Dan Meyer opened his site 101qs.com some time ago now, and I have to say it has been rather engaging to see what the results have been.  You enter the site thinking you have some pretty top notch photo or video prompts that are bound to produce wonder and amazement, and yet somehow you find your perplexity score slowly going the way of the buffalo. At first it was disheartening.  You think to yourself how could my amazing collection of gumballs stacked on dominoes in the shape of a sierpinski triangle at the burning man festival not provoke the question, “How can we derive the gravitational constant?” The question now becomes, "Is that the point of 101qs?"  What do we want out of these videos and pictures?  Do we want everyone to be on the same page or do we want multiples questions to stem from each video?  Do we want both?  Is 101qs giving us what we want?

Clash of the Titans

 Over at Dan’s site people have been discussing these last set of questions and we find, naturally, Dan promoting his brand of “Make the prompt scream the question you are looking for” and Karim Ani saying, “There are more interesting questions that go beyond a one minute clip or picture.”

I think many of us, including Dan and Karim, find ourselves right in the middle of these two conflicting axioms. On one hand we desire that students seek for themselves.  We desire that they personally invest in interesting questions that provoke grand thoughts about life the universe and everything.  Yet we also recognize that they are young whippersnappers who have little experience beyond their hometown, school, and even neighbourhood; they may not have the capacity to think beyond the world of their home.  We then as teachers must make the hard decision of how to lead them to these wonderings.

How many “how many” questions can we put up with?
One of the biggest critiques of 101qs right now is that the questions are too simple.

• How many dominoes?
• How many combinations are possible?
• How many tickets?
• How many gumballs?

These questions have all been taken from the top of our list of most perplexing images.  Sure they represent different math (in this selection alone we have rates, combinations, volume, and area covered!), but the depth of questioning is shallow to say the least, and this is coming from teachers, who have experienced this world and are confronted with questions that affect our humanity and interactions with the world at large.  “How many dominoes?” just doesn’t cut it when we live in a world that is torn apart by famine, poverty, super-consumption, and an economy that seems to be hanging over us like the sword of Damocles.  We the teachers need to see how we can bridge this gap.  Students are certainly engaged by these problems, but how do we turn them, and mathematics as a whole, into more than a daily puzzler? If our subject, and this website, is turned into only a collection of neat little brain teasers, then we have missed the point of our roles as teachers.

Finding the Middle Ground

Just looking at the top of my site you will see clearly that I have drunk Dan’s Kool-Aid.  I love anyqs, and the whole three act process.  I know Dan's framework has directly made me a better teacher, and helped me to focus on more engaging class discussion, but I am beginning to find myself wanting more out of it.  In my comment on Dan’s blog I express that my main answer for this question is that we must understand that  101qs.com, in its infancy, is only presenting the first act of a fuller narrative.  We must use these videos as starters to the greater questions.  Students want to experience mastery of concepts, they want to feel positive about their abilities, and we can enter these students much easier into this subject that we love so much with a question like “How many gumballs are in that dang machine?”  It is fun, it’s nice, and students say to themselves, “I can do this!”  Then they take to the math, and they realize, “I need to know a lot of information to solve this.  What shape is that thing?  Is it a prism?  No, it’s a ball shape!  What is the volume of a ball?”  We enter with our sequels to these stories to propel their thinking, “How many gumballs could fit into this room?  Into this whole school?”  Students start adapting their thought to new situations, and they begin to see that this one little problem can extend far beyond just this picture.

Going for the Home Run

Once we have given students these chances to use their knowledge in differing situations we unload the brain busters.  We ask the hard questions, we develop projects from here. After seeing so many of these “How many little things can fit inside one big thing (gummy bears, tickets, dominoes, gumballs, teacups...) the question that has been arriving in my mind is this, “Why do we measure things in g, mL, etc. and not gummy bears, or gumballs?”  Get students to debate, and then create their own measurement systems.  Have them create conversion charts, and think about how to create a system that measures mass, volume, as well as linear measurement.  Have them reflect on the advantages and disadvantages of having their own measurement system.  Have them present their measurement systems to the class, have them create lessons about the Billy-Standard-System.  Then show them why the metric system is so awesome! They started their journey in the “How many?” river, but they are now swimming in the “What if?” ocean.

Where to Now?
Have I pulled this stuff off? Not yet, I’m still young, but I know that this whole 101qs thing is Dan Meyer’s attempt to pull the stunt on us as I want to do with my students. “Take some pictures,”  he says, but underneath it all is the possibility to go wherever we want.  So yes, if we discount these “How many?” questions as paltry, then that is all they will ever be, but if we keep pushing, we can turn these low floor questions into high ceiling discussions and projects.  So grab your camera, grab your phone, and get some first acts loaded.  We’ll work on the rest together later.

I am learning more and more about how this whole problem based learning shtick works, and I have to say I love it.  Today was an example of how much I love it, and how worthwhile it is.  I have been struggling to motivate the use of the Pythagorean Theorem in a natural way so that students can jump in.  Enter Mr. Piccini's Summer Purchase...

I started off the "story telling," by discussing how it was time for my wife and I to upgrade our T.V. I showed them the picture and asked them: "What problems do you think I may run into?"  I realised after that this was a little too much of the "Guess what is in the teacher's head" but the question was so natural they needed to ask "Will the TV fit under the shelf?"  We talked about what it meant for a TV to be 40".  Almost half the class knew that it meant the diagonal.  I asked what do we notice about the shape of a TV is when cut down the diagonal.  Clearly there were two triangles, and thus began our exploration.

For the next part I stole the great investigation from Dan Meyer found here.  This worked so well it was unbelievable. Students were very quick to see the relationship between the sum of the small areas and the large area.  Students enjoyed the manipulative nature of this exploration, and the result was clear and accessible to the students.

We did some practice and then came back to my T.V. the next day.

We started the next day with whiteboards, and I had students write what information we knew and what information we needed to know.  I reinforced to students that I did not want to renovate my wall because I am lazy, but I am not too lazy to move my speakers.  They said then that we needed to know the height to the shelf. So I gave them this...

Depending on how hard you want to make this problem you can do either cm or inches.  Inches is the easiest.  Since students recognized that we need information on the diagonals, we need to talk about what a good diagonal measurement would look like for this space.  For that I broke out geogebra, to show students how sizing TV's looks.  I used these two geogebra apps.

We talked about what the different shapes of TVs look like, and what your average wide screen would look like.  Using the geogebra animations the students discussed how the proportions always stay the same.  At which point we could talk about ratios.

At this point students needed guidance on how to find the dimensions of the space, but it came quite naturally to talk about the largest possible TV that I could fit in my living room.  Students found that this was a 55" TV, and as it turns out...

If you don't believe in collaborating online via blogging etc. let this section be a testament to this.  Neither of these extensions were my own thoughts, they were completely lifted from others, awesome!

• From Karim in the comments there is also this: "What is the largest standard TV (4:3) that could fit in this space?

Online collaboration for the win!

This was such a simple execution, but it gave the students a real challenge, and a real-world application to try from the get-go.  I had a debrief with my students in one class, and they said they loved how visual, real, and engaging it was.  I never expected to hear that.  The only complaint was from students that finished really quickly.  I was not ready with sequels, and in fact, I still can't think of any. I never thought that this specific problem would have as much engagement as it did, but once students got rolling they were hooked. All in all I was happy today, and I sure beat the socks off this version of the problem.