Wow. Today I approached Precalculus class a little different than last year. I asked my students to work in groups and guess the average high temperature in Naperville for the month of January. Then I gave them the answer which happened to be 32 degrees F. Then I asked them to find the average of all the months of the year. When they had finished this they graphed it with the month being the x-axis and the temperature being the y-axis. Then, in their groups I asked them to make as many observations about the graph as they could. We spent about 5 minutes going over many ideas such as there is a max point, and it is periodic, and then someone said it. They said it looks like a sin graph! Awesome! This made my day.
Then I had them draw in the midline and tell where exactly it hit the y axis and it's meaning to the problem. Quickly the students found that this was the average high temperature for the year.
We covered other things like the midline and the amplitude and the phase shift. The period seemed boring to them, but was an important fact.
Then, we looked the actual graph that www.weather.com has on it. We went to the site and typed in our zip code 60565. Then we scrolled down to find AVERAGES . This gave this terrific graph.
Then I asked them to predict what the graph would look like from Honalulu HI. They used all kinds of precalculus vocabulary with each other and described how it would be different.
We looked up other cities like Barrow AK, and Death Valley CA. We also looked up Sydney Austrailia and found that the graph was shifted over significantly.
This lesson was different than last year because they were very interested in their own predictions. I think they were much more engaged.
Thanks to my colleague Kevin Bell for introducing me to the www.weather.com site.