Chapter 14.4, Problem 8MC

a. Shawn used small cubes to build a bigger cube that was solid and was three cubes long on each side. He then painted all the facts of the new, large cube red. He dropped the newly painted cube and all the little cubes came apart. He noticed that some cubes had only one face painted, some had two faces painted, and so on. Describe the number of cubes with 0, 1, 2, 3, 4, 5, or 6 faces painted. Have each member of the group choose a different number of faces and then combine your data to see if it makes sense. Look for any patterns that occur.

b. What would the answers be if the large cube was four small cubes long on side?

c. Make a conjecture about how to count the cubes with different number of painted faces if the large cube were n small cubes long on a side.