## Five Favorites — 101Questions [4/28/12]

April 28th, 2012 by Dan Meyer

- Locked iPad,
*Jeff*. I love that math makes large, incomprehensible numbers a little more comprehensible. How many days, weeks, or years will I have to wait to try another passcode? - Bake House Piano Drop 2012,
*Jeffrey Kirby*. They really only had one shot at this. No do-overs. So how did they calculate the position of the ground piano for impact with the flying piano? - When you wish upon a star …,
*Statler Hilton*. I want to see what this looked like from the air. This had to be carefully laid-out and diagrammed. - Giant Domino,
*Ian Frame*. A gaggle of these popped up after my NCTM talk yesterday (during which I plugged 101questions). These enormous objects litter a small acreage surrounding the Philadelphia convention center, inspiring a pile of interesting questions related to scale. “How tall is the person who is playing with this domino?” will get you first-order similarity. “How*heavy*is he?” gets you the third order. - File Cabinet — Act 1,
*Andrew Stadel*. Crazy bananas. Thankfully, only one of us has to do this for*all*of us to use it and, lucky for him,*he*only has to do it once.

Also interesting:

- Floor 13 please,
*Luke Walsh*. I had a back-and-forth with Karim Ani over this first act. As of this writing, all four of Luke Walsh’s “students” want to know how heavy the average person is. Meanwhile, Walsh asks his students, “What is the area in square feet of this elevator?” That difference interests me. It seems, perhaps, typical of the student-teacher relationship where I can always override my students’ preference by the power vested in me as a teacher, a grown-up, and a person who is several feet taller than they are. All other characteristics of a task being equal, though, I’d rather its question be something that occurs naturally to them or that seems natural when I pose it. 101questions helps me locate those natural-seeming questions.

Plus my own listing:

- Portal Laser. I uh got kinda heavy into Portal this last week. Both of them.

on 28 Apr 2012 at 6:21 pm1 MaxI checked out your conversation with Karim on Storify (so neat to be able to archive tweets). Seems like in the specific case of the elevator photo, the student voices suggest there’s something more salient about weight in that photo. For me it’s because I have an elevator phobia and think more about crashing than squeezing in. That and I didn’t stop to think about how frickin’ huge a 31 person elevator is. Regular elevators are a tight fit with 15 people, I now recall from riding around during jury duty.

But to me, the question isnt about does the teacher ever get to assert things in the classroom, it’s about design. What do you do when a draft doesn’t go where you hoped? Edit. Maybe we need some help comparing this elevator to others. Start with video of 10 people squeezed into another elevator, then this photo. Or show people getting into the elevator and count and stop at 31 never showing the inside. Kids wonder how big is that elevator inside!

I hypothesize that it’s rare to have a scenario that’s mathematically interesting that can’t be captured in some media to provoke questions worth exploring. As a teacher, I am happy to lecture when students ask good questions, and to suggest further exploration when things are humming along, and even to tell kids about a better way to do something. But I also have to trust my subject that it is inherently interesting. If I have to tell someone “you should notice and care about this” something’s wrong and more importantly, it’s not going to work. That’s why playwrights’ mantra is “show, don’t tell”

If students aren’t seeing what I’m seeing, I need to show it, not tell them how to look.

on 28 Apr 2012 at 7:52 pm2 Nathan KraftI’ve noticed that in some of my videos I really use a lot of mathematical context to push the student where I want him/her to go. I’m wrestling with the idea of whether or not this is a good thing. As someone who is implementing these videos, I’d like for there to be some predictability in the question(s) that are formulated. I just uploaded a treadmill video, and I put so much information in there to get the students to see where I was going with it, that it just plain sucks (or as I like to correct the kids, inhales vigorously). It’s obvious that I’m trying way too hard.

