Really? She Told Me to Drink My Homework!

We tested our cup stacking predictions by actually measuring the height of stacks of 15 cups of various types. Many students found their predictions to be fairly close to the actual results, while others were pretty far off. We talked about what on the cup was causing the stack height to change (lip or taped part) and what was constant (the "excess" or body). We talked about the formula for how to predict the stack height, regardless of how many cups were in the stack.


Tonight's Homework: There are two parts to tonight's assignment. First, determine the formula for the stack height of each of the different types of cups we measured in class. Be sure to include both the lip and the "excess" numbers in your formula. (Most students finished this in class today.)

Part Two will be done at home. Using a cylindrical glass, fill it with your favorite beverage. Measure the height of the liquid, and then take a drink. Measure the height of the remaining liquid. Repeat this procedure until all of the liquid is gone. Create a well-labeled data table. Graph the data. Include the line of best fit for each cup. Determine the rate of change for each of the different types of cups. Summarize your results. Discuss things like:
•what are the y and x intercepts, and what do they represent:
•is this data continuous or discrete? How should it be shown on the graph (solid or dotted line)? Why?
•What is the rate of change for each type of cup?
•What is the formula that describes the height of the liquid based on the number of sips taken.