That’s from Connected Math.
What I Did
- Simplify the prompt. It’s already pretty spare, but I’m going to get rid of the information for a minute.
- Add intuition. A choice between two items like this lends itself really well to a guess. But when the information is already included, students will start to calculate right away.
- Justify the constraints. One set of dimensions is given in feet and the other in meters. Why? Is that just a contrivance for the sake of a math problem?
That’s everything. If I’m teaching this material tomorrow, I don’t have time to whip up a video or a photo.
So I’ll tell students, “Two students drew pictures of their rooms. Which is bigger or are they both the same?” (Good catch from Chris Lusto on Twitter: “‘How much greater?’ omits the possibility they have equal area. Why do that?”)
I’ll ask them to write down their guesses, then share with a neighbor. Then we’ll take a quick poll.
A student may ask if the two drawings are at the same scale, which would make for a nice, quick discussion (“Good eye. That’s really important to know. They are.) but it isn’t an essential moment.
I’ll say, “Okay. I’m going to give you the width and height of the rectangles and we’ll find out who guessed correctly. But first I have some bad news. Rodney is from the United States and Emile is from France. Do you know why that’s bad news?”
Here’s what I expect to be pretty interesting as students work with the fact that there are 3.28 feet in a meter:
- I imagine most students will convert the meters to feet. But some may run the other way. Do they arrive at the same conclusion?
- I imagine most students will convert the linear dimensions and then multiply. But will other students multiply the linear dimensions and then convert the area? Will they arrive at the same conclusion?
- If they convert in their last step, will they multiply by the conversion factor twice as they should? (ie. 2.5m – 3.5m – 3.28 f/m – 3.28 f/m) or just once? If no one makes that error, I’m for sure going to throw it out there that “a student from another class got a different answer.” Then they’ll construct an argument for or against.
What You Did
Good ideas from the blogs:
- Andrew Shauver made Rodney and Emile brother and sister and brought in some realia with a floor plan.
- Caren Hickman makes over a different task, one about food, with the goal of using real data and giving students some choice over the constraints of the problem.
Good ideas from the Twitters:
@ddmeyer instead of asking whose room is bigger, maybe ask which room would need more carpet (or other type of flooring)
— Erin Wade (@ewade4) June 13, 2013
@ddmeyer tie in linear equat & $$ to purchase/install carpet. Also if every so many sq ft requires an elec outlet how many would there be
— Sarah Lowe (@spilarcik_lowe) June 13, 2013
@ddmeyer Picture of soccer field vs picture of football field. Soccer data in m and football in yards. Which one is bigger?
— Ignacio Mancera (@Ignacio_Mancera) June 14, 2013
@ddmeyer I'd remove the numbers, the last sentence, and maybe add "They want to know if their rooms are fair." #mathchat
— David Wees (@davidwees) June 14, 2013
@davidwees The word "sketch" is misleading. Measurements suggest precision, "sketch" does not. Would add they're siblings. @ddmeyer
— Jenn Borgioli Binis (@JennBinis) June 14, 2013
@davidwees or that they are exchange students, one in US, one in Canada. Will rooms during exchange be similar to home rooms? @ddmeyer
— Jenn Borgioli Binis (@JennBinis) June 14, 2013
Every problem at it's heart is "measuring squareness"@mpershan @ddmeyer
— eddi vuliÄ‡ (@zidaya) June 14, 2013
@ddmeyer 1) Draw a picture of your bedroom. Estimate the dimensions (don't specify which units); 2) Who has the biggest bedroom?
— Jessica Drake (@jess_drake_) June 14, 2013
Call for Submissions
You should play along. I post Monday’s task on Twitter the previous Thursday and collect your thoughts. (Follow me on Twitter.)
If you have a textbook task you’d like us to consider, you can feel free to e-mail it. Include the name of the textbook it came from. Or, if you have a blog, post your own makeover and send me a link. I’ll feature it in my own weekly installment. I’m at email@example.com.
Jason DyerJune 17, 2013 - 10:23 am -
The sides are only off by a handful of pixels, so I’m not sure if the “intiuitive guess” part is quite fair as given. I’d start with the picture here, but then show them something like this:
This reminds me a little of an experiment I do in teaching logarithms. I show a square, give them the area is 50, the show a comparison square and ask what the area is. If the new square is larger, they always overshoot, and the specific exponent they overshoot by can be found with logarithms and something called Stevens’ Power Law.
Rebecca PhillipsJune 17, 2013 - 1:48 pm -
You might also consider – after they’ve measured their rooms – sharing something like this: http://www.jamesmollison.com/wherechildrensleep.php
Stephanie ReillyJune 17, 2013 - 3:48 pm -
I wouldn’t guess that kids would convert the area correctly. Even my 12th grade physics Ss struggle with that. This may actually be an interesting activity for them to drive home the conversion dilemma.
