For dramatic effect, I feel you MUST stop the video when the man kneels and reaches for the first one.
I am MUCH MUCH MUCH more interested in whether it’s gonna work than I am in the question you want me to ask, which must be How big is the fourteenth domino?
First, I don’t know what math students could do to resolve the question, “Will the dominoes topple?” Maybe it’s more perplexing than whatever comes next for them, but to warrant airtime in my class or on my blog, it needs to be perplexing and mathematical. That’s why I cut the video where I did.
Second, I don’t “want” you to ask a question. I want to present you a scenario that’s rich in questions and see if mathematical tools can offer you some answers. It’ll pay off massively negative dividends to pretend a problem space is open when it really isn’t, to ask a student for their questions when you’re only interested in your own.
The first question I thought of was also whether or not it would work… As a physics teacher, that could definitely warrant airtime in my class – perplexing and physical. Great video! Thanks for sharing.
Man, I didn’t think much of this one when I first saw it, but now it’s blowing my mind. Only (spoiler alert) 29 (or less) steps from a block so small you need a tweezer to hold it to the Empire State Building is so amazing I had to verify it myself.
This is quite an intriguing problem. And when you start thinking about what a little amount of force is required on the first block, it becomes quite astounding. My physics is rusty so I haven’t figured out the PE and KE conversion going on, but it looks interesting. I suppose this is nitpicky…. He states that the first domino is about 5mm high and about 1 mm thick, then he states the largest is over 1 m high. If my math is correct, if the 1st one is exactly 5mm, then the largest would be about .973 m. I suppose I can live with that, but the thick should be 194.6 mm or 7.7 inches, and the thickness look more like about 3 to 4 inches. But I could be all wet on this. I am fine with experimental data having error(or variance) but I feel much better when something as simple as measurements are more accurately stated.
Though the link to the skyscraper seems a bit forced somehow.
Wondering if there is a way of shooting it to make that link more natural? Finish with a picture of a skyscraper perhaps?
In your third act/extension:
I’m stuck by how you work out the how long you need to construct the 29 dominoes. Do we not need one of the measurements of how far they are spaced?
Three more questions that occurred to me whilst watching Act 1:
1. Does the time for the last block to touch the ground follow any pattern. How long would block 29 (the skyscraper) take to hit
2. The sound when each block is hit, appears to change in pitch. Does this follow a pattern?
What would the sound be when block 28 hit block 29.
I’m am reminded of the story of Pythagoras discovering harmonies. Supposedly by listening to a blacksmith strike tongs.
3. It also got some good link to similarity of the dominoes as well. Thinking in terms of volume of the blocks, cost of the material etc.
There are 13 total dominos, so the largest should be 1.5^12 * 5mm not 1.5^13. This only makes the largest .65 m.
This issue is that if you start with a ratio of 5:1, height: thickness, the final domino will still have that ratio. Looking at the video, it is definitely many more than 5 times as tall as thick.
The guy says it is “more than a meter tall”. Looking at it, I think that the final domino is about 1.15 m tall, and 17 cm thick.
He says “about 5mm high and 1mm thick”. If you use 5mm and just change 1.5 to 1.57 then the final domino is about 1.12m. (Another teachable moment: very small difference in base of exponential function can lead to a very long change down the road.) Using that ratio and a final thickness of 17 cm would mean a starting thickness of about .76 mm.
It would be nice if the ratio is exactly 1.5, but I don’t know that it is based upon the video.
This is a brilliant “first act,” my favorite of the 3. I love the way the director focuses in on the actor on his knees using tweezers to manipulate the first domino – then shows that he can barely lift the 13th. Care was taken to amplify the visuals and sound was good.
I immediately though about sky scrapers ….. I think high-school students would too, and their questions would lead to an awesome second act. Wow……
First, I don’t know what math students could do to resolve the question, “Will the dominoes topple?”
Me either. I’d better sign up for Brittany’s physics class, I suppose.
Dan
Second, I don’t “want” you to ask a question. I want to present you a scenario that’s rich in questions and see if mathematical tools can offer you some answers.
But you want me (as a student) to ask questions of a particular type. You don’t “want” me to ask whether the dominoes will fall, so you show me the answer to that. And by the way, I’m totally cool with that; I think it’s part of the teacher’s responsibility.
Dan
It’ll pay off massively negative dividends to pretend a problem space is open when it really isn’t, to ask a student for their questions when you’re only interested in your own.
Agreed.
