Do you use activities from Desmos? Have you tried their snapshot tool? This tool was so helpful orchestrating a recent classroom conversation.

We started by noticing and wondering about the plots without the context. We noticed that it looked like a line and had a somewhat constant rate of change. We wondered who these people were with such big feet.

This is data from NBA players (mostly 2017-18 Warriors). JaVale McGee is the far right dot with the size 20 shoes. We then entered our own height and shoe size and the remainder of the task was left for homework.

Before school on the day the task was due I prepared the conversation using student work and thinking. Desmos’ new feature snapshots has made this so simple. Click on the camera icon and go to the conversations tab. Your student responses will be waiting to be dragged into a screen like the one below.

We started with a conversation about what makes a good fit for a line. I chose four graphs that had reasonably good lines that were different enough for us to debate which fit best. Groups and then the class discussed together the criteria they would want for a line to be a good fit.

Most of the groups selected the top right graph. Click on the top right arrow and that student work will be displayed. I had intentionally tried to select graphs of students whose voice isn’t as often present in the classroom. “Mary” appeared very pleased that their graph was chosen by the class.

This screen gave us an opportunity to discuss how the heights and shoe sizes of basketball players related to the y-intercept and slope.

Back to the snapshot view for our second collection. We compare our class data with the data from the Warriors.

Several 8^{th} graders thought that our class data had a stronger correlation because it was more clumped. After our conversation, we were not convinced yet which was a stronger correlation so I had them consider a few questions.

- I told them a new 8
^{th}grader was standing outside with size 8 shoes and asked them to predict the height. - I then told them a Warrior was outside the room and asked them to predict the height.
- Finally I asked everyone in the room with size 8 shoes to stand up and we observed their varying heights.

*I made myself a note. In this conversation we wondered what it meant to be an outlier with some thinking that the green triangle of dots in the top right represented an outlier for our class data.*

I was still unsure they were convinced. Our next shapshot helped.

They noticed that the lines from our four students were more varied than the lines for the NBA players. I think it helped to convince us that the student data was as consistent. They speculated the following about why a line wasn’t as easy to fit for the student data.

- We aren’t done growing yet
- Men’s and women’s shoe sizes are different
- The NBA players were wear similar types of shoes

Again we took a closer look at the graph they selected (lower left) and appreciated the work of “Stefan”. We noticed the much lower y-intercept and wondered if that was the height where we changed from children’s to adult’s shoe sizes.

On the last screen I asked students to compare the two models. We wondered as we became adults if we would follow the path of the green line or shift more towards the orange line.

There was at least one outstanding question that I will use to launch the next class. What does it mean to be an outlier in two variable data? I am ready with that snapshot.

First…

and then…

I have used a lesson related to student heights and shoe sizes for over 30 years. Shifting the lesson to Desmos last year really helped capture the student thinking. Orchestrating the conversation with the new snapshots feature led to a discussion that included so many voices in the classroom. I can’t wait to see what Desmos will come up with next.

If you are interested the height shoe size activity can be found here.