Special Triangles

thingiverse

These specially designed triangles are ideal for spatial composition and decomposition exercises that challenge students to think critically about geometry. Perfect for early elementary grades, they're also suitable for middle-upper elementary as students transition from identifying features to understanding properties. PDF files include blank frames for composing shapes, but the larger square frames may appear slightly larger than intended - a fix is in the works. Standards: CCSS Overview and Background Spatial Composition and Decomposition My colleagues and I recently published a comprehensive volume on spatial reasoning with Routledge, which features exercises similar to these triangles. Check out this review from a teacher who used our book: http://cohort21.com/rutheichholtz/2016/06/02/do-you-see-math/ For more resources, visit my academic page: https://ucsb.academia.edu/DavidHallowell My work builds on the pioneering research of Professor Douglas Clements, who extensively explored shape composition and decomposition activities. This lesson plan outlines a developmental trajectory for these exercises: Lesson Plan and Activity The PDF files contain frames that children are asked to fill completely, but less experienced students may leave gaps or cross frame boundaries. Encourage them to think strategically about filling the entire frame with no gaps or boundary crossing. As they work on this activity, discuss strategies like using flips, rotations, reflections, side lengths, and angles to solve the problem. Once they've mastered the basics, ask if they can visualize how to apply these concepts to larger shapes. Can they predict how many shapes they'll need to fill a larger frame? How do they arrive at that conclusion? Materials Needed A 3D printer, filament, paper, and laminator are all necessary for this activity. I use a Lulzbot 5 with ColorFabb nGen filament, which provides excellent orthogonal edges when calibrated correctly. To achieve the best results, slow down the recommended nGen profile slightly and use a modified version of the settings. For minor cleanup, use a razor to remove excess filament. You can also laminate the frames after printing for repeated use.