I like all of the suggestions you’ve given Max. And I would propose that the “problem” with this picture is not so much that he came up with the wrong question, but that his eye was trained to see more than his students’ eyes. When I looked at this picture (as I’m sure many others have), I didn’t give much notice to how many people could fit. I just saw two different values, my mind shouted out “rate”, and I moved on. I wonder, if I looked at this picture for a few seconds longer, and my mind didn’t immediately think rates because it looked like a rate problem, would I have seen what Luke saw? And I wonder if my middle-school students would have seen it also, because unlike some of us, they haven’t done thousands of rate problems in their lifetimes, and that might not be their first thought.

on 28 Apr 2012 at 8:23 pm3 KarimTo be honest, I find this a bit disingenuous. The 101qs format doesn’t actually gauge whether students (in this case teachers) “want” to know the answer; rather, it’s simply asks for the first — ie most obvious — question that comes to mind.

In this case, the first question that occurred to most people was, “How heavy is the average person?” We had the elevator weight (5000 lb.) and the number of passengers (31), so this question seems pretty predictable.

It’s just not that interesting. Instead, there are any number of more interesting questions, for instance

How might the situation be different if it only men rode it? With 31 people getting on and off, how long would it take to get to the top floor?Sure, we can debate whether “interesting” is in the eye of the beholder, but I’m not convinced that most people reallywantedto answer”5000/31.”Again, I just think it was the most obvious. Which is exactly the point I was trying to make in the Twitter thread: that sometimes the job of a teacher is to get a 12 year-old to think like someone older than a 12 year-old. (Incidentally, this is why I think the 101qs site would benefit from some kind of “care/don’t care” rating system. You can ask me the first news station that comes to mind, but it doesn’t mean I care to watch it.)

The thing is, it seems that Dan agrees that it’s sometimes okay to trump a student’s question with a better one:

http://storify.com/mathalicious/what-does-want-mean

on 28 Apr 2012 at 8:39 pm4 Karim@Max

“I hypothesize that it’s rare to have a scenario that’s mathematically interesting that can’t be captured in some media to provoke questions worth exploring.”

What about,

How would you determine the odds of finding life on other planets?”orAs you earn additional income, is each dollar worth the same?These are mathematically very interesting — the Drake Equation and fraction multiplication; non-linear functions and diminishing returns — but it would be quite hard to capture either in a single media clip (without forcing it or presupposing the question).

I think that media — photos, video clips — can provoke very good questions, and many of the prompts on 101qs do exactly that. However, I think it’s dangerous to assume these are the

onlykinds of tasks that are perplexing or mathematically rich. A teacher recently did the XBOX Xponential lesson about whether video game consoles have followed Moore’s Law (and whether we’re building the Matrix), and said his students loved it.Are you prepared to disqualify this because the question didn’t arise organically from a single clip? Similarly, what would this mean for the majority of Valerie’s [excellent] financial literacy lessons on your own Math Forum site?

(By the way, great seeing you at NCTM!)

on 28 Apr 2012 at 10:16 pm5 Dan MeyerKarim:Are you sure — I mean, really sure! — that your questions are more interesting?

Because I worry for you, bud, and your conviction that “interesting” is some objective quality you’ve got the read on. I just give this stuff away, so I have a little elbow room to disregard the people who don’t find a particular task interesting. But you’re a businessman, and in this thread you’re reduced to telling the market “You dum dums don’t really want what you just said you want. How could you? It’s dumb!” As far as business plans go, it seems wobbly.

Definitely. No denying that. But there’s a cost to that decision, which the benefits have to outweigh. And “You kids are too dumb to have any idea what you want to learn about” will drain my account right quick.

on 29 Apr 2012 at 4:00 am6 KarimHold on a second. “You dum dums don’t really want what you just said you want.” Is that even close to what I said, or did I actually say, “Is the first question you write necessarily the one you most

wantto answer?”This isn’t about Mathalicious. It’s about 101qs assumption that “What’s the first thing that comes to your mind?” is a good proxy for “What’s the most interesting — or perplexing — question you can think of?” If that’s the operating assumption, then I fear that you’ll be left mostly with a bunch of “how long until…” or “how many will fit…” questions.

How confident am I that “my” questions are more interesting? Take your top-5 from this week, and in particular the domino question. I suspect most students would immediately ask, “How tall is that domino?” But your question asks, “How tall is the person who plays with that domino?”

