Though I am teaching a lot of material to my students, they seem to be handling it well. After the first week of class, the grades are: 7 A's, 4 B's, 5 C's and 2 F's.

We went through a lot of the basics of geometry:

- Points, Lines, Planes

- Angle types (adjacent, linear, vertical, supplementary, complementary) and their properties

- Angles created by transversals, and all the theorems associated with parallel lines cut by a transversal

- Basic formulas for perimeter, area, and volume, integrated with algebra

- Triangle sum theorem, exterior angle theorem

- Lots of word problems and angle webs too

This is a short week due to the 4th of July. We will be working on triangle inequalities, the Pythagorean Theorem, special right triangles, and the like.

Hopefully, their energy will stay strong as we move through the curriculum. It's interesting to see how some students love working with Sketchpad and learn a lot by using it, and others really feel like they don't learn from the guided explorations. This just gives me further belief in the idea that both guided exploration and direct instruction are necessary. I have reassured the students who are not enjoying Sketchpad that all concepts we explore in Sketchpad will also be taught through direct instruction with lots of examples for them to practice. There is definitely a benefit to having a 5-hour class!

A beautiful combinatorics argument

11 hours ago

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