The linear and quadratic motion detector experiments have been done with strong middle level students, regular Algebra I students, and double period Algebra I students. The linear experiments are also part of a book, Amazing-STEM, published this year by Michigan State University. These lessons were inspired by the College Preparatory Math curriculum, or CPM. These lessons use a motion detector connected to a TI-nSpire and a document camera. The motion detector records an object’s distance from the detector on a graph in real time.
When teaching linear equations and systems of linear equations, students are asked to come up in front of the class and they are instructed how to walk in front of the motion detector. For example, a student might be asked to stand five tiles (feet) away from the detector and then be asked to walk toward it at a steady pace. The class, sitting in groups, will then sketch graphs of their own to predict the result. The student will actually do the walk, then as a group the class discusses where we might have gone wrong, why the line looks the way it does, and how to adjust. With stronger students, I have extended this lesson to include function notation and piecewise functions. For systems, you can use two walkers. For quadratics, also pictured below, students can make predictions and compare the graphs of a full water bottle rolling toward and rolling away from the motion detector. These lessons get at the meaning of slope, velocity, and acceleration in an applied setting. Students participating in any of these experiments must read descriptions of walkers and sketch the graph; they also must write their own stories with applied contexts of their own making and choosing. Student distance-time stories were then posted in public places in the school and featured in science fair style at student exposition days.