I recently heard you say that, if for no other reason than the practical, the class needs to agree on a single question to solve. (Totally reasonable. It’d be pretty tough to monitor 31 students’ separate problems.) So in this case, which question should the class pursue: how tall is the domino or how tall is the person?

The person one. It’s a better question. Why? Because it goes a step further; you have to answer the domino question en route to this one, and that — your! — implicit “can we get

moreout of this?” is what makes it better. This transcendence is the definition of better! (This strikes me as very similar to Steve Leinwand’s comparison of assessment questions in the US versus Japan.)That said, I get the sense that your “business model” remark wasn’t really about my 101qs “on the nature of ‘want'” comment but rather the types of lessons we post on Mathalicious. So let me address that:

How many possible shoes can you design on NikeiD.com; at what point does this lead to paralysis by analysis; and is Zappos a better business model?Or,How many direct ancestors do you have in each precious generation; how far back would you have to go to be related to everyone on Earth; and if everyone can trace their ancestry back to the same people, does this mean that everyone alive today is related?How confident am I that these are more interesting than

How many pennies will fit in that jar?orHow long until the tank is full?*Very.Whether they make for a sustainable business is another thing altogether, but if Mathalicious goes down, that’s the bat I want to go down swinging.

*How about,

How much will it cost to fill up the tank with ________?Two more words.on 29 Apr 2012 at 4:01 am7 Karim(actually, a few more than two words. Eek!)

on 29 Apr 2012 at 5:12 am8 josh g.Honestly I think the elevator one just isn’t that successful; when I first looked at it, nothing grabbed me visually so I was left wondering about the numbers on the screen. Which is exactly what this *shouldn’t* be about.

I think the piano example is a better choice for this mini-debate though. Dan, right now you’re the only one who’s posed the question, “How did they know where it would land?” The other three posts are scattered around how far and how fast the piano fell. I don’t think that negates your question from being interesting – I think it just isn’t the first thing people notice about the video (unless you’ve tried to set this sort of projectile-target thing up before). But just because the initial first reactions are “Wow how fast did that piano smash the other piano?” or “Whoah how far did they drop that?!?!” doesn’t mean the “Hey guys, just how *did* they know where to put that thing?” bombshell won’t grab students once you reveal it.

on 29 Apr 2012 at 6:01 am9 mr bombasticOne of the better pieces of advice I have read on this blog was to just ask the question if you are not willing to go with the questions the students come up. Attempting to contort their question into yours isn’t the way to go either – this is dishonest and fools no one.

I think the issue is usually that the question isn’t very good for that class, not the fact that the teacher is the one asking it (not saying student generated questions aren’t a plus).

on 29 Apr 2012 at 6:43 am10 BreedeenI think that there is a vital and subtle difference from the teacher posing /another/ question that s/he finds interesting, and the teacher posing /the/ question that s/he finds interesting.

Finding the balance and creating a culture in your class that allows the teacher to be able to add questions to the pool without negating the importance and the worth of students’ questions. This seems to me to be a large step towards being able to get students to think beyond their “first” question, as Karim mentions, to perhaps a more compelling question that may or may not require answering that first, more obvious question along the way.

on 29 Apr 2012 at 7:03 am11 David WeesI’m not convinced that it is necessary to have all of the students working on the same problem. In my experience, students will ask about 4-5 problems (more is usually better) and that their obvious questions are often the easiest to answer. You can then group students up by what types of questions they asked, and then have them switch up which kind of problem they are solving.

One also has to be careful about steering the class toward a specific problem. Otherwise, you will end up with a game in the class called “Let’s guess what the teacher is thinking” which is itself not a thinking activity for the students. Too many class spend their time guessing rather than thinking.

If the key is to get students thinking about mathematical reasoning, then it doesn’t really matter what problem they solve, so long as they eventually get into meatier, more difficult problems, instead of always looking for the quick, cheap, and easy problem to solve.

One way to help students work on more challenging questions is to give more context to the problem, and be willing to tell a bit of a story to get them thinking. The farmer, king and rice story is a good example of a story that justifies a discussion of exponents. Obviously population growth is another one. 101qs is a way of starting a story, surely more involved stories are necessary too. I doubt that every interesting mathematical idea can be captured by a single piece of multimedia.

