• Overview
• Introduction
• The Hook
• Time versus Distance
• The Monkey and the Penguin
• The Race is On
• Connections to Higher Math
• Instructional Strategies
• The Race Track
• When Students Talk About Mathematics
• Monitoring Student Progress
• Mathematical Discourse
• Dimensional Analysis

# 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! 