Gum Ball POW
For this problem of the week, we were assigned a probability type problem. In each scenario, there was a set of children who wanted the same color of gumball. Each gumball costs 1 cent. The problem is asking us to find the max amount of money the parent would have to spend in order to get all the children the same color gumball, considering the number of kids and the number of colors of gumballs. For the first scenario, it was very basic. There was two children and two different colors of gumballs. I made a quick diagram to show what the max amount she would need to spend is, which I will explain in the next paragraph. Basically, I went through every combination of gumballs before getting two of the same color. The max amount of money the parent would have to spend is three cents, because you can get one white, one red, but the third would have to complete the pair no matter what color it was. For the second problem, I repeated what I did in the first. Except the variables were changed, instead there were two kids and three different colors of gumballs. I did the same process, going through the sequence until I got a pair of the same color. The max amount she would have to spend is four. It was more than the first problem because instead of there being two colors of gumballs, there was three. For the third problem, the the variables were changed even more. There were three children with three different colors of gumballs. The max amount would be seven cents.
At this point I was able to easily able to do these problems and create my own. Heres a few pictures of my work and the process I used to solve the problems.
At this point I was able to easily able to do these problems and create my own. Heres a few pictures of my work and the process I used to solve the problems.
For the chart, c= colors of the gumballs, k= the kids, and x= the cost. The charts showed a trend in the data, showing that the cost was x more amount than the kids. For the drawing, this is how I went about seeing how many different gumballs I could get before getting four of the same. I also came up with an equation, c x (k-1) + 1=x. For my example problems, I tried many different things including four colors and four children (as seen above).
I think this POW was simple, and finding patterns and making charts was easy. This POW taught us more about probability and even variables. For the most part I drew things out and did things visually more than I used equations or cared to look for patterns. The habit of a mathematician that I used for this POW was visualize because I drew out every problem and thats how I came about really understanding the problem and even being able to do them in my head.
I think this POW was simple, and finding patterns and making charts was easy. This POW taught us more about probability and even variables. For the most part I drew things out and did things visually more than I used equations or cared to look for patterns. The habit of a mathematician that I used for this POW was visualize because I drew out every problem and thats how I came about really understanding the problem and even being able to do them in my head.