Favorite Math Problem
The four numbers a < b < c < d can be paired in six different ways. If each pair has a different sum, and if the four smallest sums are 1, 2, 3 and 4, what are all possible values of d?
Reflection:
Problem solving is a key aspect in mathematics. When looking through the NCTM standards in relation to the Common Core, there are many expectations for students that rely on problem solving skills. For this particular problem, students will use number & operations, algebra, problem solving, and reasoning to solve for the possible values of "d." In math, it is important for students to understand what they are learning, instead of memorizing and applying an algorithm. Whenever it is possible, students should be exposed to a lesson in which they are able to draw their own conclusions and come to a hypothesis on their own. This will build a better foundation for students to then build upon in later lessons. Even when students are using an algorithm or applying a memorized skill, they are still coming to a conclusion. They need to know what algorithm to use and how to apply it. This in itself is a problem solving technique. The student needs to see a problem and decide where to go from there; is it is completing the square? Is the quadratic equation needed? By asking themselves these types of questions, students are already entering the problem solving aspect of a mathematics class. |