In this assessment, students investigate the maximum number of regions in a circle created by a different number of chords. In Part A of the investigation, students first discover how to draw chords in a circle to ensure the maximum number of regions in the circle. In Parts B and C, students use the patterns they found previously to describe and then suggest rules in the form of recursive and explicit formula. Finally, in Part D of the investigation, students use their choice of mathematical methods to verify (and in the extended version justify) their rules found previously.

Math Concepts:
chords
regions
sequence
quadratic sequence
recursive formula
explicit formula

MYP Related Concepts:
patterns
systems

MYP Key Concepts:
relationships

MYP Global Context:
Identities and Relationships