• We’re a little weak with graphing lines. Some open-ended, Desmos-driven, instant-feedback style practice may help.
• Domain and range? Yeah, not so much.
• Inequalities? Haven’t done them justice. Yet. (Growth mindset, baby!)
• Vertex form for quadratics? Still struggling.
• We tried Des-man a few days before this game and found nothing but pain and frustration. Some could be attributed to me (in particular, a bungled launch of the activity), some to students’ lingering struggles (noted above), and most of the rest to the declining state of our netbook cart. (But they seemed so cool in 2009!)

At any rate, to get that bad taste out of my mouth and set the stage for greater success on the next Des-man go around, I created the Dot Capture Game. Here’s what you need:

• Students (working in pairs)
• Devices (we actually used 50% smartphones, 25% tablets, 25% laptops)
• The world’s greatest, most beautiful graphing calculator

And of course, the handout:

Getting Started

Give a brief intro—or none at all—and turn ’em loose. If your experience is anything like mine, you’ll find yourself the weaving in and out of some great (albeit trivially-inspired) conversations about slope, intercepts, point-slope form, domain, range, inequalities and shading, vertices, direction of opening, etc.

This is definitely not high-quality modeling stuff (it’s not even low-quality modeling stuff), but it proved a great way to engage students with meaningful (read: productive) practice on a variety of topics related to graphing.

Oh, and the winner in my class? Here you go:

Final Thoughts

After trying this out in Algebra 1, I thought I’d throw it at my Algebra 2 and Precalculus students to see what they would do with it. It turned out to be good practice in those settings as well. Before sharing with these followup classes, a quick tweak to the handout was in order. In my first class, several students lost their graphs and expressions after hitting a deadly combination of keys on their device, and only one or two had been keeping a shiny written record. So to protect against future heartache, I added a second page to the handout. Here’s what one of them looked like at the end of class:

Update

Here’s a sweet suggestion from Desmos:

@mjfenton What if Ss rolled two dice to determine which curves they had to use and the numbers also represented the coordinate to capture?

— Desmos.com (@Desmos) May 22, 2014

I’m a big fan of Michael Pershan’s project Math Mistakes. If you’ve never checked it out, it’s worth exploring. And while I’m meddling with your life, here’s a tip for your entire department: Start each meeting by spending five minutes exploring one of the mistakes posted on Michael’s site. On a rotating basis, have one member of the department share a “provocative” math mistake from the blog (or maybe even one from his or her own classroom). And once duly provoked… Cue the discussion!

Amble

I included the following uninspiring question on a recent assessment:

The first two assessments I graded included the following responses:

Student 1

Student 2 ((My apologies for the retype. I added some feedback before snapping a photo.))

Comment Fodder

So here’s my question (er, set of questions) for you:

1. Are these mistakes equally egregious?
2. What misconceptions are contained in the first mistake? How would you address them?
3. What misconception are contained in the second mistake? How would you address them?
4. Would you grant any credit for either response, and why?

…and then launched into an algebraic confirmation of that solution.

Now on the one hand, throwing a Desmos-generated graph into a “detailed solutions” handout is a great move because, well, just look at it. It’s beautiful. And hey! Multiple representations! Plus it took about 30 seconds from start to finish. No brainer, right?

Well, on the other hand, including something like that is dangerous, because when you find yourself writing the solutions to questions 6 and 7 (as I did just a few moments later), and these questions ask for a graphical display of the solution to a one-variable linear inequality… Well now you’ve tasted greatness, and you won’t settle for anything else.

There’s just one problem: Desmos doesn’t do linear inequalities in one variable.

Okay, that last sentence is actually not true. Desmos will graph linear inequalities in one variable. You just have to ask nicely. Check it out:

I imagine I’m not the only one to do this (and it would still be pretty cool if Desmos would add one-variable number line graphing functionality… Pretty please?), but I thought I’d share how to do it anyway, just in case anyone is curious (and wants to give one-variable graphing a little Desmos-love).

Here’s How

The best way to explain is to throw a few images in here and let them do the talking. Drop me a line on Twitter (@mjfenton) or in the comments if you have any questions (or tips for how to make this even easier or more awesome). Or if your name is Eli and you have a new feature to announce.

Graph 1

Graph 2

Graph 3

Graph 4

I’m amazed anyone reads this blog, and even more blown away that people have posted so many thoughtful comments. Shortly after my long-winded sky-is-falling post, I added a quick note about launching an activity with as few words as possible. There were a few great comments on this shorter post about how to improve one particular activity (matching equations, intercepts, and graphs of quadratics).

The comments that caught my eye include:

Could you build on the task with an addition to the end where they create their own quadratic and then write up a key for the graph, intercepts and factors? They could switch it with another group and verify their answers? – Dan Anderson

One thing I’ve done occasionally with matching activities is deliberately leave one out. So they end up with an equation that has no graph, or vice versa, and have to generate the missing one. For added chaos, leave out one of each – just let them know that this was done… – Gregory Taylor

Love this activity! I think the concise written directions are a good idea, too. On my first day of Algebra 2 class, I had a similar but less pretty handout where each quadratic has a graph, an equation (in some form or other), a table of values, and a word problem. Each kid as they walk in the door gets one, and they need to find the others who have the same quadratic in order to form their groups of 4. – Joshua Zucker

Activity Revamp

So tonight, while standing guard next to the boys’ bedroom door (they have a tendency to leave their beds when they should be drifting off to dreamland; my wife calls it whack-a-mole, probably because of this)… Where was I? Oh yeah, standing guard…

So while I was standing sitting guard next to the boys’ door I revamped my rather unassuming matching quadratics activity to include some of the suggestions above. (Disclaimer: My activity doesn’t include Joshua’s table of values or word problems, but I think those are awesome ideas, and will probably find a way to include them in another activity, either for linear or quadratic functions.)

For reference, the old activity handout is here. And for what it’s worth, the new one is here. My game plan is to start with an entire-class matching activity and follow it up (either on the same day, or on another day for review/additional practice/to beat a dead horse) with a small group activity (groups of two or three students, matching at their tables). For my students who don’t hate school and who think meaningless competitions of an academic nature are enjoyable (read: third period, not fifth period) we might play three quick rounds of “fast as you can” matching. Fist bumps to the fastest group in each round, and fame and glory for the fastest time of the day.

I think the new wrinkles make it a much better activity. We’ll see what my students think/how they respond. If you use it with yours, let me know how it goes.

P.S. The handout no longer includes directions, as I’ve included those on a slide that can be displayed for the entire activity. (Once we start cutting up the old handouts, the directions made their way to the blue bin by the door pretty quickly.)