The Uncertainty Game Show

I'll start this out by admitting that I hate sig figs. Always have. I mean, I understand the importance of reporting a reasonable number of precision according to the measurement tool, but I have always found the math of sig figs to be tedious and hard to understand. Because of this, I have been searching for another way to frame the idea of uncertainty without getting into the nitty gritty of significant figures. 

In the world of engineering, uncertainty is analogous to confidence. The more uncertain your measurement is, the less confident you are in that figure. When reporting dimensions and results, engineers do so using tolerances or confidence intervals, a range of numbers that they have confidence (usually in 95% or 99% sure) will capture the actual result. There is a lot that goes into the selection of these intervals, tighter ranges cost more but fail less frequently and vice versa so engineers need to find a balance. My goal with the Uncertainty Game Show was to create a scenario where students found themselves struggling with this balancing act while learning about this different framing of uncertainty, precision, and confidence.

The Game Card

I started out by having every student pull up the Uncertainty Game Show Game card. This is just a blank table with spaces for them to record their answers and keep track of their points. We are 1:1 iPad so I had them download the .pdf file but it would work just as well to print these out or have them recreate the table in their notebooks.

Uncertainty Game Show.pdf
File Size:	28 kb
File Type:	pdf

Download File

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Uncertainty Game Show - Google Doc

The Rules of Play

• All questions are looking for a numerical answer
• For each question (8 total), students need to record their answer and uncertainty
• The uncertainty is treated as a +/- value to create a confidence interval
• The larger the uncertainty, the less points the answer is eligible for
• 0 points are awarded if the correct answer isn't captured in the confidence interval
• If the answer is captured in the confidence interval, points are awarded based on the uncertainty that the student wrote down. The point values are listed on each answer reveal. Students do not get access to this table when they are first deciding on their uncertainty so it doesn't factor in to their answer. 

Example:
Question - With wisdom teeth, how many teeth does an adult human have?
Student A:   Answer = 40    Uncertainty = 5
Student B:   Answer = 45    Uncertainty = 15

If the correct answer is in the range of 35-45, then Student A will earn points
If the correct answer is in the range of 30-65, then Student B will earn points

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The answer is 32
Point values:

• 0-5  |  4 points
• 6-10  |  3 points
• 11-20  | 2 points
• 21+  | 1 point
• Incorrect  |  0 points

Looking at the answer and point values listed on for the question:
Student A is awarded 0 points because 32 is not in the 35-45 range
Student B is awarded 2 points because 32 is in the 30-65 range and their uncertainty was 15

When all questions are read and the answers are given, students total up their scores accordingly

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Let's Play!

Below is the Google slides presentation that I used to conduct the game. This game has 8 questions. All 8 questions are posed first without any answers and then the next slides circle back with the correct answers and point values. Feel free to use this slideshow or modify with your own questions.

Click here to create a copy of this Google Slides presentation

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Reflection

This was a really interesting activity that has many layers of complexity for students to think about. Some interesting takeaways from our first ever Uncertainty Game Show:

• You can be exactly right with your guess but still get 1 point if you report a large enough uncertainty
• You can be totally wrong every time but still get 1 point if you intentionally set your uncertainty at 1000 (the winners always had more than 8 points though so you would never win with this strategy)
• One class voted that I award 5 points to anyone who reports an uncertainty of 0 and gets the answer exactly right.

I'm very interested to hear if anyone tries this out in their classroom. What other guidelines could be included to help frame this discussion of uncertainty and engineering?