Best Of 101questions [4/14/12]

A few of my favorite listings on 101questions this week:

  1. A Fistful of Quarters (and Dimes), Nathan Kraft. Provokes the comparison of the value of a coin against its weight, which seems at first like a useless ratio. But remember the nickel thieves? If someone let you carry as much change away as you could lift, which kind of coin would be the smartest pick?
  2. Pennies, Friedrich Knauss. Provokes the comparison of the value of a coin against its surface area which, again, seems like a totally useless ratio until you see a photo like this. If you were going to carpet your floor with a particular kind of currency, which would be the smartest pick?
  3. Handshakes, Craig. Love the clip. I find the question, “How long would it take to infect the whole office?” irresistible.
  4. Coins, Steve Phelps. I’ve noticed these kinds of first acts are difficult to pull off. (Check, please, also uploaded last week, is struggling, for instance.) They’re often too cluttered or they place students too high up the ladder of abstraction too quickly. Steve Phelps strikes a nice balance here. Moreover the task is open to several correct answers, which is unusual for material you’ll find on 101questions.
  5. 1982 Osborne Executive vs. 2007 iPhone, Carl Malartre. I tried a similar approach with Evolution. I like Carl’s more.
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. Seems to me from clicking through the 101qs archive that a lot of the uploads are limited to the K-8 level. The next-gen step for the site will be to make wcydwt work for advanced algebra, trig, and stat.

  2. Have been out of communication for a few weeks (T mobile UK does NOT love Mombasa! Side note: i am a millionaire in Kenya which thrilled me…) i’ve not had a chance to play with 101qs for a while – as such, love this wrapping up of new material – cheers.
    Keeps me in the loop, and encourages me to get back on it.

  3. When I first saw the penny problem, I wasn’t that interested. But now that you’ve posed the value to area question, I really want to solve it. I think it shows that it’s probably worth your time to see what others have asked when you can’t think of anything.
    I’ve also had a lot of issues with videos not loading. Not sure if I’m the only one.

  4. a different eric

    April 16, 2012 - 4:51 am -

    I was looking at a few of these… and thought, “I wanna know the answer! Where’s Dan’s part 2 and part 3?”

    Wait a minute… you mean I might have to figure these out without a Teacher’s Edition???

    There’s nothing like having kids run up to me in class asking me, “Is this RIGHT?” and I get to reply, “I have no idea… explain to me what you did.” Their reasoning becomes more important to them and not their answers.

    I would love to hear how some of you how the kids accountable for 3-Act Math work. 90% of the kids are engaged and rockin’ class… but it’s that 10% I’m struggling with.

  5. Eric, I have the same problem (that 10%). And I find that they are less of a problem depending on how much information I give prior to having them work on it. But then I worry that I’ve given away too much, especially to those who would have figured it out on their own.
    I know that there’s another discussion on this (“They Really Get Motivation, Don’t They”) and from my own experience, I find that students typically feel more confident solving a problem if they have already solved something similar to it. And so I find myself asking, should I show how a similar problem is done before we do one of these activities? And I guess that it really depends on the makeup of your class. If they are strong for the most part, don’t give them anything. If there is a mix, and you have a number of students who struggle to do anything, maybe it’s best to put those particular students in the same group, and then, most of your coaching could be with that one group.
    As I experiment with this, I’m sure I’ll have more to say on the subject. I’d love to know how others use these videos/pictures with those 10%.

  6. @Nathan @Eric, the second act of these problems is where students get the tools, information, and resources for answering their question from act one. A brief explanation is a valid response to students who ask you, “How do I get an answer to my question?” Lecture is problematic when its use is unmotivated, unsolicited, or the students aren’t familiar enough with the context to make use of it. The advantage of the three-act structure isn’t that it eschews lecture in act two. It’s that the first act gives students a reason to want a lecture.

  7. a different eric

    April 16, 2012 - 3:15 pm -

    @Dan… that makes a lot of sense. I’ve been trying to do these without much lecture… or we’ll do some of the nuts and bolts (like how to find the area of a circle investigation) followed by a cool problem the next day.

    Did you ever assess the work from 3-Act math? I made up a very loose worksheet for the kids to fill out while we do them so I don’t have a page full of numbers to look at (the overall question, too high – too low – guess, questions we need answered, work and calculations, and overall answer) but I’m having trouble giving grades for it. I don’t want to punish kids for not coming up with something valid… at the same time I don’t want kids that just sit around and copy all the groups calculations to get the same credit as the ones busting their rears the whole time. I also want the kids to develop the ability to make good arguments that I can “read” as opposed to “interpreting”… so maybe that’s how I start?

    Or maybe I don’t collect anything at all? The reward is in the work and being able to be a part of the discussions… I’ll know if they understand it during the Concept Quizzes?

  8. As far as assessment goes, I grade all classwork and homework for completion only. Completion, in this case, will include all the first act elements (guess, high / low, if applicable, etc.), then also the work in act two. Sometimes a calculation of margins of error in act three. Sequels are at the discretion of the teacher.

  9. I know that you hate people looking for the formula.

    But I am trying to solve the Penny Circle problem and I have the following coins for each circle diameter:

    Diameter (inches) Pennies needed to fill
    1 1
    2 5
    3 12
    4 21
    5 35
    6 52

    22 ?

    Even when I insert the correct answer for the 22 inch circle, I can’t see how.

  10. Hi Nick, I don’t hate seeing people look for a formula. I don’t find it productive to give people a formula for which they don’t have any intuition. Here’s what I’d do. Load those values into a table and graph them. Notice that the graph doesn’t look linear at all. Try a quadratic. Drag the slider for “a” around until you see a good fit. Then go out to x = 22.

  11. Thanks, for that Dan,

    I wasn’t being critical – I really brought into your way of teaching Math.
    I am a primary teacher for the UK and Maths is not my degree subject, not finding a solution at first really brought insecurities out.
    However, I still persisted at it and so did the class and I must say I have been so impressed with the way the children have responded to it.
    We cover only basic algebra at my level, but on the follow up activity of working out the circumference of the circles, I actually saw two amazing formulas created for working out the 22 inch circle. Considering that these children have not really had major working with algebra, the two, different, formulas were extremely impressive.
    I am a big convert mate, but the removal of the structure is also challenging me. Which I am loving!
    Thanks – I might come asking for more pointers in the future.