But don’t you spend quite a bit of time and burn quite a few calories shaping classroom media in such a way that particular questions have high probabilities of popping up in classrooms? Again, I’m cool with that, but I’m not sure I’d describe Dan Meyer problem spaces as being particularly “open”. Nor do I think they pretend to be; they are fabulous at opening students’ eyes to the mathematics they may not have previously noticed in their worlds.
Oh…and I gotta admit my mind didn’t go to skyscrapers at all. How big is the fourteenth domino? was mine, and maybe, How many such dominoes can fit in this hallway?
But let’s assume my mind does go to skyscrapers…I’m pretty unsatisfied by the reveal in Act Three. The man tells me. But as other readers have noted above, the man’s domino scale factors are not perfectly reliable. I guess I don’t have a problem with an unreliable narrator. Should I?
I don’t ask students for their questions if those questions don’t interest me or if I’m unprepared to take them somewhere. Or if I don’t think the problem space lends itself to more than one question. I’d say I’m happy to take the pyramid of pennies, the water tank, and the ticket roll (to name three) anywhere the class wants to take them. Otherwise, I just ask the question I’d like them to consider.
So the fact that neither you nor a student would naturally wonder the question, “How many dominoes would you need to knock over a skyscraper?” isn’t material to me. (I wouldn’t wonder it naturally either but once it was posed, I found it engrossing. Which is unusual, for me.) In the lesson plan, I don’t invite the teacher to ask her students for their questions. I invite her to just ask the question.
There’s a larger issue here about the extent to which every video or photo is a manipulation by virtue of the videographer or photographer having selected an angle for the lens and a location for the tripod, but I find it all kind of dizzying at the moment.
Thanks for the clarification Dan.
So in some cases the teacher is allowed to direct the students to a particular problem.
I was not understanding that before, thinking you wanted the students to ‘intuit’ that link (to skyscrapers) themselves.
Silly me!
I have to agree the skyscraper question *once posed* was intriguing.
I used this in class with two of my Algebra 2 classes today. The kids liked it and were intrigued by the problem overall!
Some things that could be improved for the skyscraper question itself:
There are issues with the measurements and/or the 1.5 ratio as previously stated going from the 1st domino to the 13th or 14th one it doesn’t make it tall enough. A good thing about this is that it led to some interesting discussions about where the error could come in. It also forced my students to conceptualize a little more about how big 5 mm and 1 m are.
It would be better if you could see all of the dominoes more clearly. We were trying to count if there were actually 13 and it was too hard to tell.
The reveal was a little disappointing. Not that you should actually make a domino the size a skyscraper, but something more than just telling us.
The other thing that the kids were really curious about was where the 1.5 came from. They also wanted to know if it made any difference where the domino hit the next domino. I would like to come back to this problem when we do sequences and series as I think it would fairly interesting for them.
[...] in the problem of modeling domino chains (see, for example, the video on the dy/dan blog [3ACTS] Domino Skyscraper). This problem is harder than the ones in the book, as it requires careful thinking about how [...]
Quick question about the images of the skyscrapers. The website says that it is copyrighted material. Is it alright to use in a classroom? To project or to make copies for kids? Should permission be asked? I am assuming that is for commercial use, and we know education is far from being a commercial enterprise, save for those online gizmos and degrees you can buy.
I’m not a lawyer, but if it were me I’d do it. I tend to ask forgiveness later rather than permission now, though. I won’t be surprised if that lesson gets a takedown notice.
Hi – thanks so much for the resources on this, it is really interesting and I’m looking forward to using it, but I would appreciate some help on the question of the dimensions … by my reckoning for the 13th domino to be over a metre tall the first one would have to be bigger than 7.7mm high. That’s going to make quite a large difference as students work out the dimensions of the other dominos – did you ask the skyscraper question assuming the first domino was 5mm high or after asking students to work out what the actual height must have been?? Many thanks!!
This lesson worked pretty well as an introduction to exponential growth and functions. It even got some of the more reserved students excited, which was cool. Thanks for the video!
Looking at the video some more and doing some calculations, I would bet that the original domino has dimensions of 10 mm high by 5 mm wide by 1 mm thick. Using those numbers (and a ratio of 1.5), the 13th domino ends up being 4’3″ tall, 2’1.5″ wide and 5″ thick which seems quite reasonable with what is shown in the video. My guess is that maybe he just misspoke and the width was actually the 5 mm dimension. Anyway, I have already mentioned how the height to thickness ratio cannot be 5:1.
Anyway, if you want to end up with dominos that look like the ones in the video, I would use the starting dimensions of 10 mm high by 5 mm wide by 1 mm thick.
