Overview and Background

Spatial Composition and Decomposition

My colleagues and I published the pictured volume last year with Routledge. Here is a teacher review of the book: http://cohort21.com/rutheichholtz/2016/06/02/do-you-see-math/

Also, see my academic page for many resources: https://ucsb.academia.edu/DavidHallowell

My work is built on the excellent work of Professor Douglas Clements' investigations of shape composition and decomposition activities. Here is an overview of the developmental trajectory

Lesson Plan and Activity

The PDF files contain frames that the children are asked to fill completely. Less experienced children will leave gaps, cross the frame boundary, etc.They need to be encouraged to completely fill the frame with no gaps or boundary crossing. A discussion of strategies helpful once children have had time to do the activity for a bit. Do they try the basics? Flips, rotations, reflections, etc. Do they use side lengths? What about angles (most advanced)? Once they get the basic (leftmost, small frame), do they visualize how to iterate to fill a larger frame? Can they predict how many shapes they'll need to fill the larger shape? How so?

Materials Needed

3D printer, filament, paper, laminator. I use ColorFabb nGen on a Lulzbot 5. I've gotten really nice orthogonal edges by calibrating the bed and using a modified version of the recommended nGen profile, which I slowed down a bit. I recommend using a different color filament for each separate triangle class. I use a razor after printing for minor cleanup. You can laminate the frames after printing for repeated use.

Special Triangles