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