Last Digit of Product of Powers

In this assessment, students explore the method used to solve a fairly common problem that often appears in mathematics competitions: finding the last digit of the product of two large numbers expressed in exponential notation. As part of this task, students discover patterns in the last digits of the powers of 2, 3 (and later 7 and 17), apply the method of column multiplication, and put all their findings together to discover how to solve the given question.

Math Concepts: exponents last digit powers of 2 powers of 3 powers of 7 powers of 17 remainder patterns
MYP Related Concepts: generalization patterns
MYP Key Concepts: relationships
MYP Global Context: Identities and Relationships

Angles in a Circle

In this assessment, students investigate the relationship between two types of angles drawn in a circle: central angle and its corresponding inscribed angle. Throughout the task, students use a ruler to draw radii and chords and use a protractor to measure central and inscribed angles. Through these measurements, students predict, then discover and describe the relationship (in words and in the form of a mathematical equation) between central and inscribed angles. Then, students verify their findings for central angles that are either obtuse, straight, or reflex angles.

Math Concepts: central angle inscribed angle measuring angles
MYP Related Concepts: patterns space
MYP Key Concepts: form relationships
MYP Global Context: Orientation in Space and Time

How Many Coins?

In this assessment, students investigate the number of coins needed to give back change for amounts of purchase between \$0.95 and \$0.05, using 5-cent, 10-cent, 20-cent, and 50-cent coins used in Australia and then using 5-cent, 10-cent, 25-cent, and 50-cent coins used in the United States. Then, after analyzing these two coin sets, students are asked to design their own sets of coins creating and analyzing their own set of values. This is a fairly simple task that allows students to mathematically approach a simple concept and encourages them to design a set of values for which the number of coins needed is as low as possible.

Math Concepts: number operations percentages
MYP Related Concepts: quantity systems
MYP Key Concepts: logic relationships
MYP Global Context: Globalization and Sustainability

Creating Density Towers

In this assessment, students investigate the mathematics behind a simple but fun scientific concept / experiment, called Density Towers. Given three rules to follow (purely for mathematical reasons and maybe for the sake of aesthetics), students work through creating 2-, 3-, and later 4- and 5-layer density towers. In the process, they identify what thickness is not possible for layers (using factors and fractions of the whole), and how to create different layers given a set of rules and a goal to follow.

Math Concepts: fractions density tower
MYP Related Concepts: change representation
MYP Key Concepts: aesthetics form
MYP Global Context: Scientific and Technical Innovation

Sustainable Housing Communities

In this assessment, students are asked to write a report to determine the optimal number of houses that should be constructed in a growing community to achieve carbon neutrality. This report involves finding linear relationships between the number of trees, houses, and carbon production and consumption. This ideal number is found through writing simultaneous equations and solving them both graphically and algebraically. The students are also asked to provide a statement of accuracy and discuss any other relevant factors in their report.

Math Concepts: linear functions coordinate geometry systems of equations
MYP Related Concepts: systems
MYP Key Concepts: communities development
MYP Global Context: Globalization and Sustainability