Take Graphing to Great Heights—One for the Ceiling!!

I have been thinking about writing about this graphing idea, and with the fall equinox upon us, I wanted to make sure and get this posted! One of the best graphs I ever did in my classroom was one that used data collected over time: namely, we measured the length of the shadow of a metre stick each month, at noon, around the 20th/21st of the month (there would be some slight variations of the date as we needed full sunlight to see the shadow, so if it were cloudy for some days, we measured on the first available sunny day!) I would ask two students to do the outside measuring. One student would hold the metre stick perpendicular to the ground. Under the tip of the metre stick would be the end of the roll of string. The second student would roll out the string to the length of the shadow, and then cut the string. They would bring the string inside and measure the length of the string. Additionally they would cut a piece of masking tape (blue or green work best) the length of the string which we used to construct a graph on the ceiling. Across the front of the room, close together, were tags for each month of the school year (September through June for us). For each month we put up the length of masking tape showing the actual length of the metre stick’s shadow for that month and recorded the measured length on the tape. It was amazing the difference in length of the shadows, especially comparing December and June, the winter and summer solstice months respectively. I live and work in northern British Columbia where we have relatively short winter days (though certainly not as short as in Dawson City, Yukon where I lived for over three years!) Still, even here in Fort St John it was interesting to note the change in the shadow over the months. The first time I did this with a class, I went home that evening excited to tell my husband how long the December shadow was, but he did not believe me! He thought it seemed too long, and he was sure the students had made an error in measuring. He and I had to measure the shadow of a metre stick at home that weekend so he could see its length for himself before he would believe how long it was! I wish I had taken picture of one of the “shadow graphs” my classes had made on the ceiling of the classroom. It was a powerful representation of the combined effect of the earth’s orbit around the sun along with the tilt of the earth. I would love to hear about this if you do it with your class. I have a couple of classes in my district that are about to embark on the measuring task in the next few days. I am looking forward to seeing the graphs on the ceilings of those classrooms! Mathematically yours, Carollee PS: Alternately, one can graph the shadow of a metre stick over the course of a single day, measuring the length of the shadow every hour or every two hours from sun rise to sunset. That is also fascinating data to collect. It might even be interesting to gather both sets of data!