How many ways did we find?

By: Anna Grace and Tenley
We have been working on a math problem were we have to find all the possibilities to build a town. All the buildings in the town had to be the same hight. We had to fit exactly 60 families in the town. We used cubes to help us solve this problem.  One family could fit in one cube. After we thought we had all the ways we had to organize it and prove it. My partner and I used opposites to help us. Here is an example of an opposite. If my partner and I found out that 5 towers of 12 worked then we would use that and switch it around so it said 12 towers of 5. When we thought we had all the ways we made a chart to organize it. We made two columns. The first column said "number of buildings" and the second columns said "how high." Then under the column that said number of building we wrote the number of buildings. Next we wrote how many cubes high the buildings were under the column that said how high.Then we made a very thin column and numbered the ways we had thought  of, there were  12 we had thought of.Then to prove it we made a chart that looked exactly the same but instead of  having  12 lines it had 60,then we wrote all the ways we had in it. Then we counted the empty spaces. We counted 48. We added 12 to 48 which made 60. We had  found all the ways.