Matrices
Matrices are an easier way to do many mathematical problems such as, bug diffusion and sand-demented population. They are a little bit confusing; however, you don't cover them in math until you take Algebra II. For example, when we used the matrices in the bug diffusion we put the total number of bugs at the beginning of the problem in one matrix. Then we put the percentage of the number of bugs that move during each transition in another matrix. When you multiply the two together you get how many bugs moved from each tree during that transition. You can also raise the first transition to the fourth power to get the total number of bugs on each tree after four transitions.
In the sane-demented problem we used matrices to figure out how many sane become demented and how many demented become sane. You can do this by placing the beginning figures in one matrix and the transition percentages in another. Then you would multiply them together to get the number of each after one transition. Once again you can use the raising to a power to find how many there would be after a later transition. However, each time you do this you must remember to change your starting figures in order to get the correct number at the end.
Matrices do make transitions easier, but if you are not sure how to do them then maybe you should just work them out the long way until you figure it out.