* First, some exploratory activity meant to introduce a new topic and important vocabulary terms
* Some project- or lab- based learning that lasts about 2 or 3 weeks, interleaved with skills taught as needed
* Concentrated skills practice / "review" after the project
* Quiz or test on the skills
Just off the top of my head, the units where this learning structure was very applicable included:
* Tessellations (we made triangular, quadrilateral, and custom tessellations using rulers and protractors, which motivated some triangular congruent properties)
* Measurement and conversions (we learned to measure everything from lengths to volume to mass, and practiced some unconventional or indirect methods as well)
*Right-triangle trig (lots of outdoors measurements involving angles of elevation and depression and inclinometers)
* Quadrilateral trig (using KFouss's problems and some paper folding to see why quadrilaterals are built from non-right triangles, which are built from right-triangles)
* Scaling (we did logo projects and calculated how that impacted the perimeters and areas)
* Perimeter and area (using blueprint of houses on coordinate planes, with circular and concave portions)
* Surface area and volume (kids designed and built their own 3-D composite solids)
* Construction of reflections (mini-golf course designs)
* spatial projections (going from 3-D views to drawing 2-D views, and vice versa, using the computer to verify their hypotheses)
Some of the other traditional topics (integration of algebra with geometry; some coordinate-plane concepts; proofs and counterexamples; and basic geometry visualization based on language) we didn't do through projects, but I tried to still make those parts of the class as interactive as possible. Most of the topics you can illustrate through patty paper, move-around demos, and just plain fun things. Geometry is definitely my favorite class to teach, but I am always looking for new ways to spice it up! I find that after doing a project, the kids are solid with the basics and are ready for me to push them a bit farther on the paper assessment.
Here are some more ideas of projects, from a school in Columbus, NJ. (Sorry but I couldn't find the teacher's name!) I like this list. It has a variety of ideas, so that if our Geometry team decides to do different sets of core topics this year, I can still incorporate projects into my class. I think that it will make a nice complement to the visual / artistic activities from the beginning of Discovering Geometry: An Inductive Approach.
That's it for today. Till tomorrow!