# Carpets and Sponges

The construction of the Sierpinski carpet begins with a square, which is cut into 9 congruent sub-squares, from which the central sub-square is removed. The procedure is then repeated to the remaining sub-squares, ad infinitum. Similarly, the Menger sponge begins with a cube, which is cut into 27 identical sub-cubes, from which each central sub-cube is removed. The procedure is then repeated to the remaining sub-cubes, ad infinitum. In this assessment students investigate the area of a Sierpinski carpet and the volume of the Menger sponge at each stage, and ultimately finding a formula for the area of the Sierpinski carpet and for the volume of the Menger sponge at stage n.

Math Concepts: patterns sequences algebraic expressions
MYP Related Concepts: patterns simplification
MYP Key Concepts: relationships
MYP Global Context: Scientific and Technical Innovation

# Optimizing Drink Cans

In this assessment, students use their knowledge of modeling a real-life scenario with various functions, finding the minimum points/values of their model, interpreting their findings in the given context, and commenting on their findings.

Math Concepts: modeling optimization
MYP Related Concepts: measurement models representation
MYP Key Concepts: relationships
MYP Global Context: Globalization and Sustainability

# Leaning Towers

In this assessment, students use their knowledge of coordinate geometry, including gradient (slope) and y-intercept, to discover patterns between center points of leaning towers made of squares placed in a Cartesian coordinate plane. Students suggest relationships between x- and y-coordinates of a series of center points, and then between center lines of different leaning towers. Based on their findings, students make observations and generate formulas.

Math Concepts: gradient slope y-intercept pattern coordinates coordinate geometry
MYP Related Concepts: patterns simplification
MYP Key Concepts: relationships
MYP Global Context: Orientation in Space and Time

# Squares in a Coordinate Plane

In this investigation we place squares in a Cartesian coordinate plane and investigate the pattern the coordinates of their centers follow if the squares are placed according to a particular arrangement. This is a simple investigation to help students discover writing function rules for linear functions.

Math Concepts: coordinates linear functions graphs plotting points Cartesian
MYP Related Concepts: patterns simplification
MYP Key Concepts: relationships
MYP Global Context: Orientation in Space and Time

# The Optimal Shot

In this assessment, students use their knowledge of the Pythagorean Theorem as well as non-right angled trigonometry to find the optimal location (from which the star forward, Jonathan Angle, should shoot the ball) that provides the optimal angle on the goal.

Math Concepts: Pythagorean Theorem cosine rule cosine law optimization GDC trigonometry
MYP Related Concepts: models
MYP Key Concepts: logic
MYP Global Context: Orientation in Space and Time