If you’re the sort who likes to figure this WCYDWT thing out for yourself, here’s the clip I’ll be discussing after the jump. Also: my readers outside of Burma, Liberia, and the United States can safely skip this one.
Whenever a student asks me how tall I am, I always answer “79 inches.” (It’s a math teacher thing.) The student’s first reaction is, inevitably, “Seven foot nine?!” The student’s second reaction, after dividing 79 by 12 and seeing “6.6” on her calculator is, “Oh. Six foot six.”
This drives me nuts. Once a student has the idea that decimals are inches, it’s nearly impossible to convince her otherwise.
Apparently, high school freshmen wrote the 2003 remake of The Italian Job. Halfway through the opening heist, Seth Green tells Edward Norton to mark “14 feet 8 inches from that west wall” but Norton measures out 14.8 feet on his distance sensor. Decimals aren’t inches, Ed! You’ve gone 1.6 inches too far!
I don’t know the extent to which that error should scuttle the entire plan but Mos Def makes the same mistake on the floor below so the whole thing looks pretty grim.
This is a clear application of entries #7 and #43 from the WCYDWT taxonomy.
#7: Put the student in the same mental frame as a character from a TV show or movie. Have the student solve the character’s problem.
#43: Allow overconfident learners to pursue incorrect answers.
So you put them in the same room as Edward Norton by giving them a piece of grid paper. You tell them every minor line represents an inch. You’ve really stacked the deck with this one, having drawn major grid marks every 10 lines, instead of every 12. You’re inviting the likely error.
You play the clip as many times as they want. Encourage solo work on this one. (Edward Norton was alone in the room, after all.) After a given time, you invite a confident student up to the board to draw a safe you know in advance to be incorrectly placed. At that point, most students have decided this activity is really easy and way beneath them. This overconfidence is gasoline. As students discover differing answers to the same totally easy problem, they’ll argue and debate. These frissons around the room are the little sparks in the combustion engine of learning.
If a student miscalculates my height by an inch, it’s no big deal to her. The stakes are too low and the percent error too insignificant. But if a student blows up the wrong part of a floor and loses millions of dollars in gold bricks she thought was a sure thing, that’s productive frustration, even though the stakes are imaginary. We can work with that.
BTW: Delise Andrews offers a handout that is much better than mine. Thanks, Delise.
Bill Van LooMarch 23, 2010 - 9:13 am -
re: “entries #7 and #43 from the WCYDWT taxonomy”
Is there actually a WCYDWT taxonomy? If not, when can we expect it?
Jeremy GrisbeeMarch 23, 2010 - 9:19 am -
I can see how the students would come to the red square, but I’m not sure how you got the blue square where it is. Shouldn’t the NW corner of the blue be 14.666… from the west wall and 8.416… from the north wall. How did you come up with your blue square.
If my numbers are right, I can imagine students saying that as long as you’re just blowing up the floor, you can just put a little more explosive paint around the edges to cover up your mistakes. I’m not sure how I would come back with that one. Maybe my numbers are wrong.
Dan MeyerMarch 23, 2010 - 9:45 am -
@Bill, I’m just tap dancing here, making this stuff up as I go along.
@Jeremy, remember that each bold line doesn’t correspond to a foot. Crucially, here, the NW corner of the safe is 176 inches from the west wall, which puts it 17 major grid lines and 6 minor grid lines away. Check me on that, though.
Also: as the clip makes clear, the safe has to drop through two floors and fall safely into the cargo area of a boat. I agree that we could probably overcompensate with the magical blow-up paste and make sure it fell through both floors. I’m not sure how to overcompensate with the location of the boat, though.
AmberMarch 23, 2010 - 11:47 am -
I have been a long time follower, but have never spoken up before. I love this one! This is one of my frustrations even with my honors Geometry students. I always talk about this when I am discussing different base systems with my Algebra 2 class as well.
By the way, I am always so excited when I check my Reader and see that you have a new WCYDWT post. I feel like it is Christmas and I am so excited to open it. Thanks.
