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