Points and Regions

In this assessment, students investigate (1) the number of chords and (2) the number of regions in a circle created by a different number of chords. In Part A, students discover how different number of points marked on a circle result in different number of chords/regions, then in Part B they use the patterns found previously to suggest a rule, in the form of a recursive and then an explicit formula, for the number of chords in a circle. In the last section(s) of the assessment students discover (or use) the formula for the number of regions in the circle.

Math Concepts: points regions sequence quadratic sequence quartic sequence GDC regression line recursive formula explicit formula
MYP Related Concepts: patterns systems
MYP Key Concepts: relationships
MYP Global Context: Identities and Relationships

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

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: models
MYP Key Concepts: logic
MYP Global Context: Identities and Relationships