David CoxMarch 23, 2010 - 12:18 pm -
I love this one. Can’t wait to put it in front of my “advanced” kids and watch them implode. It’ll be borderline cruel, to be honest, because these kids are waaaay over-confident when it comes to calculations. I may have to get some video of the process.
Question though: At what point did you reveal the answer to your students? Or did they figure it out on their own?
Dan MeyerMarch 23, 2010 - 1:32 pm -
@Amber, awesome, thanks for saying hello. Do let us know if you use one of these in your classes. Feedback is the grease in this machine.
@David, my schedule’s jammed until next week. Whenever I drop it on my students, though, I don’t anticipate saying, “this is the right answer.” These rarely require a heavy touch. I’ll facilitate an argument, basically, and I will be very, very surprised if the class consensus isn’t also the right answer.
Jeremy GrisbeeMarch 23, 2010 - 3:37 pm -
Whoops, I must have been reading quickly through and not seen “every minor line represents one inch”. Careless. Thanks, Dan.
Jeremy GrisbeeMarch 23, 2010 - 3:39 pm -
Btw, I guess I should jump on the praise bandwagon. This activity, as well as your others, are great and I not only anticipate seeing new ones, but they have really inspired me to create these myself in my own classroom. Thank you for making so much of what you do available for use and criticism.
Cassidy73March 23, 2010 - 4:00 pm -
My immediate thought when I first watched the video was to recreate the scenario in my own room which has a drop ceiling. Once the students are set on their solution, we move the tile and find a bag of chocolates shaped like golden bars for the class to enjoy. I think I’d like to run the part Dan has outlined, so we have a good understanding and example, then start moving tiles around.
graceMarch 23, 2010 - 4:03 pm -
Just curious– what would you do if every student made the same mistake? As I ask I’m wondering what the likelihood of that is, but especially since you’ve set them up with a trap, I could definitely see more unsuspecting students falling into it than I’d hope.
Aside from that, I also really love this activity :)
curmudgeonMarch 23, 2010 - 4:38 pm -
I see different complications to this mess.
Check the frame directly after the explosion: The explosive paint was on the ceiling of the room below, yet somehow cut the floor joints and made a perfectly square hole in the top room’s subfloor and finished floor? If you are truly going to blow a hole in the floor from below, the blast would spread far larger than what was shown by the time it made it through the space between the joists. Unless you used shaped charges, which this was not. I would think that this would also round off the corners, too. But who’s quibbling?
A much bigger problem for me is the idea of a typical four foot high safe, weighing some 600 pounds, filled with “millions of dollars in gold bricks” (at $500k per 27.5 pound brick/400ozTroy) meaning another couple hundred pounds AT LEAST. Let’s be generous and say 500kg total.
Suddenly eliminate the floors so there is nothing slowing that puppy down on a straight drop to the boathouse. Falling two floors and into the boat, total 8m maybe? This sumbitch is going to be MOVING with a holy pantload** of kinetic energy, something like 40kJ meaning 12.6m/s or about 30mph.
And that flimsy little frame on that dinky little speedboat is gonna stop it? Not hardly. And the boat isn’t gonna roll some or create a big ole wave splashing against the sides of the boathouse? And the safe was twisting before it dropped through the hole but somehow was straight and perfect after it dropped through the hole?
I’m bummed about the 1.6 inch error, too, but everything else just fries me.
** holy pantload is the technical term for “a lot”
curmudgeonMarch 23, 2010 - 4:42 pm -
Don’t get me wrong. I love what you’ve done with this. The engineer in me rears his ugly head occasionally.
Adam GlesserMarch 23, 2010 - 5:30 pm -
It’s been a while since I watched the movie, but wasn’t the boat just a ruse? I recall the boat having a safe on it, but the actual safe falling under the house into the water, to be collected during the boat chase. If true, this should satisfy curmudgeon’s concerns a little.
Dan MeyerMarch 23, 2010 - 5:52 pm -
I hope you get inspired to share them from a blog too. You see how much better my stuff gets when you guys pick at it?
