Exploring Slope with Stairs & Steps

As much as ever before, mathematics teachers are searching for ways to connect mathematics to real-life scenarios within STEM contexts. As students develop skill in proportional reasoning, they examine graphical representations of linear functions, learn to associate "slope" with "steepness" and rate of change, and develop skill in calculating slopes of lines. Slope and rate of change, however, do not exist only in math class. Engineering applications associated with ramps, staircases, and roller coasters rely on analyses of slope and rate of change. In science class, students learn about velocity and speed, each of which connects to slope and rate of change. Technology can be used to support students as they explore slope and rate of change in these and other contexts. Given these connections, slope is an ideal topic with which to bring STEM into the mathematics classroom. This article presents a series of science- and engineering-related activities addressing rate of change that occurred in a middle-grades public school math class. As students worked through the activities, they developed an understanding of slope and rate of change within STEM contexts. The activities were developed as part of Expeditions in Science, Technology, Engineering, and Education through Mathematics (ESTEEM), a professional development program funded by the Virginia State Department of Education and held at George Mason University in Fairfax, Virginia. The two activities helped develop students' thinking about rate of change and slope within STEM-related contexts. With exposure to hands-on activities like the staircase problem, students come to understand how math can be used to solve problems in engineering. This article presents one example of the many ways that teachers can bring science and engineering connections into math class. As teachers think of these ideas, they need to continue to share them so that we develop not only a mathematically literate but also a STEM-literate citizenry.