I’m guessing that most of you reading this are familiar with the awkward acronym for the **M**ath **T**witter **B**log-**o**–**S**phere – one of the joys of tapping into this community is that they are *remarkably *generous about sharing ideas and resources. Today in our Geometry classes (I teach only one of the five sections we have at our school) we used an activity written by Kate Nowak (@k8nowak on twitter). It is an activity based in GeoGebra and allows the student to explore the ratio between lengths of legs in a right triangle. You can find the document we used here . I modified (very slightly) the document that Kate originally posted here. Next time I use it I will tweak it a bit. I have only twelve students in my class and chose not to explicitly team them up. They talked with their neighbors as they are usually encouraged to. However, the directions either need to be tweaked so that team references are excluded or I need to clearly team them up. I am also debating question 7. A number of students did not make the explicit leap from using the ratio they found on page 1 and using it here. I don’t necessarily want to give away too much but I may add a little prompt that they should consider the work that they have already completed. We set up a google spreadsheet and in the next couple of days I will refer to this repeatedly to show that different students working on different triangles were arriving at the same ratio. We make a big explicit deal about scale factors *between *similar figures. I do not think we spent enough time pointing out that scale factors *within* figures will also match up for similar figures. I will definitely make this more of a point of emphasis next time through my text.

I cannot thank Kate enough for sharing this activity. My students worked well and I am convinced that they will have a more solid grasp of trig ratios moving forward. As I plan out the rest of the unit I am also going to be borrowing from Sam Shah’s latest post about trig. You can find that over here.

Man – the benefits my students are reaping from people that they will never meet – such as Kate Nowak, Jennifer Silverman, John Golden, Jed Butler, Sam Shah, Pamela Wilson, Meg Craig, and so many more – is just remarkable.