I will categorize this post as “sometimes you just need a worksheet”. #SYJNAW for my twitter peeps.
I have always kind of disliked teaching the circles unit in geometry because of all the different rules – tangent / secant angles, chord-chord sides, chord-chord angles, blah blah. This year I put together a learning segment on circles that involved satellites in geostationary orbit. It was based on my experiences working at Lockheed Martin and my engineering background. I will write about it when I have time. But for now I will just attach a couple worksheets I made of problems that I put on a homework, or threw in a test. I figured I would just share these, because you know… some times you just need a worksheet.
These problems themselves involve tangents, central angles, and trig functions. The actual learning unit is very similar, but requires the students to contextualize and decontextualize. So without further comment – here’s some of the practice problems I used:
The Goods: (sorry I only have pdf’s, I create things with Adobe Illustrator)
Show them this website and ask them if they can figure out what it is all about:
This site shows the exact opposite side of the earth from anywhere on earth. So if you dug a hole straight down through the center of the earth, this site shows you were you would end up. Every student in my class had heard the old saying about “dig a hole to China”, where it is believed that if you dug a hole straight through the earth, you would end up in China. Apparently it’s not true, you would end up in the middle of the Atlantic. Students will definitely ask you to find where you would need to start digging if you wanted to end up in China (Argentina).
That is about all you need to pose the question “If you were to dig a hole to China, how deep would the hole be?”
I give the students the circumference of the earth. This lesson is teaching them to find the radius from the circumference.
C = 2(pi)r
At the end of class come back to the fact that if you give them radius, they would be able to give you diameter and circumference. If you give them circumference, they should be able to give you radius and diameter.
I do not give any handouts.