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.

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!

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.

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?

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.