The concept of polygonal numbers is closely related to regular polygons. Namely, polygonal numbers are numbers that are represented by dots arranged in a shape of regular polygons. In this investigation, students discover patterns for polygonal numbers (starting with triangular numbers and then square numbers, pentagonal numbers, and so on), derive explicit formulas for them, and combine their findings to verify and justify an explicit formula for one of the polygonal numbers.

Math Concepts:
triangular numbers
square numbers
pentagonal numbers
hexagonal numbers
polygonal numbers
quadratic sequence

MYP Related Concepts:
patterns
systems

MYP Key Concepts:
relationships

MYP Global Context:
Identities and Relationships