Triangular and Tetrahedral Numers

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Update: Flattened the spheres for easy printing. No raft is necessary now. Models for triangular numbers {1, 3, 6, 10, 15, ..., n(n+1)/2}. They can also be used to model tetrahedral numbers {1, 4, 10, 20, 35, 56, ..., n (n+1)(n+2)/6}. The spheres are intentionally welded with each other for easy use with students. The activities can be used at many K-12 levels, depending on the instructional goals. The formulas can be established using mathematical induction; they are as interesting as the visual structures. To print, please use raft for better adhesion to the bed. Print Settings Printer: Flashforge finder Rafts: Yes Supports: No Resolution: .2mm Infill: 5% Post-Printing Removing raft Carefully remove raft. How I Designed This I used 123D Design, which is adequate for this project. Just align the spheres and allow a bit of overlapping (about. 0.2mm). Standards CCSS Overview and Background Number sense The models allow for the exploration of number patterns at multiple levels. For young children, they could learn about the connections between visual configurations and numbers. For advanced students, they could focus on the algebraic exploration and seek a function for the progression of triangular and tetrahedral numbers. Of course, art should be sought at all levels of math instruction. Lesson Plan and Activity Open-ended! Materials Needed Models of various sizes and drawing board. References Conway, J. H., & Guy, R. K. (1996). The book of numbers. Copernicus. New York, NY.