Bring In Styrofoam Cups And Watch The Magic Happen

I haven’t blogged in such a long time as school got busy and blah blah blah. Hopefully, I will give myself a kick-start with all the buzz of the MTBOS and the event that they have planned which everyone should check out here:

Anyways, I did the cup stacking lab that I stole from Dan Meyer It was a lot of fun and I really think my lower level Algebra II students learned a lot from it! We started the day with our opener as usual and then I held up a Styrofoam cup and proceeded to ask the students how many cups tall would I be if this cup is around 10 cm and I am around 200 cm tall. Instantly, shouts of 20 came pouring out the students like it was a no brainer. I stacked up 20 cups (one inside another) and put it next to me on the floor and some were shocked they were wrong. One student volunteered to come up and show me what they meant. Great! They figured out what problem they solved, so now they have to solve the original problem that I wanted: figure out how many cups stacked inside of each other would equal my height. I put the students into random groups and told them that if they needed info/supplies or whatever, they would have to ask. This is where the fun began.

I watched as some students squirmed for a second or two until one group told me they needed something to measure with. I responded with: “Okay” and walked away. Then someone else from their group shouted out to me and asked if they could have something to measure with like a ruler. “Sure.” I pulled one out of my pocket. Before I could get away someone else asked if they should measure in inches or centimeters and be the helpful teacher I am, responded with: “I don’t know. I haven’t measure the cups…..what does your group think is best?”

I walked around listening to the groups, offering rulers and measurement of my height of six foot four inches. I loved that they would then ask for my height in cm and I would say that I don’t know. When they would get disgruntled that it wasn’t in the same units I would just smile and walk away. I enjoyed watching students problem solve and persevere as they googled the conversion or did it finding the conversion rates in their student plannerbook they all received at the beginning of the year.

After everyone had their secret guess, i put them up on the board and we talked about how every group got their answer. We discussed, and they did most of the talking, about how you could get an equation out of what everyone did….well except for one group that did proportions but the students argued why that wouldn’t work and I moderated their talk. What does the slope mean? What does the y-intercept mean? We had such meaningful discussions about these things. Then, we stacked up the counts and found out who was correct. Many groups nailed it perfectly throughout all 3 of my classes I did this in and others were close. Some were off and we talked about sources of possible error and why things don’t always work out well. I have never seen my students participate so long and so engaged in a discussion yet this year. They were really into and wanted to keep talking about it the next day!

At the end of the day we did this, I showed them the document below that they were going to do as a lab write-up. On the second day, we went through and talked about how they were going to complete this. Students pulled out their chrome-books and we went to town as students discussed their strategies with each other and talked about how they could turn what they did into a linear equation and answer some questions about evaluating and solving.

If you are teaching slope at all, you have to do this activity! It was fun, students were engaged, they had great discussions about math, and it was less than $10 to get cups for a lesson. In our next unit on systems of equations, I plan to bring this back and maybe have a different cup and ask students when the two stacks would be equal! More great discussions and more engagement! What more could a teacher want?