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
When I read debates from guys like these I imagine this, but with better vocabulary.
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.
Sadly, the interactive iPad version comes out next year.
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.
Ever wonder why companies make the decisions that they do? My wife and I drink more pop than I am willing to admit, and one thing I noticed while at the store is that the twelve packs of Coke and Pepsi do not have the same design. Let's look at them (warning I do not know if this works in the States).
This is also a precursor to this lesson
Act 1 - The Boxes
I asked my students which one uses the least amount of cardboard, and in relation, which company made the best choice for the environment?
This was a good starter. I had kids talking about which looks bigger, and a trend over at least two classes (I'll see later on in the future), is that the majority of students say that Pepsi is the clearer waster, or they have equal amounts of carboard.
Act 2 - The Measurements
I ask students what do we need to know to solve this? Students came up with volume, area, dimensions etc. at which point I introduce them to our cm cubes.
We talk only a little bit about the difference between volume and surface area. In fact I do not use the words in particular, we talk only about "How many cubes are necessary to build this prism?" and "How many squares can we count on the outside?" an idea I lifted from Christopher Danielson
. I gave students the following sheet and basically said, GO!
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Here I talked to students a lot about short cuts. It was great when they said they had no short cuts, and I ask, "You just counted?"
"Yes," replies the student. I then proceed to count one-by-one each outside square. Before I can even get to three, the student interrupts and says, "No, no, no, you times the length by width for one side, then times it by two. You do this for three of the sides, since they each have an equal side" (paraphrased). Bwa ha ha! I laugh to myself, they have it, and I didn't have to write a single formula on the board!
Bringing it back to the pop box now only involves asking, what do we need to know to solve the pop box, problem. Students tell me they need the dimensions of the box so I give them these...
Act 3 - The Reveal
This is also a good time to have students talk about anything we are missing. My wife after a few days of seeing me make this asked about the overlap, and if that makes a difference, I haven't looked into it yet, let your students do it too!
- The boxes are designed with the following can configuriations...
How many different configurations can you find, and which one of these uses the least amount of cardboard? Do any of them use less cardboard than Pepsi and Coke's configurations?
- Write a letter to one of the companies that explains your mathematics. Suggest for them why you think they should switch or keep their design.
Reflections and Moving Further
This was extremely engaging for one of my two classes. I think for me the pay out of the reveal is not as great as most of these 3act stories, so it can lose some students. I want to work on that out for next year.
What else I need to do is to prepare more guiding questions to start off the investigation, so students can be invested in the problem earlier. They have not seen surface area before and so are not acquainted with it. Students knee jerk reaction at this age is to find volume (well actually they just say lxwxh without knowing what that means), so I want to guide them away from that. If they focus on volume to early on they count the problem off to early.What I really liked about this investigation was the next day when I wanted to teach them surface area of triangular prisms I handed them the nets, and asked what do we have to do now. Students quickly came up with the idea that we needed to find the area of each separate shape and them together. They knew the only formula they needed was to find the area of the triangle. We talked about the relation between rectangles and triangles. This was a fairly easy process, because students can see if you cut a rectangle down the diagonal it makes two triangles (therefore bh/2). This was a fairly simple review of the area of a triangle and extension of their learning of Surface Area. It was fantastic to see how quickly they adapted to the new information!
Students were able to further adapt this to other nets that used basic shapes, and it was a very simple natural extension of the same logic (Thanks to Kate Nowak
for the idea of nets and surface area).My only hiccup came with cylinders.
I was ill prepared to lead students into a discovery of the area of a circle (technically they learned it last year... but they're only in grade 8), so I fell back onto lameness. I hope to alleviate the lameness, any suggestions? I have learned that great teaching comes from thinking through all aspects of the lesson and leading them through the inquiry. My cylinders lesson bombed, because I was lazy and had little prepared! I was humbly reminded how easily it has to slip into bad teaching, let's change that Timon!
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...
Act 1 - My Living Room
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.
Act 2 - Exploring the Pythagorean Theorem
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...
Act 3 - The Reveal
Sequels (Updated May 27, 2012)
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.
