As my students have worked through a series of linear graphing challenges this month, I’ve been looking for a way to challenge them to synthesize (and hopefully even extend) what they’ve noticed over the past few weeks.
I think I’ve found my culminating challenge.
My goal is to elicit a variety of equation styles (point-slope, slope-intercept, etc), and my hope is that the restriction (which numbers they may use in the equations) is not only clear enough, but also provides the right dose of structure to encourage students to think more deeply about the relationships between the rate of change, intercepts, non-intercept points, and the parameters in each equation.
To give it a test run before sharing it in my own class, I hereby offer you this:
How many different equations can you write using only the numbers included in the ordered pairs? Can you get to three? How about five? Maybe even 10? Or more?!
Do the work in Desmos, and drop a line in the comments!
As always, feedback—on the challenge in general, or the restriction in particular—is 100% welcome.
I struggled with the wording in the original challenge. As I shared above, my goal is to draw out from students a variety of equation forms, each one utilizing information revealed by a particular point or pair of points. After some back and forth on Twitter, I settled on this reframing of the task:
I’d love to know whether you think that drives more quickly and clearly to the heart of what I want students to focus on (while leaving it open enough that students will feel freedom to tinker and explore).