# Chords and Regions

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

# Birthday Cake Sharing RLP

This real-life problem explores the concept of sharing with students and asks students to consider what to do when a situation is presented to them where it is impossible to be completely fair with everyone. It asks, what can you do to make it as fair as possible? To answer this, students will need to create a seating chart to split birthday cakes that are spread out across 3 rooms in such a way where the amount of cake each person gets could be considered as fair as possible. Students will need to back up their proposal with reasons. To do this, students will need to figure out what fraction of a cake each student will get in different scenarios. This assessment can also be done with decimals.

Math Concepts: fractions decimals equivalent fractions operations with fractions
MYP Related Concepts: models quantity
MYP Key Concepts: relationships
MYP Global Context: Fairness and Development

# Area of Regular Polygons

In this assessment, students investigate areas of regular polygons (equilateral triangle, square, regular pentagon, regular hexagon, and so forth) that have the same side length. Through algebraic work, they will discover an area formula for each of these polygons, as well as a formula for the area of a regular polygon with n sides, each with a side length of 1 unit.

Math Concepts: area regular polygon SOHCAHTOA equilateral triangle square pentagon hexagon
MYP Related Concepts: measurement models
MYP Key Concepts: logic
MYP Global Context: Identities and Relationships

In this assessment, students investigate two sets of patterns that arise from a sequence of square grids, in which some of the squares are shaded while the others are non-shaded. After observing the pattern in the given sequence, students focus on the pattern of shaded squares and suggest a general rule for them in the form of both a recursive and an explicit formula, then turn their focus on the pattern of non-shaded squares and discover a general rule for them in the form of an explicit formula. To close their investigation, students select and apply their choice of mathematical problem-solving techniques to verify and justify their previous findings.