Flubmaster

Have you ever seen someone take a potentially excellent mathematical task and destroy it by flubbing the presentation? Have you ever done that yourself? I’m 2 for 2 so far (with a heavy emphasis on the second offense), so it’s with some excitement and a little bit of nervousness that I share my first Three Act task.

Running with Scissors Smartphones

About two years ago I began running with a smartphone to track my distance, pace, etc.. Initially, this on-the-run-phone-death-grip was a result of the fact that I was too lazy (cheap?) to purchase an armband case. However, after a while I found I liked running with my phone in hand. Several months ago I looked down and thought, “Hey, I could take screenshots while I run and…”

The Task

The result of that brainstorm, and much marinating and tinkering afterwards, is this, my first real attempt at a Three Act task.

Request for Critique

I’m fairly certain there is an interesting task contained within the screenshots I’ve grabbed, but (as hinted at in the introduction) I’m afraid I may have bungled it away.

First and foremost, I’d love to receive your general feedback. What works, what doesn’t, what could be improved? Is there an interesting task buried in there, and have I done it any justice?

I also have a few specific questions in mind. If you’re interesting in reading and/or responding to those, head over here. I expect I’ll want/need feedback on most (all?) of my Three Act tasks, so I threw something together to keep a running tally of my Three Act uncertainties, should anyone be inclined to weigh in on specifics.

I know it’ll require a bit of browser-tab-juggling,  but please leave any feedback in the comments below, or hit me up directly on Twitter (@mjfenton).

Thanks in advance for sharing your thoughts. I look forward to getting better at this with your help!

Which Run? (a.k.a. Now I’m Just Rambling)

I’ve captured screenshots of seven or eight runs over the past few months. Depending on the run, I’ve taken screenshots at every 1/2, 1/3, 1/4, or 1/5 of the total distance (or sometimes every 0.25, 0.5, or 1 mi), plus the “countdown” at the end (every 0.01 mi for the last 0.13 mi of the run).

With the various total distances and screenshot “splits” I’m considering creating a series of problems of varying difficulty, all of which require students to think proportionally, interpolate, extrapolate, and explain their reasoning. I think a series of these problems might exist best as simple stills of three screenshots, maybe like this:

Sequels would include, “When was Mr. Fenton at the 1 mile mark? How far after 23 minutes? 37 minutes?” And so on.

Getting On With It

Okay, ramble over. Time to hit “Publish” and see what the world thinks of what I have created, not what I might create.

Postscript

This afternoon was my first experience adding more than a single image to Dan Meyer’s 101qs.com. It really is a Three Act task paradise. Thanks, Dan (and everyone else who contributed to the site’s quality by using it and asking for Dan to make it better).

UPDATE: Okay, so my warning about messing up the presentation was apparently quite warranted. I never bothered to check if the distance meter in the middle of the screenshots was accurate. Thanks for nothing, Nike… it’s not even close. That essentially kills a major strategy I intended students to use in solving the problem.

There were a few suggestions on Twitter for how to use this not-to-scale-ness as part of the lesson, one of which seems particularly worth exploring.

For now, my solution was to re-do the Three Act task to offer students enough information to find the solution along another path.

The results are Nike Running 2A (given distance, find time) and Nike Running 2B (given time, find distance). Again, I covet your feedback.

I’m a little worn out after my last couple of posts, so I’ll aim for something more cheerful today.

Several years ago (okay, maybe closer to 20 than several) my mom went on a trip with a friend to Monterey. She stopped at a game shop, picked up this little gem, and brought it home for me and my sisters to play.

The game consists of 81 cards. Each card has four attributes (color, number, shape, shading) and each attribute has three flavors (red, green, purple; 1, 2, 3; squiggles, ovals, diamonds; and open, striped, solid). The goal:

Find a set of three cards where each attribute is either all the same or all different on the three cards.

If that explanation isn’t sufficiently helpful (it usually isn’t enough for my students), then check out the online (semi-creepy; I usually mute the audio) tutorial here.

At any rate, I have since played untold thousands of games of set, first with the physical deck of cards, then using the (free) online daily puzzle, and more recently on the iPad app. Partway through my first year of teaching I began playing the daily puzzle with nearly all of my classes nearly every day of the week. This year I’ve begun using the iPad app (since it offers a few additional ways to play, including a basic mode where the shading component is simplified by using only the solid cards). Regardless of how I’ve accessed the game, here are a few of the benefits to my students, at least as I see it.

