We spent most of today's class on Stacking Cups. None had done this activity before so it was perfect. I have blogged about it starting here (2014) and here (2015). They started with the Styrofoam cups. They had to figure out the number of cups needed to reach my height (stacked one inside the other). I gave each group 10 cups and set out rulers and measuring tapes and let them go. Someone asked my height and I said about 5'7", but told them they were welcome to measure me. They did not feel the need to do this. They worked away measuring their cups, graphing, coming up with an equation and then determining the number of cups needed. Once each group had a number we started stacking the cups. That's when they asked how tall I was again, and felt the need to measure my height accurately : ) They were all within 1 cup of the correct number, which was awesome. We then repeated the process but made it wide open. They could use Styrofoam or red cups and could stack them any way they liked. They did lots of cool stuff.
They struggled somewhat with finding the equation to represent the quadratic pattern (for the picture immediately above) and I let them struggle knowing that we will be doing quadratic visual patterns tomorrow. I did, however, show them how to enter data in a table in Desmos and perform a quadratic regression.
I also introduced them (virtually) to Alex Overwijk whose students did a very impressive cup stacking job:
Next they had to figure out how to use the same number of the two kinds of cups to reach the same height, given that the red cups would start being stacked on the table while the Styrofoam ones started on the floor. I loved that one group had forgotten to account for the height of the table and when they changed their equation, their graphs intersected at a negative number of cups. Hmmm. They realized that they had added the height of the table to the wrong equation and when they fixed that, this is what they got:
This is such a good activity. It combines linear and quadratic and they need to match up algebraic expressions, tables of values, descriptions in words and area models. Some cards have more than one match and some have to be filled in. It is really excellent as it ties together many concepts.
I left my class some linear visual patterns to work on for homework. This is fun homework!
I spent a good chunk of the rest of my day with the teachers in the Biology Institute as they were working on STEM activities. Jeff Lukens walked them through some data collection activities and I contributed some of the "mathy" side of things.
The evening talk was given by Frank Griffin from Cate School in California. It was funny and inspiring.
In between there was a lot of good food, including ice cream : )