This activity deals with four colored cubes. Each cube is colored differently with blue, green, white, and red blocks. The object of the game is to line up the blocks so that no color is repeated on any given side. For example, each row will have only one white, one blue, one green, and one red block. There are several ways of solving this puzzle and over 40,000 different arrangements. If you don't have an organized way of solving it, you might just go insane!
1. Can you describe the cube to someone without using the cube or showing it to them?
2. Can you use the opposite pairs of sides, for each cube, written out on paper to find a solution?
3. Can two blocks be matched up so that each side has two different colors? Three?
1. Give the cubes to the students already made and colored and let them try to solve it on their own. Do not give any hints, just let them have fun.
2. Give blank cubes to the students and have them color them their own way to create a puzzle.
3. Ask them to write out the pairs of colors for each block (3 pairs per block) and use the pairs to solve it.
Reference:
Wilson, Robin J. Introduction to Graph Theory Third Edition. Longman Scientific & Technical. England, 1985.
KERA
2.3 Students identify and describe systems, subsystems, and components and their interactions by completing tasks and /or creating products.
2.11 Students demonstrate understanding of change concepts on patterns and functions.
NCTM
Standard 1: Mathematics as Problem Solving
Standard 3: Mathematics as Reasoning