I tried out the NCTM Illuminations worksheet regarding Law of Sines and Cosines. Mostly because I have an in-class field trip for programming so I’ll miss one of the sections of Precalc Honors and needed a subplan. These precalc students had a ton of practice last year with these topics, so this is more of a refresher activity. The worksheet walks the students through deriving the law of sines and cosines from right triangle trig.
Interesting quote from a student:
I like this, I don’t have to think much.
Yea, I agree. The activity had steps that the students had to think a lot about, and in the process, got lost in what they were doing, and why. Too much reading and following set steps and not enough playing. I don’t blame this particular worksheet, I blame worksheets. I just don’t like them that much. </bias>
Remember that student who needed 7 post-its to write down her identity?
Well she plugged it into desmos and found errors! She fixed them, and then emailed. Here’s the desmos confirmation. I had to make it permanent.
(Video of the laser engraver for those interested)
Guess my equation : Trig edition. Give me a cosine equation for this curve. Give me a sine equation. Give me all sine and cosine equations for this curve. Wash, rinse, repeat (careful, these three words kill thousands of computer programmers in their showers every year).
Day 1 of Advanced Computer Programming. James Tanton’s Exploding Dots. Fantastic lead in to binary numbers and it also does a really good job of challenging those kids who “knew” binary numbers before today.
At the beginning of the activity:
“Oh yay, I love these.”
“Yes, marble slides!”
“I like these things.”
And here’s a couple students working on the marbleslide challenges after the bell that ended school (they worked for 15 min after the bell):
Yep, great stuff.
I made a Desmos Trig Graph Activity Builder thing. This is the second version of the type of question that asks the students to create a graph that goes through given points. Before the revision, they would just fiddle around with the sliders until the graph looked like it went through the points, but zooming in would show the gap. I have rigged it up so that a shaded circle appears over the point when their graph goes through the point (not just gets close). And on the graphs where the students are supposed to match a given graph, the entire screen will turn red if they’ve come up with the same graph.
It’s that time of year, time to make your own trig identity!
Also time to introduce one of my favorite words!
And… there is always one of these students…
Fun project in programming class. We live coded (I talked while adding code on the projector, and they discussed questions and copied the code) this basic simulation using objects and arraylists in processing. The magic happened when they were given some time to tweak this basic sketch:
We also played with taking an input image, polling a random point for it’s color information, and then drawing an ellipse on a blank background with that color information. They had some really cool results playing with this sketch as well:
Students were playing with the mouse where the circles under the mouse would be modifying the original colors. Some students were changing the original color to black and white, some had inverses, some chose to just display the red channel. Very fun.
Solve for [blah]. I made this problem up originally with the tough instructions. It was really hard for them without being able to work across the equal sign. I added the “wimpy” version, and despite the wording, I encouraged all the groups to take that route.
When they thought that they had it, I had a desmos window open where they could enter a blah(x) function to see if their identity held.
Really cool matching problem from the CME Precalculus textbook:
Led to some fantastic discussion among the group members about trig identities, even odd functions, and how to simplify expressions. Loved it.
Still sort of bothers me that we brush by the idea that the integration sign can work on infinite sums…