Stacking cups and stacking cups.... how high do they go??

The learning process of my students always amazes me when we tackle a problem. The intent of the lesson is often the least of what they learn in the doing of the assignment. Take today's Stacking Cup problem had my students measuring 5 different types of cups, creating a table of their data, then graphing the data, all ultimately to recommend the size packaging needed to ship these various cups. The intent of the lesson is to examine a constant rate of change, consider the meaning of a y-intercept, and how those concepts apply to a real-life situation.

Oh, but that was the least of the learning taking place!

First off, creating a table with so much information was difficult for students to organize. They want a template, a how-to, but I refused to give them one, so they struggle within their groups, trying to figure a logical way to organize.

Then the measuring itself. Final measurements needed to be in millimeters, but of course, the rulers measure in inches or centimeters. Seemingly an easy conversion becomes torture for some groups. Then the actual measuring of the cup heights. The ruler edge is not the zero mark. Do you lean the ruler against the cup? That isn't really the height, is it? Even once they start recording measurements, the inconsistencies cause problems. Why aren't the measurements increasing consistently?

Then, the creating of the graph. Whoa.... you would think some of them are building the Eiffel Tower! Backwards and upside down, and oh, can I borrow whiteout... and what do you mean not a bar graph?

It is fun to watch the process of learning, and even more fun to listen as they work among themselves trying to convince their partners of their way of thinking. I love problem based learning. I love the wheels turning in their heads, the smoke pouring from their ears, and the smell of brains wrinkling!

One guy did proclaim it boring, and even as I poohpoohed him, I began to fear for his safety in the hallway, as his classmates haranged him for his negativity :)

We finish tomorrow, sharing our graphs and talking about the actual slopes, y-intercepts and reasons for our linear relationships.

A good day in 7th grade :)