So, I am kind of on a binge right now with my 3 act posts, but I have had this one for awhile and I have not posted it, but after reading this comment
on Dan Meyer's blog I decided I should put this up as a possible elementary level 3 acts lesson. Here it is....
Act 1 - Mmm Juice....
I have a goofy little set up for this, where I say I'm making drinks for my friends, do I have enough?
Ask them what they think? If so how many glasses do you think I can fill? Give me a number that is too high and a number that too is small. Ask your students what information we need to know. Then we are on to Act 2 (and here is where the differentiation comes in...
Act 2 - Measurements (Grades 4-6?)
Act 2 Measurements (Grades 8-10)
If you want students to find the volume of each of these containers you can use these pictures to do the trick (jump-high-five for differentiation!).
Act 3 The Reveal
- How many cans of juice do I need to give one cup of juice to the whole class? To the whole school?
- How big of a container do I need to hold all the juice for the whole class? The whole school?
So apparently I really like pop as you can see here
. Before we begin I feel I have to let you know my teeth are not rotting, and I do not have a coke addiction, okay clear? So here's what you came for
Act 1 - The Really Big Bottle!
This is the Coca Cola store in Las Vegas Nevada, and when we went in for a drink, we were pleased to read the trivia on our drink tray. This is what we found.
Act 2 - Measurements
The trivia tray also had some vital information for our cause, here it is. I was trying to figure out the best way to edit these images. I would like to here some critique of my design, to try to find out what looks best, but this is my attempt.
The way I saw solving this was to map some function to the coke bottle, and use our lovely calculus to find the volume by rotating, so I developed a bare bones Geogebra app with sliders and the picture to find a sinusoidal function that would work (an assumption I made, too much for students?). I wonder if this should be an Act 2 artifact or if students should come up with this themselves.
Act 3 - Reveal
As I am sure you have seen these sorts of answer reveals on trivia trays, they have the answer flipped upside down, and once again, I am not sure of the best way to present this reveal. So here are my two copies of the reveal.
As I already stated I used rotation to find the volume, then I had to convert to ounces, and then divide by 8. With GGB I found these equations and these points.
And I allowed wolfram to do the rest
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In wolfram it converts it to "ounces" but the final answer is really number of 8 ounce coke bottles, and with a number greater than 6 million, I think I can say that we need to have a talk with the math coordinator at Coca Cola Las Vegas. (Assuming I used my math right, could you guys check that for me?)
I can think of only a few...
- Create a scale picture on GGB (using either a cylinder, or a sphere from the front, or a bottle) to show the true size of 8,000,000 ounces.
- If we could fill this coke bottle with 8,000,000 ounces, how full would the bottle be? Did the "math coordinator" account for coke bottles having air?
- How much would it cost to fill a coke bottle this large? How much would it cost a consumer to buy that much Coca-Cola?
And without further ado the complete package zip file
Well here it is! One of my best moments of stumbling onto curriculum. I would first and foremost like to thank Delano Pauw. He is the creator of all the media and the toppling artist; I just happened to find him on youtube. Check out his channel
. He really is amazing, and with a quick e-mail he gave me Raw footage, dimension shots, and estimates. All from way off in the Netherlands (this interweb thing is so cool!).Without Further Ado, here is the domino spiral (now featuring sound).
Act 1 - The Spiral
Based on twitter results the most natural question to ask is how long will it take for all the dominoes to fall? That is what this WCYDWT is based on.
Act 2 - Dimensions and Time Measurements
So here it is, I wanted to make students work for the dimensions a bit. Is this too mean? Anyway these work well!
I will give students a printed copy of the picture from which they can gather the dimensions. Then play the first lap of the spiral to have students get the rate of fall. If you want to make this whole process longer give them dominoes instead of the video and have them come up with the rate of fall from experimentation. If you are physics minded throw this in their face
I am pretty sure I don't understand a single thing in that pdf, but I haven't taken the time to go through it, but it could give some neat extensions.
Act 3 - The Reveal
Here it is, the moment we have all waited for!
Sequels and Extensions
This is the part that I find the hardest. Where can this lesson grow legs. Please give me a hand with making this more worthwhile, but here are some ideas that I have so far.
