## Sunday, December 5, 2010

### The Skeleton Tower Problem

This is Skeleton Tower, use the problem solving strategies we have learned to solve the problems below.  Discuss how you solved the problems and which strategy or strategies you used.
(a) How many cubes are needed to build this tower?
(b) How many cubes are needed to build a tower like this, but 12 cubes high?
(c) How would you calculate the number of cubes needed for a tower n cubes high?﻿

1. (a)66 cubes. I counted 6 in the middle and each of the four legs I counted 15, so 15 x 4 + 6 = 66.
(b)To find out how many cubes when it's 12 high, i saw that there was a pattern. Each leg was 11+10+9+8+7+6+5+4+3+2+1 = 66 So it's 66 x 4 +12 = 276.
(c)To find the number of cubes n high, I looked for a pattern. I drew pictures(strategy) of towers 1 high, 2 high, 3 high, and so on. I made a table(strategy) of how many cubes comprised each tower and I looked for a pattern(strategy). I found the pattern was to multiply the height, n, by the sum of the height and the previous height, or n(n+(n-1))

2. (a)66 cubes. I just looked at the picture and counted the cubes. I didn't think about counting one leg of the tower and multiplying by four...good idea, thanks
(b)To find out how many cubes when it's 12 high, I just drew a picture(strategy) of a tower 12 high and counted the cubes, I got 276.
(c)To find the height n high, I tried to make the problem simpler (strategy) I drew pictures of towers 1,2,3,4,5,6 high and counted the cubes, I made an organized list(strategy) of the heights and total cubes, I was looking for a pattern(strategy) but I could not find the pattern.

3. (a) 66 cubes. I actually used sugar cubes to rebuild this tower and counted the number of cubes (Act out or use objects strategy)
(b) I didn't have enough cubes so I built the center of the tower 12 high, then one leg of the tower using sugarcubes and multiplied the leg times 4, I got 276 cubes.(find a pattern, use objects strategy, make it simpler)
(c) To find the height n high, I used my sugar cubes again. I found that if I took the cubes from a leg and stacked them on the opposing leg, I could create a rectangular wall. It made it easy to calculate the number of cubes by multiplying the height and the width. I made walls of varying heights and made a table of the heights. I found a pattern, and to calculate n high, it's n(n+(n-1))

4. This is Skeleton Tower, use the problem solving strategies we have learned to solve the problems below. help me with math