Ok, back from break well rested and ready to finish off the semester. We have two weeks left and we need to cover trigonometric ratios and interior & exterior angles of triangles. That should get us to roughly 25 standards for the first semester, about 5 per unit (and also per month). I'm very happy with how the pacing of this new curriculum has worked out.
The intro activity I used today is the same as I've used for years to start this unit (because I like it, not necessarily because I'm lazy). Have students work in groups of 4-5 (this is key, they NEED multiple data sets to draw conclusions) and draw a right triangle with a common angle (between 20 and 70 deg to make life easier). The students all thought that common angles make congruent triangles, so I'm not sure if I should spend more time on similarity != congruence beforehand next year, but for now we're on a time crunch.
The idea is to get proportional triangles, but the students don't really see that coming. Then they each measure the sides of their own triangle (another key point, they each need their own triangle) and fill in a data table with both their, and their group members' data. They finish by evaluating set ratios, and then answer some leading questions about what they found.
I know it's not the most student led investigation in the world, but it does tie in ideas of ratio & similarity to expand on what we've already talked about with very specific right triangles to help branch out into a broader world.
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