- How many dominoes of each colour?
- Graph the time of each revolution vs. its radius, find the slope (I don't actually know if this is worthwhile I haven't tried it).
- Switch the variables around and find some bigger domino topples, ask them how many dominoes were used.
They are kind of lame, but like I said I cannot think of any. Delano did speak about the calculations that he had to go through in creating this, maybe he can comment about that, and an extension could be that kids make their own (I am all about building these as a project).
One spot where I am a total n00b when it comes to inquiry and teaching is my question techniques. I want to learn good leading questions that prompt students just enough to get them over hurdles. If you guys could give me some in the comboxes that would be excellent! Here is my start.
- What are we trying to solve?
- What unit will it be in?
- What would make our final time longer or slower?
- How can we determine how fast the dominoes are falling?
Once again, no skills here so I need your help.Enjoy.
Listening to Dan's talk on iTunes has makes me really want to post this, because this is the one problem that actually caught my curiosity. I was driving home one day, noticing these nice dotted lines on the highway as I came home. I wondered what I could do with it, and so I made my carpool friend drive home one day...
Act 1 - Roadlines
I especially like this, because I feel like it is the "wizardry" of mathematics, something so innocent, could tell someone so much.
Act 2 - Measurements
Some other very vital information is what is the distance. Well if you are from the US of A (do americans actually say that?), you can use this great article
, just keep in mind my video is shot in Canada (so Km/h), or as my Blair Miller helped me find you can use this resource for British Columbia...
Or just pull out Google Earth and measure, that mother is pretty precise.
Act 3 - the Reveal
And there it is. I feel as if I may have cheated you guys out of the reveal, just doing the picture in picture. Would have been better show me pull in the camera onto the dashboard? What do you think?
Where I could see this going is A) develop the general case for m/s to Km/h. Or better yet lines/sec to km/h (MPH if you are a friend of Uncle Sam (do Americans ever say that? I need to get cultured)). For some reason I feel like this would be a sweet app, have students make it. I also thought of bringing in movies, car chases, to see how fast they are really going. This one
even mentions some of the speeds in the intense Bullitt
car chase.How else could I extend this? I don't know, but I think my grades should have fun with it...
For anyone that does not know how to properly pronounce this mini-activity's title please watch this...
This video is fantastic but absolutely useless as math education
(I think maybe you know better than I).
...and substitute "Coke" for spoon.
With that being said, I introduce you to this!
Act 1 - The Image
What questions do you have about this image? Post them on my twitter
. Then continue reading...
So this is my new lesson/starter activity. I plan on using this to get kids thinking about volume again, and my future goals for this lesson will be elaborated further down. Anyway this all started when I was thinking about the recent trend in twelve pack boxes for pop. They use to be 3x4 and now they are 6x2. My students had a lot of problems this year with Surface Area (mostly due to me), and I thought this would be a great way to introduce it by buying some, and asking the question, "Which box is better for the environment?" I liked the idea and, so I was stuck thinking about pop.
I went shopping with my dad last weekend (we were home for a family event) and there were these new "100 calories" Coca Cola Slim packs and I grabbed out my phone and snapped some picture (Dad looked at me funny he is not used to this side of me yet). Anyway I walked down the aisle, and found the new Pepsi slim cans! But they were a different shape, but same price! Boo ya! Math lesson here I come. Anyway I bought those as fast as I can, and this weekend I went to town. I'll present this once more in Mr. Meyer's three acts since I appreciate the narrative...
Act 1 - Any Questions?
A nice simple video, and Twitter has quickly shown (not from hundreds of people), that I was on track with my question. Students will ask questions about the video, and share them on the board. I am anticipating that students will either inquire about volume or surface area, both tracks I am willing to head down.
I am just having too much fun with these. If you want the answer to the previous one, just post in the comments, and I will upload it tonight.
I want to turn this one into an Any Q type question, but I feel like it is too Mathematical to start off with, and my send students away, let me know what you think.
I love Google Trends, and if you have any ideas of classroom incorporation I would love to hear it...
Bonus: For fun on Google Trends look up "Spark Notes," it almost makes me giddy!