The obvious choice for my favorite thing is Desmos. What is not immediately as obvious is just how much Desmos influences my planning and instruction. Its influence goes well beyond the specific graphs and activities I use in class. Using Desmos and being part of the Desmos teaching fellowship has shifted my entire approach to planning and instruction.
The Desmos Guide to Building Great (Digital) Math Activities provides awesome recommendations for planning any math activity. It does not matter if you are using Desmos or some other technology or no technology at all. I have noticed myself creating lessons outside of Desmos that ask for informal before formal, create an intellectual need for new skills, give students opportunities to be right and wrong in different and interesting ways, delay feedback for reflection, and connect representations. Many times Desmos helps me to accomplish these things more easily and more effectively but it's not a requirement.
One of my favorite recommendations is to create an activity that is easy to start and difficult to finish. I continue to focus on this recommendation as I look to improve my lessons. One of the biggest challenges teachers face is the varied abilities and academic backgrounds that a single class can contain. There are many Desmos activities that are not only great to use in the classroom but are also a great model of how to actually differentiate effectively. Even if I don't use an activity in class, I can still take that model and apply it to a different topic or lesson that might not even use Desmos.
I have improved many of my lessons by incorporating Desmos, but I have improved an even larger amount by incorporating the recommendations made in the Desmos Guide to Building Great (Digital) Math Activities. Desmos brings more than a tool to your classroom. It brings a shift in your instructional approach.
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