It’s possible. It’s also possible that the few students with the right answer wouldn’t assert themselves. In that case, I’d have to consider David‘s question a little more: “When and how do you tell them they’re wrong?” My instinct is “only after everyone is really, really confident in their wrong answer.” Again, that frustration at being wrong (and not just a little bit wrong) when you thought you were 100% right is valuable to me.
Adam’s right, but the movie is clearly playing the moment like it’s plausible the safe landed like a feather on the boat, what with the bad guys frantically giving chase. In curmudgeon’s world, they would have scoffed at the boat and started shooting into the canal.
Clearly, we should crowdsource a thriller here.
curmudgeonMarch 23, 2010 - 6:10 pm -
Got it. “Garbage men in position.”
Some GuyMarch 23, 2010 - 7:04 pm -
Really? Inches? What century is this?
AllisonMarch 23, 2010 - 7:11 pm -
LOVE this! I teach science, and while I admire the lessons you facilitate, I struggle to use them in my class to teach science content.
This lesson is FABULOUS! After I read curmudgeon’s comments, I realized that in my physics class, my students could arrive at this conclusion and evaluate the plausibility of this scene..
Jeremy GrisbeeMarch 23, 2010 - 7:53 pm -
Dan, I do hope to try blogging about my exploits and adventures next year. This is my second year with 4 different preps, so it’s been a little busy trying to get my curriculum and plans lined up and still have enough time to blog about it. It’s definitely on my to-do list, and I’m looking forward to having time and mental energy to apply to it. You aimed that comment above at David, but I think you meant me, cuz you were quoting me. Every time I get on your blog, Nowak’s, Cornally’s, etc. I think to myself, “I REALLY need to do this. Look at how beneficial it is for THEM.” It’ll come. It’ll come. Truly.
Dan MeyerMarch 23, 2010 - 8:01 pm -
Whoops. Yeah, that was at you. David already blogs. That guy’s doing fine.
aaronthillMarch 24, 2010 - 5:19 am -
“This drives me nuts. Once a student has the idea that decimals are inches, it’s nearly impossible to convince her otherwise.”
I have a couple of questions for you teachers (I’m still pre-service):
When do you think that students acquire this idea? Is it a firm idea in their minds? For example, if you asked them point-blank whether .1 ft = 1 in, would they say yes. Or how many of them are just not careful when they are doing things (but if asked point-blank would know that .1 ft does not equal 1 in)?
Great blog by the way. Thanks for the work you put into it.
Ben GreyMarch 24, 2010 - 6:48 am -
If I were a student in your class during this activity, I’d likely push back on your push back. Which is probably what you want.
I’d argue that many of these handheld measuring units actually have a function built in that effectively makes the decimal unit a base-12 unit to report the decimal as inches for each reference in the field.
If that’s the case here, then they did blow up the right spot.
Though curmudgeon’s points all apply whether they hit the right spot on the grid or not. Might want to get your science folks to tag team on this one.
Morgante PellMarch 24, 2010 - 12:40 pm -
Hate to break it to you, but I’m afraid you *way* underestimate the intelligence of most high school students. I have never seen one of my friends make this mistake and neither have I. Maybe you’re remedial math students would, but I’m pretty confident most high school students (Algebra I? II?) wouldn’t think that .1 ft = 1 inch.
ihorMarch 24, 2010 - 2:02 pm -
Thought you might like this bit of coincidental trivia. Seth Green’s father Herb is a math teacher/professor at Temple U.
Dan MeyerMarch 24, 2010 - 2:21 pm -
Nice. I hope he set his son straight.
DavidMarch 25, 2010 - 2:21 pm -
Don’t pitchers throw 3.1 innings = 3 full innings, 1 out?
ChrisApril 19, 2010 - 10:10 pm -
To be clear: the frame in the boat is a decoy, the safe fell into the canal.
@curmudgeon, you are not alone. And they should standard-ize a pantload, I use it constantly. Sounds like another potential WCYDWT problem!