We also want students to work on problems that they cannot complete in a single sitting. Mathematicians often work on problems for years, but it is rare for students to work on problems for more than 10 minutes in a single sitting. While shorter and faster problems are useful for more variety of problem solving, I also think that longer problems that take much more of a process to solve are useful.

I think we need multiple approaches to designing problems for students, and helping students design interesting mathematical problems for themselves.

on 29 Apr 2012 at 7:32 am12 Nathan KraftWith experimentation, I’m discovering that a good way to implement these things is to let the students come up with their own questions that they really want to figure out. I then guide them to a solution. And then, I say, “Hey. I’m glad I could help you figure that out. And here’s something I’m really interested in [insert “good” question here]. I’d like you to help me now.” It eliminates the impression that I think their questions aren’t valuable and they now owe it to me to consider what I would like to know. And of course this takes extra time, but who cares? They’re hooked!

on 29 Apr 2012 at 8:16 am13 Cynthia NicolsonHi Dan – Thanks for all your intriguing, thought-provoking work. I don’t know how to upload it to 101 Questions, but I think a screenshot of this web page – possibly with all the contributors’ names highlighted – would prompt some perplexity and statistical thinking such as “Where are all the women?” “Is this typical?” or “Does this match the gender breakdown in our class/school/state?”

on 29 Apr 2012 at 10:55 am14 mr bombasticI think the elevator question has a lot more potential than you might think at first glance.

You have two numbers (5000 & 31), so many people will naturally want to do a computation to get an average weight of 161 lbs. But, then you might ask the class if this means everyone that rides that elevator weighs 161 lbs. You might ask what sort of variation you would expect see in a group of people; what are some ways the weight in the elevator could exceed 5000 lbs; and how likely that is to happen.

I think these follow up questions are fairly natural extensions of the original average weight question and are actually the sort of thing that you would need to consider when installing an elevator.

on 29 Apr 2012 at 1:18 pm15 Timon Piccini (@MrPicc112)@Karim and @Dan

I think you two can both meet in the middle. I feel like where 101qs works well is that we are trying to find how we can engage those students on the gut level. To paraphrase Dan, how can we introduce these tasks to have everyone step on the first rung of the ladder of abstraction.

The more interesting questions become the sequels to these first acts. So yes, we start on a low bar, but I have a number of students who would have a very difficult time even with the average weight problem. Let them be challenged by the lower level questions, they need to experience success, and bring out the more involved questions as they work through those rungs of abstraction to the more interesting problems.

I am sure we are all well aware of that fact, but I can’t help but feel as if you guys assuming that each others methods precludes the other’s from being effective. They can both accomplish the same goal, and the question then shifts to: “How many and how rich of ideas do we want to give students at the onset?” I have been favouring the 3 acts approach, because kids start with an easy question, “How long does it take for a beam of light to go to the moon and back?” And progresses to a harder question, “How far is a light year?” To really difficult question “Based on the speed of light and the closest planet, what are the chances that we will ever find life in the universe?”

Dan wants to start on the first rung of that ladder. Karim wants the student to appreciate the beauty of the ladder in its whole glory. What is best for students?

on 29 Apr 2012 at 3:23 pm16 Karim@Timon:

Thanks for such a thoughtful post, and I really admire your progression from “how long does it take for a beam…” to “will we find alien life?” It’s a lovely chain, and one that I think demonstrates the point exactly.

I hope I haven’t implied that these two approaches are mutually exclusive. (I don’t believe I have, and think the “dum dum” line from earlier was an unfortunate mischaracterization.) I think it’s important that students be able to ask and then pursue their own line of questioning, which is why our lessons begin with the open-ended “Preview” activity.

At the same time, I recognize that these student-led questions will eventually/invariably peter out, both in terms of quantity and, more importantly, interesting-ness. This is where I think the teacher (sometimes aided by the curriculum writer) can step in and push the conversation beyond these limits. Otherwise we risk losing the alien life question, which would be a shame. And from my perspective, an unacceptable one.

