A benefit of having advanced students for probability and statistics is that there is often a level of curiosity in the room that can drive an entire class period of discussion. Sometimes.
We were about to start a unit on linear modeling and correlation, and I decided to start with giving them the data and the best-fit line and then having them determine the correlation coefficient based on some examples. We used a data table of 21 common cereals, all with calories, sugar, fat, and carbs per 1 cup portion.
The students first were given time to notice and wonder and I had them determine what two columns of data were most closely correlated and least related. We came up with a list for both and then we started number crunching.
The NCTM website has a nice set of core math tools . The Java-based app lets you put in data and then will have students “guess” the correlation coefficient from a list of 4 choices. Some kids made conjectures about how correlation coefficients were calculated. Others refuted these with counter examples. It was a beautiful discussion. In the process, we compiled the correlation coefficient for all of the data sets and this answering our other question about which sets were most and least related.
Finally, I set them off on the map shell lesson about devising a method for measuring correlation. This was just the intro to this lesson. The real fun started the next day…