Love this stuff! Keep it up!
Dan MeyerApril 20, 2010 - 6:19 am -
silverMay 13, 2010 - 11:15 am -
@ Morgante Pell
Actually, it’s a more common mistake than you think. Here’s an example that I ran into just yesterday:
I brought my toddler son to the doctor’s office yesterday. He stood on the scale and it fluttered between 31 and 30.8 before finally saying that he’s 30.8lbs.
The nurse enters my sons stats into the computer and prints out a sheet that gives me information about his growth percentiles.
It’s not until after I leave the office that I look at the sheet and notice the nurse’s error. Rather than putting in that he’s 30.8lbs, she puts in that he’s 30lbs, 8oz. Incidentally, at my son’s age, that weight difference is about 3 percentiles.
So a nurse, who presumably has a bachelors degree and had to take at least one math course in college made that kind of error. I’m sure if you asked her how many ounces are in a pound, that she wouldn’t answer “10,” yet she fails to realize that decimals on that scales are not the same as ounces.
I wonder if the doctor ever notices that patient weights are never in the 9-15 ounce range.
The obvious solution (to both the length and weight issue) is to switch to the metric system.
David CoxMay 13, 2010 - 1:00 pm -
Are you sure that the scale doesn’t show the oz after the decimal? For example: could the weight register 9.15 to show 9 lb 15oz? When a pitcher enters a ball game it shows that he has thrown 45.2 innings so far this year. Everyone knows that the .2 means 2/3.
GauthierMay 14, 2010 - 4:35 am -
Great post, and comments too.
A quick look at the Leica website shows that the Disto (the measuring device shown here) has a function to switch between metric and imperical units.
I’ve never used one, but I would assume as you switch to imperical units, the ‘decimals’ would be base 12.
Of course, being French, I can’t help but agree that the metric system makes more intuitive sense, at least to our limited brains!
KariMay 20, 2010 - 9:11 pm -
@morgante: I teach everything from algebra 1 to AP. My AP students are the most frequent culprits! I tend to think, actually, that it’s almost our own (us teachers’) fault, and I lump the science teachers in there. Story problems, labs, and real lfe applcations are just so mch easier in metric that we use it mch more often as we go higher. And if we’re in a program that teaches skills and nit thinking, then we’re training kids that “the number after the decimal is a count of the next-smaller measurement.”.
I teach AP Stats and we do a lot with Normal distributions of heights, so we start talking about the mean and the st dev and my kiddies get all garbled trying to flip between decimal notation and feet-inches notation. I was thinking about this with dan’s height of 6.6 feet and how that becomes 6 feet 6 inches–a very common type of statement among my advanced, college-bound, calculus-taking seniors. Usually my next comment on that is, “oh, so, six-and-a-half feet.” it’s usually “only” a minute or two before someone realizes that we just establshed that 6.6 equals 6.5 and we have to go back.
KariMay 20, 2010 - 9:13 pm -
*”not thinking”, rather than nit.
Peterhorn33July 24, 2010 - 1:21 pm -
I love the idea of using popular culture inside the classroom. It definitely can get the job done with respect to having the students “buy in” to the fact that Math is a HUGE part of everyday life. I reference pop culture a lot in my lessons, For example, in Alg 1 I use Michael Jackson holding his baby out of a window to help teach slope ( Superman can fly straight up and save the baby but I have to RUN to the hotel and RISE in the elevator). One of the biggest pluses to these kinds of problems and references hasn’t been mentioned here yet. Not only do these ideas get the students interested but they also give everyone in the class a common reference point to fall back on. I am teaching Algebra 2 in summer school and one of my former students (Brian) is in my class. When another student had a misunderstanding about slope Brian spoke up and said “don’t you know the Superman and Michael Jackson story?” I haven’t taught Brian for two and a half years and he still remembered that stupid story and the lesson that went with it. Giving students the kind of experience you are talking about here with The Italian Job allows them to make a connection that will be remembered far longer than any lecture would.
Thank you for the great ideas.