Can the midpoint be found by simply counting the spaces? Will using rise and run help? Is the midpoint formula needed? In this activity, students will navigate through a series of graphed segments (segments they themselves graph) finding midpoints and endpoints. In each step, they’ll need to consider the best tool/approach. Students encounter easy questions where the midpoint can be found by simply counting the units on a horizontal line, for example. In some steps, students are given one endpoint and a midpoint and they must find the other endpoint. Not every point is made up of integers. Sometimes, the graph isn’t large enough to plot what they need (this is intentional).
I like this activity because students have to sort out for themselves which tool to use and when. It requires problems solving skills, creativity, as well as attention to detail. I do walk around and let them know when they are getting off track, as one wrong answer leads to everything that follows being incorrect as well.