And this is where I do see an important difference between Dan’s and my approach. From what I understand of the 101qs ethic — and I may be wrong — Dan is willing to let the conversation go wherever students want to take it. He may have in his head a particular question, but if it doesn’t go there, he’s okay with that. The upside is that students dictate every step, and this approach has a certain purity.

The downside, though, is that we may end up leaving a lot on the table, and I’m not willing to do that. When I taught — or when I write — a lesson, I know where I want it to go and weave a narrative that will get it there. Yes, I try to elicit as many of these next-steps from students as possible, but will still rest my finger on the steering wheel. In my mind, this is exactly what effective teachers do. Socrates’s questions weren’t open-ended; they just

lookedthat way.Of course, this too has a downside in that it removes some — or in some cases, maybe even a lot — of the student authorship. But the upside is that you get to have the conversation about alien life (or in the Mathalicious case, the anthropomorphic bias of the Drake Equation). And this is where I’m perfectly willing to trump a student and draw my line in the sand: my goal as a teacher/developer is not for 12 year-olds to limit themselves to 12 year-old questions. My goal is for them to consider 30 year-old questions, 40 year-old questions; questions that Einstein and Sagan and Hawking asked.

And oftentimes that takes a teacher stepping in and taking the wheel.

on 29 Apr 2012 at 4:51 pm17 Max@Karim:

I kinda cheated when I said, “media,” and I did it on purpose. I think sometimes a story or series of images or search results or lecture can motivate good questions. Now that I’ve googled Drake equation and anthropocentric I’m full of questions, like, “what the heck would non-human intelligence look like? Could there be intelligent beings the size of atoms or solar systems? Could there be intelligent rock formations? Have we found all the intelligent beings on *our* planet? What counts as communication?”

I do think good questions have to come from learners, not be asserted… but like Breedeen says, if a teacher says, “hey, here’s another question I find interesting, what do y’all think?” and the students say, “ooh, yeah! That’s totally interesting!” then those students own that question and are going to work their socks off to answer it.

Something about how you phrased reserving the right to assert what questions deserve to be worked on rankled me (and, clearly, Dan, since he put the word dum-dums in your mouth and he wasn’t talking about mystery-flavored lollipops). For one thing, the idea that 12-year-olds’ questions are less interesting than 40-year-old questions seems unverified. Less nuanced, sure, but less interesting? I had big, deep questions about fairness and justice and happiness and the future and the nature of the universe when I was 12. And if I said to a group of 12 year olds, “want to think with me about the odds of intelligent life on other planets?” and they said, “not really” I wouldn’t say, “well, that’s ’cause you’re 12 and don’t know how cool that is,” I would say, “why not? What do you want to know about?” (and they might say “how to get girls” in which case we could talk about the Drake equation after all).

All the Mathalicious questions I’ve seen are inherently interesting, and would likely interest groups of people of all ages, and you work carefully to pose them in such a way that everyone has resources to both begin to think about them and see how relevant they are to experiences they’ve had — students are prepared to think about the paradox of choice with a relevant example (custom sneakers) and equipped to think about how quickly choices grow from a few variables by working through the sneakers. It’s highly likely that the media sets them up to have just the question you predict they’ll have, and assert to them: can there be too much choice?

Seems to me like you’re starting with interesting questions and letting the math serve those questions, which I think is neat. It’s not exactly math for social justice, but it’s definitely math for good citizenship and generally being a good person.

101qs seems to have the goal of finding interesting moments that motivate the math. Making the moments interesting is super important because the math isn’t inherently interesting without a context (whether it’s a real-world context or a puzzling context: prime factorization is interesting to people who want to crack codes or make a million dollars or factor a quadratic equation or who are in any situation in which that skill is useful to a problem they’re genuinely invested in).

I find the “here’s a question” vs. “skip it” choices an okay-enough metric of a photo or video’s ability to provoke a question worth solving, and worth learning some math to solve.

I’d use 101qs to motivate a piece of math I wanted to concretize, make relevant, and get kids thinking about intuitively. I’d want to go from there to further generalizations and abstractions and thinking about the math for math’s sake.

I’d use Mathalicious to set the context for an important, interesting good citizenship conversation that requires some math skills to engage in fully.

Like you said, two really different goals.

