I worked with a 10th grader, Shania Mather. I would like to share her summary of her project with you. She worked on this all outside of school hours! I was most impressed with her ability to choose a strategy to represent the process and to persevere in finding a solution. Good job, Shania. I'm glad to have had the opportunity to work with you this year.
The Frog Project
My problem consisted of having seven lily pads and six frogs. On each side, there were three frogs of the same color. You had to get the same colored frogs from one side to the other, only going from one lily pad at a time, and you may cross a frog of the different color.
We had to find a way to model the problem so we could see how to solve it. We made papers that had seven circles in each row that were representing the lily pads. Instead of using colored frogs, I used triangles on one side and squares on the other side. The squares and triangles represented the frogs two different types of frogs. Each row of lily pads represents a new step that I used.
After I was was done with a paper and used all the lily pads, I looked back at the previous steps that I used to see what I could do different to solve the problem. I would always look back on my steps and see what I could do to get closer to solving the problem. Each time that I tried I would get a little bit closer.
I was working on the last paper before the final solution I came up with and realized that I was close to solving it. I looked back on all the previous steps before and saw something that caught my eye. I felt like if I changed a few of my steps I would solve it or at least get closer. As you can see, I added more lily pads in the end because I was getting close to solving the problem and felt like I just needed more lily pads.