Today we started cup stacking! But first we did some Estimation 180. It was good to get back to it.
I have done a version of Dan Meyer's cup stacking activity for several years, but this time I started with "cup stacking wide open" - they could stack the cups any way they liked! I started by putting one red Solo cup on the floor next to me and asked them what questions came to mind. Fairly quickly someone said "How many cups would it take to reach your height?" - bingo! I put them into random groups and handed each group a sheet for them to draw a diagram of how they wanted to stack the cups, along with a guess that was too low, one that was too high and an actual guess. Once they had that done each group got a handout and 10 cups. I also wrote my height on the board.
They had fun initially stacking the cups and having them fall which made a lot of noise. Good noise, though. You know, the trying something and having to adjust because it didn't work kind of noise. Only one group chose to stack the cups one inside the other; all of the other groups stacked the cups like this:
They collected data which they graphed then came up with an equation to represent the relationship between the height and the number of cups. They were good at this because they understood that the height was dependent on the number of cups and that each cup measured the same. They came up with their calculation for the number of cups to reach my height then moved on to a different way of stacking the cups.
They tried a lot of things. Here is a sample:
We spent the end of the period trying to see how close their predictions were to the actual number of cups needed to reach my height. But the towers kept falling down! The vents were blowing cold air and the draft seemed to be everywhere so we spent a lot of time getting nowhere. Eventually, with the help of someone holding the tower part way up, they got the 16 cups stacked and saw that the top of my head was somewhere between cup 15 and cup 16 exactly as they had predicted. Yay!