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Intro to trig graphing with Desmos Activity Builder

Background info: I co-taught this Desmos Activity to 11-12th graders taking Trig/Math Analysis. They are going to start the chapter on graphing trigonometric functions on Monday, so this is an introductory activity to help students develop some of the vocabulary and background knowledge that they will use for the chapter. This also happened to be Spirit day, with shortened classes and a spirit rally for that night's football game against the rival school.

Despite the somewhat challenging circumstances, the activity went great. Students were engaged from bell to bell. We heard comments like "thanks for making math fun" and "when can we do this again?" The biggest hit of the activity was the ferris wheel screens (11-12) with one girl claiming that she couldn't even focus on the rest of the activity because she was too distracted by those screens.

Note: The ferris wheel looks way better in the activity.
Check it out here on screens 11-12.

What I like most about an activity like this is that students begin by using informal language to describe how a graph changes, and then we build the formal vocabulary from their descriptions. I gave maybe a 5 minute lecture in the middle about how the amplitude, period, and vertical shift are connected to the standard form of the sine graph (y=a*sin(b(x-h))+k). We didn't look at horizontal shifts on this day as this was an introductory activity. Students spent the period checking their understanding of both the vocabulary, and how it related to the equation for a given graph. They even had a chance to apply their knowledge of the sine function by looking at how to model a ferris wheel rider's height versus time. The other teachers and I used the teacher dashboard all throughout to see which groups of students needed help on a particular screen.

The only challenge we ran into throughout the day was when students deleted elements on the graphing pages. Some of them deleted the slider on the ferris wheel screen (11), so they weren't able to do the task at all. We recommended that they try the following similar problem, or log in a second time. Being able to reset a graphing screen would be helpful. I've also been telling students to stay out of any construction folders, explaining to them how easy it is to mess up some aspect of the page, in which case they won't be able to complete the task.

Overall, a very successful activity. Thanks to #mtbos for giving me the ideas for the screens in this activity. Two resources in particular that were helpful are here (by Steve Phelps) and here (by John Golden).
Great activity - many thanks for sharing.

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