Figuring out Figurate Numbers

Mike Shaughnessy
Mike Shaughnessy

NCTM President Mike Shaughnessy presents another interesting "Problem to Ponder" to give you and your students an opportunity to engage in reasoning and sense-making in the classroom.

Problem to Ponder — Figuring out Figurate Numbers

The figure at the link below shows the visual pattern for the first few triangular, square, pentagonal, and hexagonal numbers. These numbers are called figurate numbers. The number of dots in an individual polygonal shape represents a particular figurate number for each pattern. For example, the first five triangular numbers are 1, 3, 6, 10, 15. The first four square numbers are 1, 4, 9, 16, and the first three pentagonal numbers are 1, 5, 12.

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