How Can We Break This?

I like this. The iPhone application RulerPhone will measure anything, in any photo, so long as the photo includes a credit card. It’s a great use of proportional reasoning, which, if pressed to name one, would be The Mathematical Skill I’d Most Like My Students To Retain After High School.

I added it to the What Can You Do With This? segment featuring The Bone Collector, which seemed like an obvious pair to me. In trying to find the best classroom entry point for this program, I can only think of the question, “How can we break this thing – trick it into giving an incorrect measurement?” I imagine someone can do better.

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. You can throw off the measurement slightly if the credit card isn’t perpendicular to the camera or it’s at a different distance from the camera than the object you’re measuring. Then there’s also the trick where you get a 3 foot long credit card and pretend you’re in Honey I Shrunk the Educational Blogger.

  2. I agree with your comment about “The Mathematical Skill I’d Most Like My Students To Retain After High School.” It’s amazing how many kids really don’t get this. I teach high school Physics and so many do not “get” ratio’s. The other skill that I’d like them to retain is percentages. (which of course is really a form of a ratio, but I won’t confuse the kids with that.

  3. Hah! I’m sure your iPhone wielding kids will be able to find this list of how to break it. In some ways, I’m impressed by how simple they made it, in others I’d think they could use the computing power in there to compensate for parallax and perspective.

  4. Angular diameter is banging around my head like a moth around a lampshade. Not sure if this app would be necessary…but a credit card (or just your hand for that matter) would be a useful measurement tool for angular diameter. Might not be a useful measurement for many outside of astronomy, but who knows?

  5. Shoot, Darren, good link. Never bothered to click it any of the previous ninety-nine times I’ve seen it ’cause I thought it was a bunch of shots from deep space or something.

    Frankly, I have no idea how to use most of them. There are some interesting “what shapes do you see here?” shots, but that question doesn’t scratch past the surface nine conversations out of ten.

    I do love this one, though – the shot of the Las Vegas housing tract – because it sets up what seems like an unfair, unanswerable question: “how many people live there?”

    As I try to pin down this visual math aesthetic, I find that the media that interest me the most are the ones that provoke those seemingly unfair, unanswerable questions, which we then answer through estimation, good sense, and mathematics.

  6. Hey Dan, I was just wondering why you named proportional reasoning as The Mathematical Skill I’d Most Like My Students To Retain After High School. Why not understanding exponential growth? (you know… because Americans have such problems with credit and all) Or interpreting graphs? Or discerning whether events are independent? (since we are such a superstitious species) Or factoring? (j/k)