FWIW, I think finding the average weight being used by the elevator company to be a very interesting question because I want to know how generous they’re being with their maximum capacity estimates. I don’t want to be on that elevator with 30 people and thinking, “gee what if a couple of these people are a lot heavier than average? What if none of us is skinny? Are we gonna crash?” [In a way, that’s more of a Mathalicious context: the average weight question is in the service of “what is a valid margin of error for engineering and safety?” which is a good-citizenship question and therefore more likely to be interesting no matter how it’s posed.]

The size-of-the-elevator question is interesting too, but if someone told me it was what I needed to solve after looking at this picture, I’d say, “who cares?” and then more of the lesson would be spent getting me to feel engaged than doing math with me. Whereas if I saw 31 people getting into an elevator and they just kept going and going, I’d totally be wondering, “what’s a reasonable range of sizes for the inside of that elevator,” and would be happy to answer that question — it’s not the question that’s inherently interesting or uninteresting in the 101qs case (whereas in the Mathalicious case, I think the question itself has to be interesting to “any reasonable person” or else it’s unlikely to be a question that leads to people being kinder, fairer, etc.) it’s that it was posed more or less artfully.

And that’s why it’s worth spending time improving your 101qs question ’til it screams out “care about this question!” whereas time is spent over at Mathalicious carefully scaffolding the math to get to really interesting conversations (that 12 year olds and 102 year olds care about when they’re equipped to relate to).

on 29 Apr 2012 at 8:08 pm18 Fawn Nguyen(Is there a character limit on a comment here?)

on 30 Apr 2012 at 7:00 am19 Jason DyerI worry that what’s coming out of 101qs has a sameness as far as what mathematics is being applied. I have time to spend maybe a week or two on ratios in class, but they absolutely dominate these kind of problems. I estimate overall the mathematics I’ve seen takes up 5% of what I have to actually teach.

Is there anyway we can solicit things that work with the “difficult” standards (like rational expressions)?

on 30 Apr 2012 at 8:46 am20 Dan MeyerKarim:I agree. The question about the person is better. You get height and you get a little extra. I think that’s a much more useful rationale for “better” than “I’m 33. You’re 12.”

josh g.I’m seeing this crop up frequently in the top ten. The pyramid of pennies features “how many,” “how heavy,” “how long,” and other questions that either subsume each other or can be solved by the same math in parallel. That’s a feature, not a bug. We all have different questions. We can start with one of those questions and watch the other answers follow quickly after. In the case of the piano, finding speed on impact is a quick calculation once you’ve calculated the piano’s path.

mr bombastic:One hundred percent agreed.

Breedeen:One hundred percent agreed.

Cynthia Nicolson:I’m not sure what “this web page” refers to, but let’s say it refers to the top ten most perplexing uploaders on 101qs, which has featured (I think) at most one woman. I find that perplexing also. So perplexing that I can’t even hypothesize an answer. The first acts are presented to users without any information identifying the uploader. Is there something inherently masculine about the super bear? About the pyramid of pennies or the domino spiral? I don’t know.

mr bombastic:Right. I mean, people make their livings navigating these issues, trying to implement safety codes. I’m not particularly convinced the question is objectively uninteresting or, per

Max, that we’re more interested in the math than the context itself, though I can only speak for myself there.Timon Piccini:One hundred percent agreed. Once students have a strong sense of the context, and confidence in the mathematical model describing it, it allows us to ask even richer follow-up questions.

Karim:This isn’t correct. See mr bombastic in comment #9. Or this post.

Jason Dyer:The spreadsheet of released three-act problems has the same kind of sameness, I think. “6.RP.3″ crops up dozens of times. I wonder what that reflects. Possibilities:

1. Rates, ratios, and proportions are the most useful math, the kind of math that most people spend their day doing and thinking about if they spend their day doing or thinking about math at all.

2. There are plenty of other great applications but the particular constraints I’ve set one 101qs (one image or one minute of video, one question, 140 characters, etc.) lend themselves best to rates, ratios, and proportions.

3. There are other great applications, the constraints of 101qs don’t preclude them, they’re just kind of hard to capture.

