Okay. Back to trig. This year, I had my students make unit circle paper plates. They were....ummmmmm...okay. Not really. One of my students was very careful and precise, and hers turned out really well. The rest of my kids? Their results were NOT photo worthy.
Dear Future Sarah,
So, you're teaching trig again. Yay!!! Here are a couple of pieces of advice.
#1: Sloooooooooooooooooooow down when you teach the unit circle!
#2: Your kids aren't going to feel comfortable with fractions dealing with pi. Actually, all fractions make them nervous. Come up with some way to combat this. Make a huge number line on the dry erase board. Make magnetic labels with various pi fractions. Have the class race to put the fractions on the number line. Make it a contest. Better yet, make lots of mini number lines on the floor with masking tape. Let them have races to correctly place the values on the number line. Change up how many dashes are between 0 and pi. Force kids out of their comfort zones.
#3: Before you ever start talking about the ordered pair values of the different points on the unit circle, let them get loads of practice with just labeling the angles in degrees and radians. Your students need more practice with this than you think. Maybe you could make this into an activity, too. Masking tape circles on the floor might be a little tricky to pull off. But, you could make a unit circle template that only has the degrees and a spot for the corresponding number of radians. Laminate it or put it in your dry erase pockets.
#4: Don't start thinking about showing your students how to use special right triangles to find the values around the unit circle until they are good with all of the above.
#5: The first time you work on finding ordered pairs, ONLY talk about quadrant one. Resist the urge to talk about the other quadrants. Pretend they don't exist.
#6: Have students cut out the special right triangles and glue them on the unit circle. Don't let them convince you that they can visualize them. They can't. YET.
#7: Have students make a flip book that walks through the process of finding the ordered pair values in the first quadrant. Students need to be able to show this process step-by-step What this flip book looks like? Not sure. I trust that you'll figure it out. Or, some kind soul with a brilliant idea will leave a comment.
#8: Read the comments on this post! Do something about them!
#9: Once students are comfortable with the first quadrant, you can let on that you know about the other quadrants again. Don't tell students there is a short cut. Repeat: PRETEND THERE IS NO SHORTCUT. Assign students to draw and label triangles for the rest of the unit circle. Let them figure it out for themselves. Resist the urge to say anything. I know it's tough. But, it'll be worth it. SO worth it.
#10: Encouraging students to memorize the unit circle is a waste of time. Spend the time you spent giving them speed tests and replace it with tests where students have to demonstrate how to derive an ordered pair of your choosing.
#11: Keeping calling the Unit Circle: Our Trig BFF. That was smart. And cute.
#12: Make the paper plate project the FINAL unit circle project. Not the introduction to the unit circle. This will make results prettier and lots more meaningful.
#13: Laminate unit circles to hand out with quizzes or tests that require their use. Keep this pile of laminated goodness in a prominent spot. Make it a big deal when a student grabs a unit circle without your prompting. Unit circle use is exciting.
#14: Unit circle cupcakes sound like a good idea. A really good idea.