- Note the figure below. It is made of cubes that form stair steps. The center of the tower is 6 cubes high. On all four sides of the top tower are stair steps that extend from the center.
- How many cubes are needed to build a tower like this, but that is 3 cubes high? -- 3 + 8 + 4 = 15
- How many cubes are needed to build a tower like this, but that is 4 cubes high? -- 4 + 12 + 8 + 4 = 28
- How many cubes are needed to build a tower like this, but that is 5 cubes high? - 5 + 16 + 12 + 8 + 4 = 45
- How would you calculate the number of cubes needed for a tower N cubes high?
- How do the answers in parts 1-5 help you?
I struggled to find the equation for "n" layers. Using the work to find the the other answers did not help me much. I tried to see a pattern and found that you are adding four to each layer starting from the top but was not able to come up with an equation that worked to show that for "n" levels. It has been quite a while since algebra class! I pulled from way back and used all the strategies I could remember, but still couldn't make an equation happen :(