Curricular Micro Teaching Lesson Plan

Curricular Micro Teaching Lesson Plan by Ben W, Doreen, Minami
Lesson: Pre-Calculus 12 - Exponential Functions: Exponential Decay
Objective:  Understanding exponential decay using a dice rolling activity.

Content Learning Standard: exponential functions and equations (solving problems in situational contexts)

Practical details: 15-minute lesson, 9 students

Materials needed:
200 Dice (the more the merrier)
Computer to graph (desmos) (one computer per group)

Structure:
Introduction (3 minute):
Gauge prior experience with exponential decay. (ie. what should the graph look like?  What are the details of what an exponential equation looks like?)
Briefly explain what it is and where we can see it in the world (ex. radioactive decay)

Dice Rolling Activity (8 minutes):
Learners will break into groups of 4-5, splitting the dice between them.  Explain rules in groups.
Each group will roll the dice together, removing the specified values rolled from the dice pool. Then record the dice that remain in the pool. Then students repeat until a specified number of rolls have been completed.
Example:
build pool of dice, and appoint record keeper
roll the pool of dice, removing the specified values (ie all 1s) and returning the rest to the pool. Record the dice remaining in the pool in our graph.
Repeat step 3 as many times as desired (ie 8 rolls)

Connection:  this activity models exponential decay of the form y=100(⅚)^x, where 100 is our starting number of dice, and each time we are keeping ⅚ of the roll.  Each time we roll, we are keeping (roughly) ⅚ of dice from the previous roll (aka our new y is the previous y*⅚)

Note:  we can let the rolling go until time for closing without regard for specifying a number of rolls.  If they roll through all of the dice early, we can ask them to try it again and see if they get the same thing, adding more data to the graph.

Closing (~4 minutes):  
Pose questions to the whole group as a discussion to have them consolidate their learning.

What is the expected formula of our dice experiment?
Did the groups get the same result?  Does it match up with our formula? -> can plot w desmos (exponential fitting) very easily
Why is the result not the expected result from the formula?
What could we change to make this experiment more ”accurate” to the formula?

Extra Qs as needed:
Would the dice that we removed also model something?  If so, what?  If not, why not?
What would happen if we started with a different number of dice?