This is an activity I did as part of a large, multidisciplinary project I taught about fractals and architecture. You can use it in any kind of project or unit where you are using fractals in some way or just want to expand some mathematical concept that can be applied to this. You can get as deep as you want with the math or keep it somewhat basic.
Grade Level: 5th – 12th
Materials: Sugar Cubes, glue, cardboard.
Prerequisite: You will first need to somehow introduce your students to the Cantor Set and maybe some of the possible two-dimensional extensions such as the Sierpinski Triangle and the Sierpinski Carpet.
Driving Question: How could the Cantor Set inspire great architecture?
Final Product: Architectural model built out of sugar cubes
Step 1: Set them up with the driving question and tell them that they are taking on the roll of an architect. Their client is asking for a massive, inspiring building to house residences and businesses, or something like that. They will be designing a building inspired by the Cantor Set and building an architectural model. Have them come up with a design and calculate the number of sugar cubes needed for their models.
Step 2: After they have finished their designs and calculations, have them build their model.
It’s that simple! You might want to create a worksheet for them with mathematical questions about their fractal-like design. These questions could be about volume, surface area of the building, the model, or the actual fractal that it is based on. Try having them build the model to scale and actually display the scale. They could also be asked more complex fractal questions about the Menger Sponge. It all depends on what level of students you have and what you are doing with this lesson.
Any questions? Ask away.