I’m pretty sure all of these are true to different extents. Once I get some CCSS tagging going (struggling to wrap my head around what that design looks like) we’ll have a better angle on the question. OTOH, if all that results of this 101qs experiment is a pile of starters for rates, ratios, and proportions that kids don’t hate, I think we can still be proud of that.

on 30 Apr 2012 at 9:58 am21 Fawn Nguyen(Sorry iPad acted up in last comment, and I didn’t realize that part had sent. I was just starting to comment.)

For a relatively new website—not including time on #anyqs—I think 101qs is already achieving its intended initial goals. I know this because:

1) I was staring at a building for longer than usual yesterday and my friend asked, “Are you looking for math?” Ever since I got sold on 3Acts, I’m always on the lookout for “perplexing” situations. This is my 8th year teaching math and I’ve always loved math, yet I was never such a math geek like I’m now. I’m jealous of Andrew’s File Cabinet Act3 because it makes him a bigger geek.

2) Max’s and Karim’s two comments are over 7200 characters each, that’s about 51 tweets worth of words! That shows high interest and passion to me. We ask critical questions of the site and of ourselves as educators; it’s a win-win formula.

We cannot ask a kid to come up with a question and not honor it. I don’t think anyone here is saying that either. But Dan has built in a sequel and an extension to each 3Act lesson, and I see the teacher’s question can always come up at this time. When I did Andrew’s File Cabinet lesson, Act 2 was about each kid answering his/her own question in Act 1. And maybe a kid who asked a 12-year-old question liked the 30-year-old question asked by another kid and wanted to change his mind, this is okay too.

My concern is the number of WHY questions that my 6th graders have come up with. For the “Leaky Faucet,” one kid asked, “Why did he use the rubber ducky?” Another kid asked, “Why is he wasting water?” So we had a discussion about this.

The best Act 1 can go horribly wrong in the hands of one teacher, while a seemingly mediocre Act 1 can blossom wonderfully in the hands of another teacher. We have that much power.

on 30 Apr 2012 at 2:22 pm22 Michael PThere are other great applications, the constraints of 101qs don’t preclude them, they’re just kind of hard to capture.To me, this is the exciting possibility of this project. Anybody have thoughts on the next batch of low hanging fruit?

Here’s what I’ve come up with:

Linear EquationsDan’s graduation problem is a start. Related: reading the dictionary. (ala http://www.youtube.com/watch?v=Q9DCoqMrKr8)Systems of Linear EquationsWe should be able to nail this. Will the two things crash? Will the second gerbil win the race? Will he make the putt through the windmill?ProbabilityThe challenge here is replicating the experience of a long-burning empirical experiment in a short video. Maybe a game show on the left side of the screen, with a tally of the results on the right side could create that experience?StatisticsOpen with a bunch of short interviews of respondents answering a question. Would that be enough to provoke a question about the aggregate population?QuadraticsDropping things out of windows? (I’ve got a couple of bouncy balls that I intend to drop out of my apartment window one of these days.) Racing things off of hills?TrigonometryI’m thinking pendulums. Will the runner crash into the swing?What else?

on 01 May 2012 at 6:24 am23 lesannoOther ideas for trig problems: calculating distance (between two mountain peaks, say) using the Law of Sines. Then calculating distance when the Law of Cosines must be used. I can think along the lines of soccer players positioned on a field, tactical positions creating non-right triangles, etc.

As for right triangles, we once used Dan’s “How tall is the lamppost?” images (http://blog.mrmeyer.com/?p=12620) to answer the question “At what angle is the sun hitting the lampost?” using SOHCAHTOA and inverse trig functions. I wouldn’t say the experience was award-winning, but it was cool. It would have been cooler if we could have calculated what time he took the photos based on the angle to the sun. Anyone know how to do that? Right triangle trig opportunities abound in architecture, shadows, just about anything that goes up from the ground. We just have to start taking the opportunities.

I’m hoping to come up with something truly awesome that uses logs or logarithmic equations. That would make my day.

