Building Pyramids A Lesson in Productive Struggle

Today we tackled a challenge. This challenge had some constraints, but was open enough to allow each group to do something different if they chose to. The task is to build a square based pyramid with a volume of 300 cubic centimetres. This followed up on us building rectangular prisms with a volume of 300 cubic centimetres.

It took some reminders with water and our solid forms to get that a pyramid with a volume of 300 cubic centimetres has the same length width and height as a prism that has a volume of 900 cubic centimetres.

Many groups chose dimensions of 10 by 10 and a height of 9.

Making the square base was the easy part. There was some trial and error when it came time for the triangles (and this is where the productive struggles began). Some groups made triangles with sides of 10, 9 and 9. That made a pyramid that was too short. Some made triangles with a base of 10 and a height of 9, which when inclined to form a pyramid left the height too short.

Some groups decided the triangles needed to be taller than 10 so that when inclined the pyramid height would be 9. They guessed and checked and ended up pretty close to accurate. Other groups used the pythagorean theorem to calculate the height that they needed for the triangles.

Another group decided to just make their own pyramid and to not care about the constraints! I guess we all choose an entry point to the task.

Next time I might give different entry points, and provide different extensions.

mild version: Make a pyramid, calculate the volume and surface area.

medium version: make a pyramid with a specific volume, calculate the surface area if there’s time (there will be iterations needed to get the volume correct).

spicy version (for those who need more extensions): make a pyramid with a specific volume, calculate the surface area and the angle of elevation of the pyramid walls.