The above is an exercise from my favorite Geometry textbook.
You know when you're going to need to find the area of a 30 degree sector? In Trigonometry, when quickly knowing how to transform a central angle into a proportion of a circle is crucial for quickly moving between degrees and radians.
That's why you need a good curriculum, to start helping these kids get ready for Trigonometry a solid two years before they've even enrolled in the course. That sort of thoughtfulness is so, so hard to achieve while trying to make sure each individual class session is awesome.
Here's another bit of curricular thoughtfulness that amazed me this week.
Do you see it? (Actually, this picture is pretty small so you might literally not be able to see it.)
Question 1: Make an angle that measures 60 degrees.This is the sort of little touch that makes this such a lovely 4th Grade curriculum. It's like, forget the progressive, weirdly controversial activities and lessons. Does your curriculum go the extra mile to make sure that kids can actually read mathematical notation?
Question 2: Explain how you know that this is a 60[degree symbol] angle."
I didn't even notice this genius move until a little 4th Grade girl asked me what that symbol meant in class.
If you're making your own curriculum -- using all your own worksheets, your own activities and assignments and everything -- you need to take a close look at some of the best work out there in curricular design. Every time I get cocky, I take a look at CME, CMP or TERC and I realize that they're thinking like ten steps ahead of me.
I'm not saying that a great curriculum's activities and tasks are better than mine. Sometimes they're great for my kids, usually I at least have to turn them inside out before using them. But for previewing, reviewing, and a general sensitivity toward common student pitfalls, I think it's going to be a long time before I can do better than these guys.