MA T H  G RA P HS A N D RE LA T IO N S H IP S  LE S SO N 0 3
Lesson #3 Homework
SCORE:
Review Note Sheet and Classwork for 5 minutes every night.
For full credit, show all of your work and explain your reasoning!
Each Question is worth 5 POINTS, unless otherwise indicated.
/30
Today in class, we took an 𝑛 × 𝑛 × 𝑛 large cube and dropped it in a bucket of paint.
We found that if you broke this cube up into unit cubes, you would have:




8 unit cubes with three faces painted (the corners)
12(𝑛 − 2) unit cubes with two faces painted (the edges)
6(𝑛 − 2)2 unit cubes with one face painted (the surfaces)
(𝑛 − 2)3 unit cubes with no faces painted (the cube on the inside)
Cube
1. (10 POINTS) Imagine that instead of a cube, we
dropped a rectangular prism into a bucket of paint. This
rectangular prism has measurements of 3 × 4 × 5, just
like the picture.
How many unit cubes would have paint on:
a) Three sides?
b) Two sides?
Rectangular
Prism
c) One side?
d) No sides?
© Sponsors for Educational Opportunity 1
2. (15 POINTS) Answer the same questions in #1 above for a rectangular prism that
has measurements of 𝑨 × 𝑩 × 𝑪. (Note: Your answers will be in terms of 𝐴, 𝐵, and 𝐶)
(Hint: go back and track what you did with the numbers to answer #1, and then do the same things with the
letters 𝐴, 𝐵, and 𝐶. Draw pictures to help you)
3. When you do math at school, do you find it helpful to have a visual picture or image in your
mind? Describe a time when this was helpful to solve a math problem.
2 © Sponsors for Educational Opportunity