes/ misconceptions:
Make sure to refresh students' memory on the transformations on quadratics and linear functions (the more times that they see these patterns, the better chance that they stick and can be quickly accessed for the next function learned).
The M&M Hunting activity helps students picture exponential decay as well as exponential growth. I always like to follow this lesson on population statistics and videos on population graphs. I also include information on money growth. This relevant information raises student interest.