# Probability Games Investigation

In this task, students are asked to investigate the fairness of two different probability games The games (a coin flipping game and a ball picking game) are specifically designed so that they are unfair and can be proven so through the finding of an pattern in the probabilities. The coin flipping game, in Part A, has a fairly simple pattern that is based on adding probabilities of compounded events. Meanwhile, in Part B, the ball picking game’s pattern is quite a bit more complex as the game has an extra condition that changes the probabilities of events over the course of a game.

Math Concepts: probability probability of compound events tree diagrams sample space
MYP Related Concepts: models patterns
MYP Key Concepts: systems
MYP Global Context: Fairness and Development

# Financing a New Gym RLP

This assessment is suggested to be used in an introduction to financial mathematics unit in conjunction with a review of operations with fractions. The context of the assessment suggests that your school is considering to build a new gym for the school. Students will be asked to propose a financial plan for this new gym, where the gym needs to be constructed within 3 years and for the least amount of money.

Math Concepts: fraction addition financial math principal and interest rates multiplying by a percentage
MYP Related Concepts: models quantity
MYP Key Concepts: communication logic
MYP Global Context: Fairness and Development

# 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 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