For dramatic effect, I feel you MUST stop the video when the man kneels and reaches for the first one.
I am MUCH MUCH MUCH more interested in whether it’s gonna work than I am in the question you want me to ask, which must be How big is the fourteenth domino?
Two things.
First, I don’t know what math students could do to resolve the question, “Will the dominoes topple?” Maybe it’s more perplexing than whatever comes next for them, but to warrant airtime in my class or on my blog, it needs to be perplexing and mathematical. That’s why I cut the video where I did.
Second, I don’t “want” you to ask a question. I want to present you a scenario that’s rich in questions and see if mathematical tools can offer you some answers. It’ll pay off massively negative dividends to pretend a problem space is open when it really isn’t, to ask a student for their questions when you’re only interested in your own.
Cool. Never saw that before. So many interesting things in the world. Enjoying your posts so far. Thanks. Great video with the coffee btw.
The first question I thought of was also whether or not it would work… As a physics teacher, that could definitely warrant airtime in my class – perplexing and physical. Great video! Thanks for sharing.
Man, I didn’t think much of this one when I first saw it, but now it’s blowing my mind. Only (spoiler alert) 29 (or less) steps from a block so small you need a tweezer to hold it to the Empire State Building is so amazing I had to verify it myself.
This is quite an intriguing problem. And when you start thinking about what a little amount of force is required on the first block, it becomes quite astounding. My physics is rusty so I haven’t figured out the PE and KE conversion going on, but it looks interesting. I suppose this is nitpicky…. He states that the first domino is about 5mm high and about 1 mm thick, then he states the largest is over 1 m high. If my math is correct, if the 1st one is exactly 5mm, then the largest would be about .973 m. I suppose I can live with that, but the thick should be 194.6 mm or 7.7 inches, and the thickness look more like about 3 to 4 inches. But I could be all wet on this. I am fine with experimental data having error(or variance) but I feel much better when something as simple as measurements are more accurately stated.
* A spoiler in my comment*
Nice problem.
Here are my thoughts:
Though the link to the skyscraper seems a bit forced somehow.
Wondering if there is a way of shooting it to make that link more natural? Finish with a picture of a skyscraper perhaps?
In your third act/extension:
I’m stuck by how you work out the how long you need to construct the 29 dominoes. Do we not need one of the measurements of how far they are spaced?
Three more questions that occurred to me whilst watching Act 1:
1. Does the time for the last block to touch the ground follow any pattern. How long would block 29 (the skyscraper) take to hit
2. The sound when each block is hit, appears to change in pitch. Does this follow a pattern?
What would the sound be when block 28 hit block 29.
I’m am reminded of the story of Pythagoras discovering harmonies. Supposedly by listening to a blacksmith strike tongs.
3. It also got some good link to similarity of the dominoes as well. Thinking in terms of volume of the blocks, cost of the material etc.
*End of spoiler alert*
@Randy
There are 13 total dominos, so the largest should be 1.5^12 * 5mm not 1.5^13. This only makes the largest .65 m.
This issue is that if you start with a ratio of 5:1, height: thickness, the final domino will still have that ratio. Looking at the video, it is definitely many more than 5 times as tall as thick.
The guy says it is “more than a meter tall”. Looking at it, I think that the final domino is about 1.15 m tall, and 17 cm thick.
He says “about 5mm high and 1mm thick”. If you use 5mm and just change 1.5 to 1.57 then the final domino is about 1.12m. (Another teachable moment: very small difference in base of exponential function can lead to a very long change down the road.) Using that ratio and a final thickness of 17 cm would mean a starting thickness of about .76 mm.
It would be nice if the ratio is exactly 1.5, but I don’t know that it is based upon the video.
This is a brilliant “first act,” my favorite of the 3. I love the way the director focuses in on the actor on his knees using tweezers to manipulate the first domino – then shows that he can barely lift the 13th. Care was taken to amplify the visuals and sound was good.
I immediately though about sky scrapers ….. I think high-school students would too, and their questions would lead to an awesome second act. Wow……
Chad:
Here’s the article that inspired the experiment, if it helps.
Dan:
Me either. I’d better sign up for Brittany’s physics class, I suppose.
Dan
But you want me (as a student) to ask questions of a particular type. You don’t “want” me to ask whether the dominoes will fall, so you show me the answer to that. And by the way, I’m totally cool with that; I think it’s part of the teacher’s responsibility.
Dan
Agreed.
