Sixth Grade Math

We did this project as part of a larger geometry unit, so we were able to do several activities related to the Noon Day Project. First, we watched a slide show of the information given in the story “The Librarian who Measured the Earth.” The slide show also included information about some of the other schools involved in the project. This got us excited about the project and collaborating with other schools. The next activity we did prepared us to do our calculations once we had taken our shadow measurements. First, we practiced using our protractors to measure angles, a skill we had just recently learned. Then we were each given a wedge-shaped piece of a circle (from a set of “fraction circles”). We used our protractors to measure the central angle of the wedge and rulers to measure the arc length. We were then able to estimate the circumference of the whole circle. We were pleased to see that many of us were quite accurate.

As we prepared to take our measurements of the shadows, one math enrichment class that meets every day had the task of designing the measuring devices for all of the math classes and picking out the flattest pieces of ground to measure on (not an easy task, since we live in the mountains). We used two basic designs. In the first we used two metal bookends taped together to hold a meter stick upright. It was difficult to make sure that the sticks were perpendicular to the ground so we used extra tape to reinforce the sticks and the corner of a piece of paper to check that it stood at a right angle to the ground. In the second design, we taped the meter stick to a filled up water bottle. This seemed like the better device at first, until we realized that some of the water bottles did not sit flat on the ground. We then had to look for better water bottles and it all worked out in the end.

That same day, the one math class that meets during local noon went outside and took some measurements to practice our technique and make sure our devices worked properly. We were lucky we went out that day, because the rest of the week was very cloudy! The equinox was too cloudy for us to take measurements (surprising in a town that averages 310 days of sunshine each year), so we took our measurements the next day. It was cloudy that day, too, but we were lucky enough to get about 10 minutes of sunshine to take our measurements.

The next week, each student received a packet to help with the calculations. We used scale drawings and protractors to find our sun angle. We subtracted our latitudes and converted our answer to kilometers to find the distance between the two schools. Then we used this information to find the circumference of the earth. We also organized our shadow data into a table and a line graph.

Conclusions

While we found many areas where errors may have occurred in our procedure, we were impressed with the relative accuracy of two of our math classes. First, there were a number of possible errors with our shadow measurements. Our school parking lot is not exactly level, the day was partly cloudy and our shadows were very faint, and there was a slight breeze that affected some classes measuring devices. Second, our state tests were scheduled that week, so we were not able to get outside at exactly local noon, except on Monday. Only one class was able to measure at exactly local noon. The rest of the classes had to use estimation to figure out how long the shadow would have been at local noon based on our measurements. Third, our scale drawings and use of protractors to find our central angle were probably not as accurate as using another method to find the sun angle. We found a great variety of answers, even within each class!

Overall, I was very happy to be a part of this project. I was happy to find how many skills necessary for sixth grade were included in this project. My students were excited to work with students from other areas of the world and were impressed that they were doing the same project as some high schoolers. Some highlights for us were spending class time outside, getting to choose our partner schools, collaborating with our classmates on our calculations, and being interviewed by our local newspaper about the project.