# Trig Design

More in my desire to help the students less this year.

I've had a good schtick going for a few years. I take something that ordinarily would be classwork and pass out colored paper and markers and have the students do a display version that goes in the hallway. In my life as an academic teacher, these assignments were pretty scripted. In this instance we're discussing trig graphs.

Rather than the standard "here are twelve functions, everyone pick two" I came up with these specifications:

• create a set of 3 sine functions and 3 cosine functions
• "negative" amplitude must be demonstrated
• a "faster" function must be demonstrated
• a "slower" function must be demonstrated
• a vertical translation must be demonstrated
• create two graphs in desmos, one for each type
• print and identify your creations

Negative amplitude means a reflected function. Faster and slower reference the length of the period. If you've ever struggled with the whole why do I calculate the period of sin(2x) by determining 2pi / 2, try asking the student how they would complete a 10s task twice as fast. It nixes a trick and builds better understanding all at once. This is a handy if you ever want to discuss models of electrical signals.

This activity is quick thanks to the infrastructure I've been building for a few years: tons of iPads and a color printer in the room. No computer lab sign up sheets necessary.

I liked the vast variety of functions. It also brought some misconceptions to the surface. A lot of students could create a faster or slower function, but weren't sure how to tell me the actual period. This created an excellent opportunity for follow up the day after this activity. I also fielded a lot of questions about whether vertical translations affect things like amplitude and period. Again, great follow up material for the next day.

Something you may notice. If you study the work closely, there are errors. It happens. While on display, it's practice. I expect there to be errors in practice. Students self-correcting their errors between the time we practice and we assess is what I care about. If I were to nitpick these as they went up, I counteract my goal of minimal help.

Start to finish this was one and a half class periods. I'm also getting better at anticipating activities that finish early and having something ready for the ones that finish early.

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