Painted Cube
Imagine lots of small 1-inch cubes are stacked together to form a larger cube.
The large cube is 5 inches wide, 5 inches high, and 5 inches deep. Now the
large cube is painted on the outside, including the bottom. (No paint seeps
through the cracks on any other faces of each cube—only the outside face(s).)
Finally, the large cube is broken apart into 1-inch cubes.
How many of those 1-inch cubes have paint on 1 side?
2 sides?
3 sides?
4 sides?
5 sides?
6 sides?
No sides?
What can you say about how many small cubes are painted that way regardless of
the size of the big cube? (For example, imagine a large cube is made up of n x n x
n small cubes. How many of the small cubes have paint on 1 side, 2 sides, etc….)
Painted Cube
Imagine lots of small 1-inch cubes are stacked together to form a larger cube.
The large cube is 5 inches wide, 5 inches high, and 5 inches deep. Now the
large cube is painted on the outside, including the bottom. (No paint seeps
through the cracks on any other faces of each cube—only the outside face(s).)
Finally, the large cube is broken apart into 1-inch cubes.
How many of those 1-inch cubes have paint on 1 side?
2 sides?
3 sides?
4 sides?
5 sides?
6 sides?
No sides?
What can you say about how many small cubes are painted that way regardless of
the size of the big cube? (For example, imagine a large cube is made up of n x n x
n small cubes. How many of the small cubes have paint on 1 side, 2 sides, etc….)