Adapting to Remote Learning – Egg Roulette

This is the first in what will likely be a series of posts about classroom moves which I have adapted for remote learning. I hope you enjoy them!

In my freshman-year Prob/Stat course, students experience a probability lesson featuring the game “Egg Roulette”, based on a bit from Jimmy Fallon’s Tonight Show. Here is a summary of the “live” lesson: https://mathcoachblog.com/2015/09/20/an-egg-cellent-simulation/. This year, there were two considerations for how I would have students investigate the game: conducting the simulation and collecting the results.

CONDUCTING THE SIMULATION

The first class simulation involves two unsuspecting volunteers and my actual container of 12 “eggs” – filled with little fuzzballs. Click the link in the last paragraph to see a video of how it works. In the main simulation, students use decks of cards to play the game repeatedly. Give pairs of students 13 cards all of the same suit. Discard the ace. Then, the 10, jack, queen and king represent “raw” eggs. The other cards represent the “hard-boiled” eggs. In a remote environment I could have used a site like random.org to draw cards, but I also saw an opportunity to build a simulation students could use to quickly analyze repeatedly. This Desmos link allows students to play the many times: https://www.desmos.com/calculator/2b7f6p4r3o. Click the “rerandomize” button to generate repeated plays of the game. Online, we talked through a few of the simulations and I found the students quickly understood the format.

Jimmy Fallon Egg Roulette simulation on Desmos

COLLECTING THE RESULTS

I have used a number of methods for collecting class results over the year: sticky dots on a poster, Post-It Notes on a wall, digital data collection. Clearly this year we had to go digital, and the site http://stapplet.com came to the rescue. New this year, teachers have a “collaborative” option – this feature generates a class code from which students can submit their data to the class (thanks Josh Tabor and Luke Wilcox!). The results update in real time. Each student then pasted the class graph into OneNote and a discussion of Jimmy Fallon’s “meanness” – is he being nice to his guests by letting them draw first? – followed.

Results of our class simulation using stapplet

The rest of the lesson and discussion felt similar to previous years. I challenge small groups to find the probability of a player losing in round 3. This leads us to probability ideas of independence / dependence and the multiplication rule. The engagement remained high and the conversation was on par with previous years!

Let’s Explore the Activity Builder Space

Today our friends at Desmos released an update of their Activity Builder editor. You can head to teacher.desmos.com now and explore the changes – edit a previous activity, create a new one OR copy screens from activities in the library of Desmos activities.

The first thing I noticed about the updated editor was the increased freedom in screen design. Previously, elements like Graph, Note and Input were limited in their placement and number. There is more freedom now to move elements around, order them as you like, and include more of them in a single screen.

Immediately I wanted to explore this new freedom and think about intentionality in my design process for an activity I wrote and used in my AP Stats class this spring – Is My Die Fair. In this activity students “roll” both a virtual hand-made die and a virtual real die. The activity allows students to discover the chi-squared statistic as a reasonable measure of variability in a categorical distribution. Here are two ways I changed this activity with the new editor, with the intent that students will be able to follow the narrative with less arrowing through the activity.

ORIGINAL VERSION:

Screen 2: students roll the hand-made die 60 times

Screen 3: results are copied from screen 2 and students make observations.

NEW VERSION:

Students roll the die AND make a conjecture on the same screen.

Another place I was able to leverage the new block placement freedom occurred later when students begin to think about the computation of the chi-squared statistic.

ORIGINAL VERSION:

Screen 8: the new statistic is explained, and students complete a table for the homemade die only.

Screen 9: a summary statistic is shown, and students now complete the table for the real die.

Screen 10: both summary statistics are shown and students make a final conjecture about the dice.

NEW VERSION:

Screen 7: the new statistic is explained, and students complete tables for both types of dice on the same screen.

Screen 8: both summary statistics are shown and students make a final conjecture about the dice.

Share your ideas for altering your previous activities to leverage the new design freedoms. Below, you can test-drive both activities and see how I altered them. Your ideas are always appreciated…now get building!

“Is My Die Fair” – original version – https://teacher.desmos.com/activitybuilder/custom/5e713346f6e84e7dd46727fd

“Is My Die Fair” – version 2 –https://teacher.desmos.com/activitybuilder/custom/5ef38c6cad9e310dc0a6ac23

You Have an Awesome Math Lesson – Share It!

Do you have an awesome math lesson? Do you like handsome cash prizes? The Rosenthal Prize for Innovation and Inspiration in Math Teaching offers a top prize of $25,000…and the 2019 winners have just been announced by the National Museum of Mathematics! Congratulations to Nat Banting, this years winner and a fun and inspiring twitter follow. I’m really looking forward to hearing more about dice outcomes auction somewhere down the road. On the link above you can read about past winners and learn about how to apply for 2020.

I applied for the Rosenthal Prize back in the spring. At that time I looked back at old blog posts for lessons which seemed to be of interest and use to teachers, and chose one which has generated many positive comments: the 35 Game. The original post describes the game and how to leverage the results to build need for compound inequalities: https://mathcoachblog.com/2016/01/07/the-35-game-for-compound-inequalities/

I was thrilled to find out later in the year that my lesson was chosen as a Finalist for the award, but then the hard work begins. There is quite a lot to submit for this prize including:

  • A complete lesson plan
  • A video of the lesson in action
  • 3 recommendation letters

Every year the “35 Game” seems to get many blog hits and comments from teachers who use it. I am hoping that sharing my lesson plan write-up with the math community will provide guidance and usefulness to those teachers who enjoy this lesson. Any feedback you have is appreciated!

Thanks to my friends and colleagues Dennis Williams, DJ Fromal and David Weber for their willingness to provide recommendation letters. I work with inspiring and wonderful educators!