KPJune 17, 2013 - 5:23 pm -
The classrooms in my school are not uniform dimensions, so one year I convinced my students that I was indignant that I have the smallest room on my team. My teammates were kind enough to allow the students to come in to measure. If I do it again, perhaps I’ll give one group a metric tape measure and ask the other group to measure in feet.
DaveJune 17, 2013 - 5:24 pm -
Here’s my shot: http://therationalradical.tumblr.com/post/53240267417/my-shot-at-this-makeovermonday
DGPJune 17, 2013 - 6:04 pm -
I had two ideas, although they may be getting pretty far away from the original.
I was looking for a MTV Cribs video which would have large rooms of famous people, but couldn’t find one (really didn’t want to watch that many MTV Cribs videos). They could estimate sizes and compare maybe to their own room. Could be a possible 3 Act if you found the right two rooms.
Also, came across this: http://www.dimensionsinfo.com/hotel-room-size/ . Got me thinking about maybe doing something with size of the hotel rooms and number that could fit on a certain floor of hotel at certain sizes. Could be some additional work about cost per room at certain sizes and whether they should have more small and cheaper rooms or less larger but more expensive rooms.
Love the Blog! Thanks
Todd HuntingtonJune 17, 2013 - 8:07 pm -
Extension possibly more realistic:
Rooms that are not rectangular or at least require some dissections into common shapes.
ChrisJune 17, 2013 - 9:04 pm -
Another context could be moving overseas (from the US to a metric country) and trying to work out if his/her new bedroom will be as big as the one back home (this allows for the change in units). The new bedroom information could be provided by way of a floor plan (download one from a real estate website somewhere). The existing bedroom information could be provided as either length and width or total square feet. If you’re evil, a photograph of a bedroom with an object of known size in the photo (introduction to perspective)
It all depends on what sort of skills the students have and what you want them to gain from the task.
l hodgeJune 18, 2013 - 4:55 am -
If we assume the diagrams are drawn to scale, why not just measure them with a ruler and avoid the unit issue?
I like the carpet suggestion. How about two rooms of more obviously different sizes and two different carpet samples of size one square ft & 1 square meter (to scale) with prices shown. Now it is visually more of an area problem as they have the 1 square foot and 1 square meter carpet samples to look at. Also there is a bit more room for debate on which room will cost more to carpet. One room is bigger, but one carpet is more expensive per unit, but the units for the price are different, etc.
l hodgeJune 18, 2013 - 5:01 am -
Here is my attempt.
James KeyJune 18, 2013 - 6:30 am -
Rodney and Emile’s parents decided to renovate their bedrooms. They are getting brand new carpet, as well as new baseboards. Whose room costs more to renovate?
suehellmanJune 19, 2013 - 3:48 am -
I’ve been thinking about my struggling math students and what I’d want them to learn/do/become better at if I stripped out the numbers and asked such an open-ended question. I think the goal would be for them to appraise the problem — to think about a range of good possibilities and potential issues & to turn off the urge to apply a memorized formula to solve the question that they assume is embedded in the shapes and numbers. (Because most of my students probably wouldn’t even see the units in the original, they question they’d end up answering wouldn’t be the one that’s truly asked.)
So they wouldn’t go completely ‘blank’, this is how I’d start: what questions might you ask Rodney and Emile to determine the sizes of their rooms? what if they can give you any information EXCEPT numbers?how would that information help you? what if they’re terrible at drawing? how can we decide which of our questions will yield ‘significant’ information for solving the problem? how can we decide when we’ve asked enough questions?
When I revealed the measurements, I’d ask them which of their questions would have led them to the significant information and how many of them might have missed that if we hadn’t taken the time to appraised the problem first.
I hope this would model for them a process of ‘questioning the question’ and give them a way into problems that at first seem baffling — to look at everything and fish out the most ‘significant’ information before rushing to formula matching.
Roger GemberlingJune 19, 2013 - 4:34 am -
Here is another idea to consider. It is located at
pete capewellJune 19, 2013 - 1:11 pm -
A couple of years ago I was inspired by your TED talk and the three-part videos to put this together:
It doesn’t quite have the same Rodney and Emile comparing areas idea, but explores a lot of the same math and concentrates a bit more on estimation and problem solving creatively.
What do you think? How might I improve it?
ChristineJune 20, 2013 - 4:05 pm -
So when I moved to the city and had to rent a (2-bdrm) flat with a friend, the day we moved in she arrived earlier than I did – and chose the bigger room! If we had of flipped a coin to determine who got the bigger room and I’d lost I would have been ok with it. I was annoyed because we shared the rent payments equally, yet she more area (I never measured her room to calculate exactly how much more she got) but I always felt that we should have been paying rent based on the area of the rooms (assuming all other space shared equally!)