Connections to Higher Math

Connections to Higher Mathematics

Are you more of a visual learner? Are some of your students? Then consider using graphs to represent rates.

Consider the basic example of traveling at 30 mph for 4 hours. The graph below shows the situation. Notice that the distance of 120 miles can be represented by the shaded area "under" the line y = 30. In this case, the area is 30 by 4 or 120 (miles).

This is the essence of integral Calculus: the area "under" a function, given as a rate, represents the total quantity (such as miles traveled, pounds lost, or dollars paid) displaced over a certain period of time. Thus, the simple D = RT that we are teaching is directly preparing students for higher-level mathematics!

Common Error Alert

Here's a subtlety that often trips up students: in an equation such as D = RT, the units for each side of the equation must be the same. For example, if D is given in feet, and T in hours, the rate R must be in miles/1 hour so that the time unit "cancels" in the right-hand side.