2009 – Page 19

My Lesson Plan: The Door Lock

By Dan Meyer • April 23, 2009 • 17 Comments

Personally, I think that this particular image lacks opportunities for inquiry. Perhaps if it was presented with other kinds of door locks leading students to come up with and answer the question, “which is the most secure lock?” [emph. added]

This is exactly right. The latest WCYDWT? installment has provoked the usual litany of Really Interesting Bite-Sized Questions, the sort of prompts that will play great in the Applications & Extensions & Assorted Mindblowers section of your lesson plan but which, on their own, aren’t a lesson plan. Those questions don’t provoke the kind of iterated, increasingly difficult practice that students need for skill development.

Again, this image on its own is insufficient. With some creative modifications, however, it will carry you through permutations. Here is that lesson plan in its broadest strokes.

Start with the image.

Tell them the code is 1 digit long. Tell them the code is 2 digits long. Tell them it’s as long you want it to be. I respected the rule of least power here, which meant that when I took this photo I tried to stay out of the way of your lesson planning. Have them write down all the possible codes for n=1, n=2, n=3, etc. The increasing obnoxiousness of the task will motivate a formula for the general case. That’s arrangements.

Tell them the lock is a 4-digit lock. Now turn on the blue light.

Ask them to list the possible codes. You can iterate this a bunch of times until they have discovered on their own this tool that mathematicians call a factorial.

Remind them it’s a 4-digit lock. Then put up this image. It will be confusing, but only for a second. Ask them to list every possible code.

Iterate this with two and three buttons until they have generalized permutations. Then maybe you iterate the entire thing with another keypad lock.

Then maybe you dip into the comments of the original WCYDWT? post and help yourself to some very-interesting follow-up questions. I recommend Alex’s.

Let me close by saying how shocked I am at how little all of this costs.

[Update: Bruce Schneier has a good follow-up on information leakage. Two photos.]

[Update II: due to the peculiarities of many car door locks punching in “123456” tests both “12345” and “23456.” Consequently, there is a number string 3129 digits long that will test every five-number comination.]

[Update III: more information leakage.]

[Update IV: more information leakage.]

YouCube: The Latest In Cube-Based Storytelling Technology

By Dan Meyer • April 22, 2009 • 1 Comment

I’m mixed. On the one hand, YouCube is a pretty interesting way to compare remixes of a thing (ie. David After Dentist) to the thing itself.

On the other hand, this strikes me as just another one of those tool that depends entirely on a teacher’s pre-existing digital storytelling skills but which also distracts her from developing those skills. (ie. Why learn how to make one video really well when you can put six average videos on a cube!)

What Can You Do With This: The Door Lock

By Dan Meyer • April 21, 2009 • 18 Comments

Download high quality here. Here’s the pilot but I need to modify the prompt somewhat. Every math teacher reading this likely sees the mathematical potential in this image. Most could come up with a question right now like, “If this is a four-number combination lock, then how many combinations will you have to try to break in?”

Lately in these threads I get lists of those questions, which is great, but questions don’t constitute a lesson plan. So consider this the new prompt: what is the lesson plan? what will the students do? what is the best plan to provoke sustained, rigorous inquiry?

Let’s push this forward.

BTW: My lesson plan.

Yes We Can, Etc.

By Dan Meyer • April 20, 2009 • 3 Comments

Kate Kowak is to math blogging what Barack Obama was to stump speeches:

My hope is that what we are witnessing here [with What Can You Do With This?] is a paradigm shift. At the intersection of problem-based lessons, digital projectors, blogging, and frustration with poor-quality textbooks, is blossoming a new way of bringing mathematical understanding to our kids. We don’t need to buy anything new, or anyone’s permission…just the structure, and the willingness to be observant and curious, and the humbleness to imagine that there might be a better way. I think this is just the beginning. I think this is going to spread like a fire.

What You Can’t Do With This: NLOS Cannon Challenge

By Dan Meyer • April 19, 2009 • 28 Comments

This is a classic game. It’s been around in various forms longer than I’ve been alive. Choose your velocity, choose your angle, cross your fingers, and fire. Discovery has simplified the game nicely, removing some noisy variables like wind speed, which you’ll find in other versions.

I first saw Discovery’s incarnation several weeks ago and have been on-and-off obsessed ever since by the question: what can I do with this? The point of this post is to throw up my hands and report: nearly nothing. I have no idea what the students do here.

I mean, it’s far from worthless. If a student can get past level ten, then she clearly has some understanding of angle and velocity and the dialog between the two. She might even ask herself some interesting questions, like, which angle gives you the longest range? But I won’t drag the laptop cart across school for those small potatoes, for that two-step lesson plan of 1) guess and 2) check.

Here is the most rigorous, reasonable question this game can ask, a question which it is fundamentally incapable of answering: can you develop a method for hitting any target in one shot? This is a question either a) Discovery didn’t think of or b) Discovery thought of but, for whatever reason, didn’t make accessible to students.

Either way, it’s frustrating. It’s frustrating that:

there isn’t a grid for determining coordinates;
the units aren’t defined;
there isn’t a timer for determining parametrized equations;
banner advertising reloads in the middle of the projectile’s flight, making a mess of my makeshift timer.
you’re firing from the tip of the cannon, not the base of it, which adds mathematical noise;
the layouts change at random (ie. my level three isn’t the same as your level three) which crushes my one workaround here, copying level screenshots into Geogebra.
I think, though I can’t be sure, that you’re blowing up huts and tents in some levels, which, gross. Seriously.

All of which is frustrating. The game uses mathematical notation for angle and initial velocity. It comes packaged with its own assessment systemYou get 100 points for each unused shell. The student with the most points (likely) has the best algorithm and calculations.. This thing is so close to being useful.

Which makes it an interesting answer to Scott McLeod’s question, where are the Internet resources for your subject area? Because this game isn’t from some arcade site which I’m hopelessly trying to bang into a lesson plan. It’s from Discovery, which isn’t exactly apathetic to the needs of educators. Why didn’t the thing come with a lesson plan?

My takeaway here is that the people who know the Internet and the people who know instructional design aren’t the same people and they aren’t talking to each other enough. We are left to our own devices.

BTW: Just a little over a year later and Colleen King comes through for the team: Tactical Rescue Missions for Intergalactic Good. Great work.

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Year: 2009

My Lesson Plan: The Door Lock

YouCube: The Latest In Cube-Based Storytelling Technology

What Can You Do With This: The Door Lock

Yes We Can, Etc.

What You Can’t Do With This: NLOS Cannon Challenge