As I was trying to decide what do on Halloween in my classes it just did not seem like a good idea to try to start something new. Halloween was already falling on a Friday and with students dressed up and myself dressed as Olaf, from Frozen, I had a feeling there would be too much of a distraction to try and start new material. I also did not want to waste the day by doing nothing so I turned to the Three-Act-Math Super Stairs task. This task was at a level that was below where my students are but challenging enough for us to take the hour to work through it. You can find the link to the task here.
We started by watching the prologue video and then I asked students what questions they had about the videos. Each class was able to come up with a good set of questions.
One of my favorite non math related question was “how does he not fall on his face?” Apparently my students would not be comfortable doing the Super Stairs.
I did pose my own question about how long it will take will take him to do the super stairs. I was surprised that this question didn’t come up especially since the video of the super stairs ends part way through. I then asked my students what information they wanted to know. Once my students realized I was not going to tell them the answer we started to get some good ideas about what we needed to know.
After we defined what was the difference between steps and stairs and looking at our estimates for the number of steps taken. Students were confident in their answer that there was 462 steps were taken. I think it helped that this number was within 100 steps of any estimate that students gave.
We next turned to how long it would take to complete the super stairs. Each class took different approaches. My first class decided to time the amount of time that it took to do each set of super stairs. They then divided the time by the number of super stairs that happened in the given amount of time. The goal was to find how long it took to do each super stair during each set and then use the five times they found to find the average amount of time spent per super stair. They then multiplied their average by 462 to get the amount of time it would take to do the entire super stairs. My second class decided that they wanted to look at the time it took going up and the time it took going down. They talked about trying to time the turn around time it took on each super stair. The struggled with timing that and decided against timing that and figured the time for that would work its way in with their timing errors on the time up and time down. They found the average time it took for him to go up and the average go down one stair and multiplied those numbers by the number of steps up and the number the of steps down and added the times together.
My first class found the time that it should take him to complete the super stairs at 8.3 minutes and my second class found that it should take 522 seconds. At this point I was curious about how their answers compared to the estimates that the made for the time. All of the estimates in both classes were in-between 2 and 3 minutes. I asked the class if they were satisfied with the time they found even though all of the estimates were well below the time they found. I was surprised when they tossed their estimates out to go with what they found. I then showed them the final video and we talked about how our time was way off and what could have led to this error.
We talked about how their timing may not have been as accurate at it could have been. My first class wondered how by taking the average of the the super stair may have affected their answer rather than timing the time up and the time down. Someone also brought up the idea that when we found the times we may have had a problem when we were converting the units. The answer they got were pretty close to double so they wondered if maybe the times they found were for 2 steps instead of one. Unfortunately we ran out of time in both classes and were unable to fully explore that idea.
While working on this I noticed a few interesting things about my students:
- My students have a hard time asking for what information they need.
- They were mad that I was making them answer the questions instead of me answering them.
- They wanted to give up to early.
- They have a hard time collaborating with each other to work through the process.
These are all areas that I want my students to be strong in and now I must think about how do I best support them in this growth.