They’ve quickly become two of my favorite ways to build or deepen graphical understanding, whether working with middle school students or older kids (who “should know this stuff” but commonly do not).
I brought a do-it-yourself extension of the “Match My Line” challenges to Math B a couple weeks ago.
It. Was. Awesome.
How To Play
Step 1: Everyone starts out flying solo. Fire up Desmos. Add a pair of points. For this first-ever-instance of MMLCYO, I required one of the points to be on the y-axis (but not at the origin).
Step 2: Record the ordered pairs in the first two rows of the table. (Want the handout? Click here.)
Step 3: Find an equation that passes through the points. Confirm in Desmos.
Step 4: Trade your points (but not equation) with a partner. Hunt for their equation, using a new Desmos graph to confirm. Record the points and equation in “Their Challenge #1.”
Step 5: Find a new partner to trade with. Repeat this until you’ve filled out “Their Challenge #1-4.”
Step 6: Create a new equation, and run through four rounds of trading/graphing again, this time recording the results on the back (“Their Challenge #5-8”).
Every year since I began teaching, I’ve tried to help students develop proficiency with finding an equation to model two or more collinear points. The results have always been hit and miss. Until this year. Granted, this “Create Your Own” activity was not their first introduction to rate of change, intercepts, and slope-intercept form, but my students absolutely rocked this activity.
After the wrap up (details below), I asked students to rate their “before” and “after” understanding on a 1-5 scale (5 = high). The results were encouraging, with the typical student expressing a shift from about 2-3 to about 4-5 (with most giving an “after” rating of 5). Woohoo!
I think the combination of minimal teacher talk and active students (mentally and physically) made this a success. Plus, having students confirm their results in Desmos pushed students to work on the math, rather than settling for simply “completing the page.”
We wrapped things up with four rounds of whole-class “here are my two points, what do you have to say about that” gauntlet throwing. For the first two, I took the challenge, modeling aloud the thinking I had heard around their tables throughout the class period.
For the next two challenges, I asked two students to narrate their thinking as they found the equation. They rocked it.
I plan on bringing “Match My Line • Create Your Own” back in a few weeks, but we’ll shift our attention to two non-intercept points and point-slope form.
I think this “Create Your Own” approach is also packed with potential for quadratics and other Match My Function categories, and I can’t wait to weave it into my Precalculus course later this year.
Ideas for how to extend or improve this with lines, parabolas, or something else? Drop a line in the comments!
Student Sample #1
I snapped some scans of student handouts at the end. Here’s one:
Student Sample #2