Experience First

Today students work on a challenging open middle task in small groups. The goal is to continue to solidify understanding of the unit circle and angles given in radians. Furthermore, students will need to find equivalent values for both angle measures and unit circle values.

In this task, students must fill in the empty boxes using only the digits 0-9 at most one time each. It is critical that you give students time to wrestle and struggle without giving hints or tips. In our experience there is a lot of guess and check at the beginning but after around 10 minutes, students start to make important observations about the use of equivalent values, coterminal angles, and why certain angles will not be used (sqrt 2/2 already requires two two’s, so the angle will not be pi/4, 3pi/4, 5pi/4, etc. or that the cosine angle must be in the first or 4th quadrant since the output is positive). Avoid the temptation to rush in and give pointers even when it seems like students are working unproductively at the beginning of the task. Although we want students to see the patterns and structure quickly, it’s important they get to those conclusions by themselves!

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Formalize Later

You may wish to debrief the task and make a list of strategies and observations students made. This is helpful for establishing problem solving skills. For example, students will realize that 1, 2 and 3 are often used on the unit circle and so it was critical to find equivalent forms of those angles and values. Ask students why it was more challenging to not be able to use 0. You could even ask how many different ways there are to refer to the angle at 0 radians (we can think of more than 12!).

Any extra time can be spent working on homework or answer other questions related to tomorrow’s unit 4 assessment.