Triangular and Tetrahedral Numers

thingiverse

Update: Flattened the spheres for effortless printing without requiring a raft. Models for triangular numbers {1, 3, 6, 10, 15, ..., n(n+1)/2} are now easily printed. These models can also be used to demonstrate tetrahedral numbers {1, 4, 10, 20, 35, 56, ..., n (n+1)(n+2)/6}. The spheres are intentionally connected for easy use with students. The activities can be used at various K-12 levels, depending on the instructional goals. Students can establish formulas using mathematical induction; they are as fascinating as the visual structures. To print successfully, please use a raft for better adhesion to the bed. Print Settings Printer: Flashforge finder Rafts: Yes Supports: No Resolution: .2mm Infill: 5% Post-Printing Removing the raft is essential. Carefully remove the raft after printing. How I Designed This Project I used 123D Design, which is suitable for this project. Simply align the spheres and allow a small overlap (about 0.2mm). Standards: CCSS Overview and Background Number sense The models enable students to explore number patterns at multiple levels. For young children, they can learn about the connections between visual configurations and numbers. Advanced students can focus on algebraic exploration and seek a function for the progression of triangular and tetrahedral numbers. Art should be incorporated into math instruction at all levels. Lesson Plan and Activity This activity is open-ended! Materials Needed Models of various sizes and drawing boards References Conway, J. H., & Guy, R. K. (1996). The book of numbers. Copernicus. New York, NY