I suspect that the supremacy of rate- and ratio-type results from 101qs is in part due to the questioners, not the uploaders. I think even if presented with a good trig opportunity, most of us pose algebra-type questions. Maybe because we’re just in that mindset? Or do Dan’s blog and 101qs appeal more to algebra-ers?

on 01 May 2012 at 6:34 am24 Michael PLesanno, what media would you upload to 101qs to motivate a question that uses the Law of Sines?

on 01 May 2012 at 6:56 am25 Jason DyerI suspect that the supremacy of rate- and ratio-type results from 101qs is in part due to the questioners, not the uploaders. I think even if presented with a good trig opportunity, most of us pose algebra-type questions. Maybe because we’re just in that mindset? Or do Dan’s blog and 101qs appeal more to algebra-ers?@lesanno: Keep in mind the point here is to have an question just begging to be answered strongly enough that even the apathetic teenager becomes curious; if anything our mindset is too complex compared with how our students will think.

Side note: Once I had a terrific lesson where I had a picture, a little extra context, and asked “what time of day is it?” No student would come on their own thinking answering the question was even possible, so it’s somewhat outside the 101qs format.

on 01 May 2012 at 9:27 am26 Dan MeyerFWIW, I think

Michael P’scomment argues strongly for some kind of wishlist on the site. Like a stripped- stripped- stripped-down forum where you can say, “Is anyone in Philadelphia right now? I need a photo of the enormous domino piece.” Or, “Struggling w/ related rates and cones.” Or something.Jason:In general, I agree, and I try not to be too dogmatic about any of this, but check out the competition. You know? Just undertaking the exercise and asking ourselves, “What are students going to wonder here?” puts us leagues ahead of the typical student experience, which is more like, “Screw you, kid. Here’s a dog in a bandana. Let’s get our special triangles on.”

on 01 May 2012 at 12:17 pm27 lesannoMichael P: Excellent question, especially since I have yet to contribute a single upload to 101qs. I am thus an amateur. The idea is still in the formulation stage, but here are my thoughts:

-There’s gotta be useful wilderness footage in some man vs. nature movie that involves navigating or estimating distances. I’m picturing adventurers stranded in snowy mountains.

-A bird’s eye view of a region with pins in the three relevant locations. The distance between locations 1 and 2 we know; we want to know the distance from 2 to 3; we can measure the angle.

-A picture along a line of sight between two somewhat distant objects and the simple question: “How far away is the ________.” I actually tried to construct this one on a faculty work day. I followed it up with video of me measuring the relevant pieces (a navigational compass for the angles, measuring tape for the side). It was workable, but deserves to be done better.

on 01 May 2012 at 2:05 pm28 Kelly HolmanI’m a little confused about 101 questions. Is it supposed to be only first acts, or are there complete three-act videos somewhere, that you can search for something to use? Is there such a website? I tried Better Lesson, but there’s an overwhelming amount of stuff, and I don’t see a category titled “engaging” or “WCYDWT”.

A related question: Do you manage to teach everything in math this way? If you do, I’m very impressed.

on 01 May 2012 at 6:13 pm29 MikeThis is fascinating. I’m especially interested in hearing how to do this with the other 95% of the curricula, and who is building a repository of these student driven lessons, like Kelly and Jason asked. For instance, today I taught about finding the measures of a bisected angle, whose angles were arbitrary algebraic expressions. Bisected angles– sure! (mirrors, billiards) but angles of 6x-10 and 3x+5 makes it absurd.

I’m mainly posting to get notifications of the responses. :-)

on 02 May 2012 at 5:14 am30 lesanno@Kelly Holman 101qs is for the media part of the first act. Basically, the first act without the question. Dan publishes a collection of three-act problems here: http://bit.ly/IWOIos. Some of them have all three acts, plus a sequel; some of them only have certain pieces.

on 02 May 2012 at 5:52 am31 lesanno@Jason Dyer I see your point and I’m certain my materials can be improved. But I also see that, not having experience in asking my own mathematical Qs as a student, I needed to be trained in this way of thinking by seeing others’ questions. Even as a young adult, I would not have asked, for example, “Which coin would be cheapest to carpet my home in?” Now I might. If a teacher can train students to ask these questions, can’t she train students in higher level courses to ask (and care about) higher level questions? Wouldn’t that be a major goal of the class?