I originally wanted to title this post, “Estimation180: Don’t You Love It MADly,” but I thought the Doors pun would be too much to handle.

After my classes had a grasp of Mean Absolute Deviation (MAD) from the activities earlier this week, I began today’s class hoping to slide into a review of sorts for our statistics unit.

The bellwork for today happened to be the following task from Estimation180:

How much will the gray dumbbell weigh?

My students have been completing estimates 2-3 times each week this year, so the task was not out of the ordinary.  Furthermore, we already completed the previous 3 days in the series of estimate tasks.  I knew many students would be spot on (or really close) to the answer.

My original plan was for students to just make find quartiles and make a box plot for the estimate data (an idea I got from the teacher next door to me, who was modifying the human box plot idea I told him about during plan last week).  As I walked up to the board, I suddenly decided to start with MAD instead.  It was a ripe context for actually getting students to see what Mean Absolute Deviation is telling them about the data.

After students turned in their estimates, I grabbed some papers at random and wrote their estimates (in pounds) on the board:

8, 8, 8, 10, 10, 10, 10, 10, 10, 11, 15, 15, 20

I asked students to find the mean estimate for the data (about 11.2 pounds). I asked if the mean seemed like an okay representative for the data or if it was skewed.  Students pointed out that 20 was skewing the data a little, but it wasn’t drastic (like if we went with the 2000 pounds a students jokingly wrote as his original estimate).  Then, I asked students to calculate the Mean Absolute Deviation for the data (about 2.6 pounds).  I related to students that the MAD was telling us that most of the estimates were no further than 2.6 pounds away from 11.2 pounds.

Students seemed to comprehend what I was getting at with this MAD business, so I revealed the answer to the estimate and we moved onto other activities.

It was a moment of genuine inspiration and joy when I was teaching today.  I’m proud of my students on so many levels because of the work they’ve done this year, but it was an incredible moment to have a way to show students their growth from the start of the year using a current concept.