Thursday, June 26, 2014

Crowdsourcing I: Concept Intro for CCSS Lessons

I observed a class this past year using the M & M experiment where students posted the results to a Google Spreadsheet.  Recently I participated in a similar lesson using 10-sided dice to conduct the experiment.  In both cases the math world confirmed the results of an experiment in the real world in a powerful way, and served as the introductory and anchor lesson for exponential functions.  Below are the steps of the activity performed with 10-sided dice.

1.  Roll 40 ten-sided dice.  Count the number of dice that DO NOT have a zero showing on the face and record in your table.  Remove the dice that are showing a zero.

2.  Repeat for 20 rolls.

4.  Enter the average number of dice without a zero showing on the face into the GeoGebra spreadsheet. Note: It is often easier for the teacher to calculate the average, or to have the spreadsheet pre-programmed to find the average.

4.  Graph the set of points generated in the GeoGebra spreadsheet.

5.  After a class discussion, graph the function that represents the theoretical number of dice left after each roll that DO NOT have a zero showing on the face.

-Enter the function into the Input bar at the bottom of the page

If you cant see the points, select the "Move Graphics View" tool.  You can drag the axes to resize.

Clearly, this function isn't the best fit for the data.  That is because I don't actually have the original data from the three groups.  What I can say is that with even as few as three samples of data, the function fit the average value of the data extremely well.  This activity is one of many that can serve as an anchor activity for exponential functions.  Additionally it provides an authentic reason for students to use technology to model data.  The process of inputting data points, graphing them, and graphing a model function against the data is a process that will prove valuable for preparation for the SBAC test.  Many thanks to Henry Picciotto for his No Limits Workshop this summer at The Urban School of San Francisco.  This workshop provided inspiration for many new lessons, including lessons that integrate technology in a meaningful and innovative way.