But don’t you spend quite a bit of time and burn quite a few calories shaping classroom media in such a way that particular questions have high probabilities of popping up in classrooms? Again, I’m cool with that, but I’m not sure I’d describe Dan Meyer problem spaces as being particularly “open”. Nor do I think they pretend to be; they are fabulous at opening students’ eyes to the mathematics they may not have previously noticed in their worlds.
Oh…and I gotta admit my mind didn’t go to skyscrapers at all. How big is the fourteenth domino? was mine, and maybe, How many such dominoes can fit in this hallway?
But let’s assume my mind does go to skyscrapers…I’m pretty unsatisfied by the reveal in Act Three. The man tells me. But as other readers have noted above, the man’s domino scale factors are not perfectly reliable. I guess I don’t have a problem with an unreliable narrator. Should I?
I don’t ask students for their questions if those questions don’t interest me or if I’m unprepared to take them somewhere. Or if I don’t think the problem space lends itself to more than one question. I’d say I’m happy to take the pyramid of pennies, the water tank, and the ticket roll (to name three) anywhere the class wants to take them. Otherwise, I just ask the question I’d like them to consider.
So the fact that neither you nor a student would naturally wonder the question, “How many dominoes would you need to knock over a skyscraper?” isn’t material to me. (I wouldn’t wonder it naturally either but once it was posed, I found it engrossing. Which is unusual, for me.) In the lesson plan, I don’t invite the teacher to ask her students for their questions. I invite her to just ask the question.
There’s a larger issue here about the extent to which every video or photo is a manipulation by virtue of the videographer or photographer having selected an angle for the lens and a location for the tripod, but I find it all kind of dizzying at the moment.
Thanks for the clarification Dan.
So in some cases the teacher is allowed to direct the students to a particular problem.
I was not understanding that before, thinking you wanted the students to ‘intuit’ that link (to skyscrapers) themselves.
Silly me!
I have to agree the skyscraper question *once posed* was intriguing.
I used this in class with two of my Algebra 2 classes today. The kids liked it and were intrigued by the problem overall!
Some things that could be improved for the skyscraper question itself:
There are issues with the measurements and/or the 1.5 ratio as previously stated going from the 1st domino to the 13th or 14th one it doesn’t make it tall enough. A good thing about this is that it led to some interesting discussions about where the error could come in. It also forced my students to conceptualize a little more about how big 5 mm and 1 m are.
It would be better if you could see all of the dominoes more clearly. We were trying to count if there were actually 13 and it was too hard to tell.
The reveal was a little disappointing. Not that you should actually make a domino the size a skyscraper, but something more than just telling us.
The other thing that the kids were really curious about was where the 1.5 came from. They also wanted to know if it made any difference where the domino hit the next domino. I would like to come back to this problem when we do sequences and series as I think it would fairly interesting for them.
Thanks for another interesting problem!
[...] in the problem of modeling domino chains (see, for example, the video on the dy/dan blog [3ACTS] Domino Skyscraper). This problem is harder than the ones in the book, as it requires careful thinking about how [...]
Quick question about the images of the skyscrapers. The website says that it is copyrighted material. Is it alright to use in a classroom? To project or to make copies for kids? Should permission be asked? I am assuming that is for commercial use, and we know education is far from being a commercial enterprise, save for those online gizmos and degrees you can buy.
I’m not a lawyer, but if it were me I’d do it. I tend to ask forgiveness later rather than permission now, though. I won’t be surprised if that lesson gets a takedown notice.
Hi – thanks so much for the resources on this, it is really interesting and I’m looking forward to using it, but I would appreciate some help on the question of the dimensions … by my reckoning for the 13th domino to be over a metre tall the first one would have to be bigger than 7.7mm high. That’s going to make quite a large difference as students work out the dimensions of the other dominos – did you ask the skyscraper question assuming the first domino was 5mm high or after asking students to work out what the actual height must have been?? Many thanks!!
This lesson worked pretty well as an introduction to exponential growth and functions. It even got some of the more reserved students excited, which was cool. Thanks for the video!
Looking at the video some more and doing some calculations, I would bet that the original domino has dimensions of 10 mm high by 5 mm wide by 1 mm thick. Using those numbers (and a ratio of 1.5), the 13th domino ends up being 4’3″ tall, 2’1.5″ wide and 5″ thick which seems quite reasonable with what is shown in the video. My guess is that maybe he just misspoke and the width was actually the 5 mm dimension. Anyway, I have already mentioned how the height to thickness ratio cannot be 5:1.
Anyway, if you want to end up with dominos that look like the ones in the video, I would use the starting dimensions of 10 mm high by 5 mm wide by 1 mm thick.