Before beginning today's activity I wanted to clear up some issues that I had seen in Friday's homework around multiplying binomials that had a constant in front. I asked them each to expand and simplify the one shown below and then we looked at a number of ways of tackling it.
Then, on to today's activity: stacking cup systems! On their desks were 10 of each type of cup and this handout, which I copied on ledger paper.
Then I gave them their task for the day: given Styrofoam cups starting on the ground and red cups starting on the desk, determine what equal number of both types of cups would produce the same height.
They started collecting data, some groups more precisely than others. It was interesting to see that some added 2 cups, measured, added another 2 cups, measured, etc., while others added 1 cup at a time but did not use all 10 cups.
I circulated and helped them ensure that they were measuring vertical height, not along the side of the cup. My conversations with several groups about their data meant that they had to start collecting data again. For example:
S: "Each cup makes the height go up by 1 cm, so at 10 cups, the height is 17 cm."
Me, measuring 10 cups: "Is that 17 cm?"
S: "No, that's 19.5 cm..."
There were a lot of conversations about what the numbers all meant. Rate of change was interesting to talk about, especially for groups that had added 2 cups at a time. The fact that the model says that there is a y-intercept when in reality we know that 0 cups have a height of 0 cm was another avenue for discussion. One group got as far as graphing, but they had neglected the fact that the Styrofoam cups needed to start on the ground so they had to look at their models again.
Tomorrow we will have a quiz. Here is the homework I gave them today. After the quiz, they will keep working on their cup stacking systems so that they can then test their results!