The warm-up was this Daily Desmos, where they have to determine the equation of the line and we check it on Desmos:
I had them work in table groups on the big whiteboards. Here is some of their work:
Next, I had them go around the room looking at other groups' solutions and making comments on the work. Some fixed errors while others wrote comments like "where did this come from?" and "show your work". It was interesting. One group had a blank board (they were a little off-task) and they actually took the time when students were looking at each other's work to find the slope. We went over some of the errors and cleared up some misconceptions. I also had them go to Desmos on their phones to check their equations.
Next we went back to the cups. I put up the equations for the Styrofoam and red cups on the board. I assigned them random groups to answer this question: if the red cups started on the desk and the Styrofoam cups started on the floor, when would both stacks have the same number of cups and reach the same height? Many groups answered a different question - they made the height of each stack 76 cm (the height of a desk) and solved for the number of cups.
I let them struggle with this a little longer after explaining the difference between my question and the one they answered. I had my red cups travelling around the room with me as props to help me explain what I wanted them to find.
One group thought they had it solved so I pulled out the cups and we tried it out - and one stack came up short. Back to the drawing (white) board.
Eventually I had to stop the whole class and talk about what we knew and what we were trying to find. We went over what each of the numbers in the equation represented and whether it would change if you started the stack at a different height. We got to this point together and I let them continue in their groups:
Here is what they got:
The last picture, above, was for a group that calculated that they would need 65 Styrofoam cups to reach the desk so they were changing their Styrofoam cup equation by subtracting 65 from 7 - great strategy, but they did not finish : (
The consensus was about 133 cups and this is what it looked like:
We still had a few minutes left and they clearly needed a specific task so I gave them this question to do as an exit card:
Based on the results, I think they understand how to solve these equations (yay!). So much for pyramids today. That will now happen on Monday.