Here's what Unit 2 ended up looking like in my trig class. I posted Unit 1 back in September. Unit 1 was mainly a review of algebra and geometry. Unit 2 was the start of actual trigonometry! Yay!
Our geometry standards include basic right triangle trig, but I've found that my students' experience with this topic is greatly lacking. They remember learning SOHCAHTOA, but they never really did know what they were doing. It's been so fun to teach them trig from the beginning and see the light bulbs start to go off. "Oh, this is what we were supposed to do in geometry! Why didn't they ever tell us it was this simple?!?"
Before I introduced my students to the basic trig ratios, I wanted to make sure we were all on the same page when it came to naming the parts of a right triangle. My students had a hard time wrapping their minds around the difference between the adjacent side and the opposite side for some reason.
We made a simple three-door foldable with the formulas for sine, cosine, and tangent.
Inside the flaps:
My students referenced this foldable A LOT! In fact, they're still referencing during our unit on the unit circle.
Thanks to Meg, I learned about the song Gettin' Triggy Wit It by WSHS on YouTube.
If you haven't seen this video, stop everything and watch it now. I'll even be nice and embed it for you. :)
My students enjoyed the video the first time we watched it, but they had a hard time understanding a few of the lyrics. So, I printed the lyrics off for them the next day to glue in their interactive notebooks. In the future, I would print these off and have students draw example problems on the paper as they watched it.
The page unfolds to show the rest of the lyrics.
One of my students apparently got in trouble by the cheerleading coach for dancing like the students in the video. She was told that the dance moves were inappropriate... Of course she threw me under the bus and said "Well my math teacher taught it to me."
Now that we knew how to find the basic trig ratios, it was time to start thinking about radians.
I don't ever remember really learning what a radian was when I took trig in high school. I'm sure my teacher told me, but I guess it didn't really stick. We're going to be dealing with radians a lot, and I decided I didn't want my students to flip out every time radians were mentioned.
Naturally, I turned to google. Let's just say I am a frequent google user. Some people in town refer to me as "Google Girl" because I use google so much. :)
SEARCH: "What is a radian?"
I quickly found a great discovery activity that involved circles and pipe cleaners and tracing and cutting and folding paper and basically everything I love and adore in life.
I would link you to the actual activity I used, but I actually ended up combining what I liked from five or six different resources.
Step 1: Raid your kitchen cabinets for every circular lid you can find.
Step 3: Trace your lid onto colored paper.
Step 4: Cut out the circle. Fold it in fourths to find the center.
Step 5: Mark the center of the circle.
Step 6: Cut a pipe cleaner the same length as the radius of the circle.
Apparently, pipe cleaners are now called "fuzzy sticks." What is up with that?!?
Step 7: Draw in the radius on the circle. Line up the pipe cleaner with the edge of the radius.
Step 8: Start wrapping the pipe cleaner around the circumference and marking where it stops.
Step 9: Divide the circle into sections based on your markings.
If students have attended to precision, They should end up with 6 equal sized sections plus a tiny left over section.
Glue the circle in your notebook.
Define a radian as the angle that has an arc length equal to the radius of the circle.
I wasn't planning on this, but my students decided we needed to glue our pipe cleaners to the radius. They turned out looking pretty cool!
We wrote in the definition of a radian.
Then, we set about figuring out just how many degrees are in a radian. If there were just the six equal sized sections, how many degrees would a radian be? 360 degrees divided by 6 is 60 degrees. But, there are six sections AND a little section, so each section must be less than 60 degrees.
We decided to set up a proportion to determine just how many degrees are in a radian. Okay. Let's be honest. It was my idea to do this, not my students' idea. But, they did go along with it, so I guess it still counts. At least, that's what I'm telling myself. ;)
Before we could set up a proportion involving radians, we needed to review the formula for circumference of a circle. When I asked my trig students for the formula for circumference, they gave me the formula for area of a circle. They told me that "pi r squared" was the only circle formula that they knew... #sigh
When looking for information online regarding teaching radians, I ran across a song to sing that features the formula for circumference of a circle. There's just something about song that helps me remember things. And, I assume that some of my students are like that, too. They decided we should write the lyrics for the circumference song in our notebooks. It's a simple song set to the tune of Twinkle, Twinkle Little Star: "Twinkle, Twinkle Little Star. Circumference equals 2 pi r." Isn't that the most brilliant thing you've ever heard in your life?!?
They remembered from geometry and our geometry review earlier in the year that a circle is equivalent to 360 degrees. And, the circumference of a circle is 2*pi*r. We eventually found that a radian is approximately 57.296 degrees.
I'm hoping that this activity helps my students to never fear when the word radian appears.
After learning what a radian was, it was time to learn how to convert between radians and degrees. We made a much-referenced foldable over this.
Outside of Radians to Degrees and Degrees to Radians Foldable:
Inside of Foldable:
Close up of radians to degrees notes/examples:
Close up of degrees to radians notes/examples:
The next page is one of my favorites. If I'm I may have created this page in order to have an excuse to use a brad in our notebooks. Does that sound like a crazy thing to do? It probably is. It's definitely a long story...
I had students cut out the initial side and terminal side for their angle out of card stock. The initial side was glued down on the x-axis. The terminal side of the angle was attached to the paper with a brad. Apparently, these are called "paper fasteners" in other countries.
Once students had constructed their handy, dandy, spinny angle page, I asked each student to move their terminal side to form a 45 degree angle. Then, I instructed them to take a look at the angle formed by their neighbor. They soon realized that some students had made their 45 degree angle in the first quadrant, and others had made their angles in the fourth quadrant. This led to an awesome discussion.
We added notes to our page regarding how to graph positive/negative angles.
I had the bright idea to make a card sort for my students over coterminal angles. They were going to write the definition of coterminal angles. Then, I was going to give them a page with all kinds of angle measures. They would sort them into groups that were coterminal with one another. Then, they would take a blank square and write an additional angle that was coterminal with the other angles in the group.
This. Did. Not. Go. Well.
And, I'm not really sure why.
Next up, some pretty boring notes about reference angles. Sorry, nothing exciting on this page.
The last standard for students in this unit was to be able to find the trig ratio of angles formed by various ordered pairs.
I think I could have done a better job of writing out these steps. Maybe next time I teach trig I will make these steps clearer...
We took a piece of graph paper and folded it into a poof book. This let us fit three practice problems onto our page. I let students pick ordered pairs for the class to work with. I would choose the quadrant, and students could pick any ordered pair in that quadrant. This prevented all of our examples from being in the first quadrant.
First Quadrant Example:
Second Quadrant Example:
Third Quadrant Example: