This lesson involves having the students hypothesize about the different relationships that exist between the size of the cube and the number of cubes that have paint on one, two, three, and zero faces. In order to help students visualize the problem, interlocking cubes could be made available.

• Students will explore constant, linear, quadratic, and cubic functions. The functions will be modeled from numerical data that they generate by thinking of an n × n × n cube being dipped in paint, and how many of the cubes have paint on zero, one, two, or three faces.

• regression
• constant, linear, quadratic, cubic
• scatter plot
• factored form of a polynomial equation

This lesson involves having the students hypothesize about the different relationships that exist between the size of the cube and the number of cubes that have paint on one, two, three, and zero faces. In order to help students visualize the problem, interlocking cubes could be made available.

As a result, students will model the relationships between the cube size and the number of painted faces by looking at the graphical representations and then creating algebraic models.