Reasoning
Algebra - Stepped Pyramids
Stepped Pyramids
A pyramid is a three-dimensional shape made up of triangular faces connecting a base to a single point called an apex.
Here are some examples of pyramid-like structures that you might know
What is the same and different about these types of pyramids?
Can you think of any others?
These are all types of pyramids, and they are named after the shape of their base, e.g., triangular pyramid, square pyramid, pentagonal pyramid, and so on.
Egyptian Pyramids
The pyramids of Egypt are square pyramids because their base is square
Try making this model of a stepped square-based pyramid using cubes.
Add a new layer of cubes to make the pyramid higher.
How many cubes will you need altogether?
Suppose you added another layer.
How many more cubes do you think you would need?
Tell me everything you notice about this growing pattern.
Do you know how many cubes might be in layer ten? Justify your answer.
Can you think of a rule so that you would be able to predict how many cubes would be in any layer? What might that be?