Kachima is making triangular bandanas for the dogs and cats in her pet club. The base of the bandana is the length of the collar with 4 inches added to each end to tie it on. The height is 1/2 of the collar length. If Kachima's dog has a collar length of 12 inches, how much fabric does she need in square inches? If Kachima makes a bandana for her friend's cat with a 6-inch collar, how much fabric does Kachima need in square inches?
I'm not a pet owner so somebody please set me straight: is pet apparel a productive context for mathematical inquiry? Does PETA know about this?
Previously: Unnatural Currents
Yes, they make triangular bandanas for dogs, single ply. Usually cut with zig-zag scissors. My dog comes home from every stay at the kennel looking like a boy scout. every. time. This is still a terrible problem though.
Posted in anyqs, mailbag on May 22nd, 2012 65 Comments »
Am I imagining it, or are the participants (posters and respondents) mostly male? I’d love to be wrong about this. If I’m not wrong, then why would that be the case? And more importantly, has anyone noticed whether there is there any difference in class participation between female and male students when these are used in class?
I don't ask for your gender during the registration process so it's hard for me bring any data to bear on the question. But if I allow myself some conservative guesses, it seems that at the time of this writing:
- the top ten most perplexing users are all male,
- nine of the top ten most perplexing first acts were uploaded by males.
So help me, I can't figure out how the interaction on the site (ask a question and click "skip") or the nature of the tasks (a context and a question) preferences men. The reviews are all blind, too. I'm looking at a photo. Maybe it was uploaded by Candice Director. Or maybe by Dan Anderson. It's impossible to know until later.
I'm highlighting Elizabeth's comment to see if anyone can help me figure this out. I'd rather this didn't turn into a general complaint window, though. I'm interested in locating the source of any gender bias, not in airing out any other grievances.
BTW: My adviser has done a lot of work in gender and math. I should probably check in.
Too many. A really great discussion down below. Here's a link to my summary.
Posted in anyqs on May 19th, 2012 14 Comments »
- Circle or Polygon? Scott Farrar. This thing is poised to take over the all-time list once it crosses the 25-response threshold.
- Lemonade, Christopher Danielson. On some other site — let's call it Bizarro 101questions — Danielson uploaded a video in which he dropped a can of concentrate into each of those containers and started filling them with water.
- Megalodon Tooth, Jake Jouppi. I know I declared a moratorium on this kind of imagery (which is all over the site at this point) but think about the size of that shark, okay?
- Ping Pong, Bob Lochel. Great first act with strong implications for the third.
- Roller Coaster Steepness, Tom Ward. An excellent supercut of roller coasters that asks the student to first decide which one feels steepest (that's a low rung on the ladder of abstraction) before using mathematical analysis to determine which one actually is steepest.
My own listings:
Median photo perplexity: 46.
Median video perplexity: 51.
Photos own the top ten list but videos are more perplexing, on balance.
Posted in uncategorized on May 18th, 2012 7 Comments »
I'll be taking a leave of absence from Stanford during the winter quarter of 2013 (all of February and March) to work with (and learn a lot from) the Shell Centre in Nottingham. While I'm in town, I'd love to do some work with UK maths teachers — workshops or lectures or whatever else. I have four openings. If I can help out, please drop me a note at firstname.lastname@example.org.
2012 May 18: Apologies for the double-post. I just finished up some renovations around here.
Posted in anyqs on May 12th, 2012 17 Comments »
An embarrassment of riches this week. It was difficult keeping this to five:
- Too good to be true, Scott Keltner. So is it … free … then? I give this image strong odds on provoking a class debate and highlighting some of your students' misconceptions of percent growth.
- Car Chase, Ryan Brown. The current darling of 101questions. (12 questions, no skips, as of this writing.) Notice how the first car smacks into the second, which was hidden off-screen. That's stylish camera work!
- Muggsy Bogues, Tony Gumbo. The question, "How much shorter is Muggsy Bogues?" is one thing. "How many different ways can you express that difference?" is another. (eg. Absolute v. relative.) Start with the first. End with the second.
- First day of school, John Golden. "Is your height linear?" It's a striking visual and the units along the "x-axis" are identical so you have a rare moment to examine the growth of height over time using people in photographs rather than points on a graph.
- Plinko, Michael Pershan. Yeah, great cut at the end there. Where's the wisdom in putting the biggest pay-out beneath the most likely bucket? Bowen? (Related: this image, taken from this video.)
- Counting is so last winter. You'll notice that your first ten responses will generally come from the same ten-or-so people who have seen everything uploaded to 101questions and keep current on all new uploads. It's interesting to watch their tastes change. For instance, counting lots of little things used to be a lot of fun for this crowd, but now, as Tony Gumbo's Bryant Denny Stadium can attest, counting is out. (Which isn't to say that rating won't pick up once more casual users check in, just that the obsessives have made their decision about counting.)
- Speaking of obsessives, Andrew Stadel has written a great tutorial for getting the most out of 101questions.
- Veggie Juice swings for the fences. You decide where it lands.
- Closing. Timon Piccini's Cab Ride is the first first act to "close," which means 100 people responded to it. Now it goes to the very bottom of the pile on the homepage, where it'll only be seen once people have seen everything else. Initially, I thought first acts would close in a matter of hours after being uploaded. That was naive. It took months.
Plus my own listing:
At this point, I’ve posted about 300 questions. I’ve noticed that I’ve kind of changed my approach for coming up with questions for other people’s items. Rather than try to guess the question that fits as math teacher, I’m trying to put myself in the shoes of a 9th grader and decide “will they find this perplexing”? Fuzzy pictures: skip. Small font items like receipts and print advertisements that are full of numbers and words but no overtly visual content: skip. I’m also noticing that I’m beginning to skip items that are repeats of previously seen items – even just same genre items like super large ________. Initially, the questions were leaping right out at me. But now I feel like the student who says “oh, we’re doing this again.” No longer perplexed if I know what the teacher wants me to say. (Full disclosure: 2 of my 7 uploads are “world’s largest ______” related). Am I too harsh here, or are other people taking a similar approach?
I’m also finding a difference between “perplexing” and “interesting”. There’s a ton of stuff out there that is very cool and very interesting (intricate artwork, geometric designs, etc), but there is no obvious solvable mathematical question that is just begging to be asked. I skip those every time.