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"In my honors Algebra II class of sophomores, I always look forward to doing a culminating project on quadratics.  We start at the beginning of the chapter with introducing the project and having the kids break up into groups of 3 and 4 and start designing and building a catapult outside of school.  " This seems like a fun activity that could be enchanced by Logger Pro and/or Desmos (www.desmos.com). Logger Pro would allow the students to video a sample shot of their catapult and then break down the distance of their shot at specific intervals/times. Desmos would allow the students to graph the quadratic and place their catapult at the correct location in order to hit their target.

"The point here is that the technology made the conversation easier. Instead of creating 20 different examples of graphs and seeing what happens as each variable is changed, students were able to visualize the changes, both in the graph representation, and in the formula representation. When asked if they noticed anything after the "Point on the line" slider was changed, one student said they noticed the Intercept-slope form of the equation did not change. Another student responded to him with "that form of the line doesn't depend on which points you use.""

"Empower your students to think critically about data, ask meaningful questions, and communicate their conclusions."

Using this article and the tools listed (http://mentalfloss.com/article/56120/how-far-does-mario-have-run-and-swim-super-mario-bros) as the basis for the lesson: How far does Mario travel in this speedrun? Calculate the proportion of the game that this speedrun completes and leaves incomplete. Based on the time it takes for this speedrun, what's the fastest that you could beat Mario if you completed EVERY level.

Variety of applications for perimeter, area, measurement, etc.

"This resonates strongly. I shared a lesson with fellow teachers, and realized I had no good way to communicate what actually made the lesson powerful, and how charging in with the usual assumptions of being the explainer in chief could totally ruin it." Couldn't say it any better than this...Personally, this is one of the reasons I've tried to get video of classroom action and student reflections over the past several years for H21. We can write all we want about what makes a lesson powerful, but it's much more obvious and useful when we see it/hear it ourselves.