Students need a spike of interest in math class, especially when trying to solve systems of equations. Systems of equations tend to seem useless and not worth students’ time. Using the Vernier Motion Detector will prove to students that systems of equations can be applied to real world situations so it is useful and worth their time. This Vernier product can simultaneously record the motion data of two people, graph both motions on a common axis and find their intersections, find linear equations to model the motions, and compare the algebraic solution to the graphic solution. The Motion Detector will help keep students interested because it allows them using technology and actively create the systems of equations. Students can take at real world situation, create a system of equations out of it, and then solve the system.

For example, students can imagine that a student is running to catch up to his friend who is walking ahead of him. This situation can be used to create a system of equations. For this example, we would solve a linear system of equations (students would be told to walk/run in at a constant speed). For future lessons, students can use the Motion Detector to solve other systems of equations and inequalities. The motions of the two students in the scenario can be modeled graphically by plotting the distance (y) versus the time (x) on the calculator to which the Motion Detector is attached. We can find the rate at which each of the two students traveled (x) and the total distance traveled (y). The plots can be made on the same set of axes, and the point where the two lines (paths of students) intersect represents the solution (the physical location where the two friends meet). Students can be assigned to groups of three. Each student will have a duty. Two students can do the walking that is detected by the Motion Detector and the other student is in charge of working with the calculator to graph the model and recording the information. Each group will make about three different models (by changing the rate at which they walk), so that they each have an opportunity to use the technology to detect their motion. Each student is expected to participate in analyzing the data to find the solution to the systems of equations they have created. Students would make their own table to plot the x and y values on their own piece of paper. When the Motion Detector creates the graph for them,  they will sketch the graph on their paper next to their tables. Students are also expected to reason their procedures and results on their paper (below their table and graph) and to each other in order to emphasize what they learned about the actual situation. For example, students may comment on how their answer (in ordered pair form) tells them that the student could have caught up to his friend faster if his rate of travel was faster with an inclusion of what the x and y values would look like).

This lesson would align with the HAS.REI.C.6 “Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables” since students are creating linear systems of equations with two variables, x (time, rate of travel) and y (total distance traveled), by walking or running at a constant rate and solving the systems (finding the location where their paths intersect).

This example lesson using the Vernier Motion Detector will allow students to see the physical steps in solving systems of linear equations, which will make it easier to learn and more difficult to forget the concept. This is because students will have experienced the actual situation in a real setting rather than looking at several different systems of equations that just seem repetitive and meaningless. This experience will have made a positive impact on students during class, so they will have a more positive attitude toward the lesson and toward their group members. Students may even use what they learned from using the Vernier Motion Detector to inform their parents, siblings, or friends about the concepts they learned from the lesson.

The Vernier Motion Detector can be found at http://www.vernier.com/products/sensors/motion-detectors/md-btd/ for $79.