Total 3 faces painted 2 faces painted 1 face painted 0 faces painted Size of Cube number of yellow yellow yellow yellow small cubes 2x2x2 8 8 0 0 0 2³ 3x3x3 27 8 12 6 1 3³ 4³ 64 8 24 24 8 5³ 5x5x5 125 8 36 54 27 6³ 216 8 48 96 64 4x4x4 These are the cubes Patterns we discovered: inside where the paint doesn’t reach. They Always 8 because This number goes up This is a little square in make up a smaller cube We found the patterns for the 3 yellow faces are always 8 vertices in 12s as each of the the middle of each and are all cube and the 2 yellow faces columns but needed however big the cube 12 edges gains a face. Each number is a numbers. some help from our teacher to find the patterns is new cube each time square number X 6 (Look how they link to for the last 2 columns total number of cubes)
Size of Cube Total number of small cubes 3 faces painted yellow 2 faces painted yellow 1 face painted yellow 0 faces painted yellow 2³ 2x2x2 8 8 0 0 0 3³ 3x3x3 27 8 12 6 1 4³ 64 8 24 24 8 5³ 5x5x5 125 8 36 54 27 6³ 4x4x4 216 8 48 96 64 Patterns we discovered: We found the patterns for the 3 yellow faces and the 2 yellow faces columns but needed some help from our teacher to find the patterns for the last 2 columns Always 8 because are always 8 vertices however big the cube is This number goes up in 12s as each of the 12 edges gains a new cube each time This is a little square in the middle of each face. Each number is a square number X 6 These are the cubes inside where the paint doesn’t reach. They make up a smaller cube and are all cube numbers. (Look how they link to total number of cubes)
PaintedCubeArunside.docx