Math is problem solving because there are multiple steps or a procedure students need to take in order to come to a solution. However, there is not just one way that you can go about solving math problems; there are so many different approaches you can take to come to a solution. Due to the different approaches we can take to solve problems, comes with a challenge. Students must think critically in order to figure out what the best method is to use to solve problems. Through problem solving in math, students will get a sense of problem solving in real life situations. When we are faced with challenges in both the real world and mathematics and fail, there are always other methods to try until we get it correct and are successful.
Short Roads
There are four main buildings at Mount Saint Mary College. We will call them A, B, C and D. They lie at the corners of the campus. In order to improve walking distance for the students, the Newburgh Department of Transport decided to build a new road linking all four buildings together. Because they had very little money, it was decided that the new road system should be as short as possible and still allow access from any one building to any other. The engineers came up with three designs shown below.
Plan 1 Plan 2 Plan 3
Number one uses 4 miles of road, number two uses 3 miles of road, and number three uses 2.83 miles of road. The designers naturally recommend plan number three because it employed the smallest road area and, therefore, cost the least. However, when they submitted their plan to the President of MSMC, he accused them of extravagance and quickly pointed out a better design that required even less total road surface. What was his superior solution?
If you are unsure where to begin, click on Hint 1 below.
Although this problem does not require any calculations, it does require critical thinking skills which all mathematicians need in order to be successful problem solvers. I think this is a great problem for students to really think critically about different ways to rearrange the plans so they can come up with the most cost efficient plan possible. Students will need to be creative, develop different strategies, and utilize prior knowledge in order to arrive at a conclusion. While sticking to the main layout of the plan, students will need to change it in just the slightest way, but how will they change it. There are going to be multiple answers that students will come up with, but that is what makes this problem worth while. The teachers will then get a sense of how his or her students are thinking in the classroom.