For that reason (and a few more), I'm considering moving Three-Dimensional Measurement to the beginning of the year. (This module is listed third out of the five. This unit will fall in the February to March range.)
- Firstly, I notice that even the simplest prior knowledge that you'd expect sophomores (and advanced freshmen) to have internalized from elementary school is lost. (For example: area of a rectangle formula, area of a triangle formula, etc. They seem to think "length times width times height" is the answer for everything.)
- Secondly, I believe this is the unit that students expect to learn when entering Geometry. Perhaps meeting their immediate expectation and branching off from it to the other units of study would help students to better adjust to Geometry.
- Thirdly, it's so Algebra based that it will review Algebra while introducing Geometry. I think this will help ease students into Geometry as opposed to the jolt that seems to occur when students realize what Geometry really is about.
- Lastly, students have such a difficult time visualizing three-dimensional space. However, they are more accustomed to visualizing three-dimensional shapes. I want to use the three-dimensional shapes to teach about points, lines, and planes. I think students will be able to understand these terms and their accompanying concepts much more easily when looking at a prism than a strange looking diagram of lines going in three or more different directions. At least, that's what I experienced when looking at different test prep questions with my classes. The points, lines, and planes questions using three-dimensional shapes had much better results than the questions showing random diagrams.