• When we start with Set at the beginning of class, nearly every student is engaged.
• It’s a great way to develop spatial reasoning (probably a weak part of my courses, aside from this game/puzzle).
• With a little bit of thinking it can be turned into a competition between classes.
• After teaching the kids how to play, it lasts only 60 seconds (for basic) or 90 seconds (for advanced).

This last point is really what inspired me to write this post, as I’ve been searching for short, engaging activities to weave into my classroom this year to fill out the pockets of time at the beginning or end of class. While I’ve been using the Set Game to start class for years, the online puzzle only offered one game per day, so repeats in a given class period were off limits. With the iPad app, I can pull up as many puzzles as I want, so when students are finished with an assignment and there are two minutes left I can fire up the app and challenge them to another game.

Two other great ways to fill those extra minutes (whether they fall at the beginning, middle, or end of a period) are Andrew Stadel’s Estimation 180 and Fawn Nguyen’s Visual Patterns. They’re not quite as short as a game of Set, but in just a few minutes I can have the students doing something far more interesting (and mentally profitable) than sitting quietly while they wait for the bell to ring.

So here’s my list o’ questions to you:

• Have you ever played Set? If so… Cards, online, or app?
• Do you use Estimation 180 with your students? If so… How long do you spend on a typical estimation challenge (start to finish)?
• Do you use Visual Patterns with your students? If so… How often do you use them and how much class time do they take (once your students have become familiar with the concepts/format)?

And if you just answer one question, make it this one:

• What do you do with your students when your students finish an activity or assignment and you look up at the clock to realize you have two minutes left?

P.S. If you’re interested in hearing the three ways I play the game with students in class, just holler in the comments. I’m happy to share, but this post needs to be done and I need to be in bed.

Pre Algebra is on my teaching list this year. The last time I taught it was five or six years ago, and I’ve changed quite a bit as a teacher since then, so I’m building everything again from scratch. (It feels appropriate to note that my philosophy of teaching/learning has shifted more significantly than my actual practice, at least in my other classes.)

For the past week or so we’ve been constructing, measuring, labeling, identifying, and discussing triangles (where the constructing has been mostly with non-digital tools). Given three sides, given three angles, given some combination, similarity, congruence, impossible triangles, etc. Our progress has been frustratingly slow, in large part because my routine of late has consisted of me going into class with an activity and some excitement only to discover that some key element of the activity is seriously flawed. I spend the next evening revising the activity (thereby rekindling my excitement) in order to try it again the next day. I imagine (hope?) our progress won’t be quite as slow next year, but I’m not sure if that’ll be the case.

This is the activity I wrote for today. Since it’s late, I’ll cut to the chase: The conclusions students drew at the end of the activity were on the disappointing side, both in terms of the depth of insight of their observations, as well as their ability to express what they noticed.

This (here and here and here) is what I have planned for tomorrow. I’m hoping that by giving them space to record their measurements (in an organized manner) our debriefing conversation will include more insightful comments from students. We’ll see.

If you’re game, have a look at the handouts and let me know in the comments what you like, what you don’t, and how you’d make it better.

I learned about Andrew Stadel’s Estimation 180 a few weeks ago. I decided this morning it was time to stop watching and time to start playing along. We’re a bit behind the rest of the estimating world, but in first period (Pre Algebra) we worked through Days 1 and 2 and in third period (Honors Algebra 1) we worked through Day 1.

It. Was. Awesome.

I won’t spend a lot of time in this post talking about Estimation 180 in general or how I used it in class today. If you already use it, you’ve probably formed your own opinion and approach by now. If you don’t use it (or have never heard of it), get yourself over there as fast as you can.

What I will say is this: My students were more engaged today, even in those ten short minutes, than they have been in quite a while.

I imagine it had something to do with the accessibility (everyone can make a guess, even if it’s horribly, horribly wrong), the anticipation (“Am I right? Am I right? Am I right?”), and the way these estimation tasks present a natural, un-intimidating opportunity for students to defend their responses by explaining their reasoning. The reasoning—to students, at least—often doesn’t appear very technical or mathematical, but it’s great exercise anyway. And it’s a healthy start to making sure this is a regular part of my students’ experience.

So where to from here? Well, for one thing I’ll continue to use Estimation 180 with these students. But beyond that, I’ll try to incorporate those three elements (accessibility, anticipation, and ready-made opportunities for answer-defending) into other tasks and courses.

I just have one question: When this year’s Pre Algebra students have me again next year in Algebra 1, will there be an Estimation 181-360?