The most difficult aspect of being a teacher is finding a way to get students interested and active in the learning. One solution for this problem in regards to teaching mathematics is to present students with practical issues that they can relate to. With this in mind, we create a story and a problem involving real situations that an individual may find themselves in. For instance, students will one day find themselves in a situation similar to the picture above. By this, a problem can be posed:
Jesse is a college student who takes the freeway on his way to school. Normally, Jesse leaves at 7:00 A.M. to arrive 15 minutes before his 8 A.M. class.When he drives down the freeway to get to school, he averages a speed of 60 miles per hour. Suppose that Jesse wakes up late one day and ends up leaving for class 10 minutes later than he normally does. How fast must he drive to arrive at campus at his usual time?
For a problem like this, students will have to first decipher the details. This means that they will have to sort and organize the information to discern the useful details. Following this, students will have to set up equations using rates and distances. First, they will need to find the total distance that Jesse travels on the freeway. Using this information, the students will have to then find the speed he must travel to make up for his later departure. In other words, we are looking at how a dependent variable (his driving speed) changes when an independent variable (his driving time) is altered. Seeing as how a vast majority of students will be driving to school or work in the future, this particular problem is all too relative to situations that they will, or even already have found themselves in.
This example problem is aligned to the following Common Core State Standard for Math:
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.