Domino Spiral

10/17/2011

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).

Guiding Questions

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.

4 Comments

Dan Anderson link

10/18/2011 09:05:32 pm

Ok, I figured out the math. It took some work, and unless there is an easier path, the math might be limiting for most students. To solve it, I "assumed" that it wasn't a spiral, that it was a set of circles. I solved it by counting the number of dominos in a couple of rows (first through sixth, and then the last), and doing a quadratic regression on them. This quadratic regression told me the number of dominos in circle. Then using a spreadsheet (attached at the bottom), I found the total # of dominos, and then found the time. The final calculation was 40.8 seconds.

The reason this might be tough for most students are the assumptions that I made of it being a quadratic (although the linear regression isn't bad either). And I neglected the spiral design, and went with a set of circles.

How did you solve it?

Spreadsheet: http://bit.ly/qG101b

Timon Piccini link

10/18/2011 09:53:49 pm

I took a much more naive approach. I saw this as Dan's ticket problem but with a rate of fall. I used the domino dimensions to find the area and calculate number of dominoes (a la these guys http://www.youtube.com/watch?v=Vp9zLbIE8zo). So for each domino the dimensions were (2.3cm+0.7cm)x(0.7cm+0.7cm).

Then I used the circumference to find the rate of fall (with each domino having a length of (0.7cm+0.7cm).

It did seem almost too straightforward, and I thought maybe I had some good ol' fashioned confirmation bias. Check my math out (it's not pretty to look at but here it is).

Here is page 1 http://tinyurl.com/698dywa

Here is page 2 http://tinyurl.com/64mdt8t

John Scammell link

10/18/2011 10:54:21 pm

I am going to play around with the math on this one later on today. I am certainly perplexed.

Thor-Erik Rødland link

5/6/2013 06:27:51 pm

A great task! My student had a lot of great questions and several ways to find a solution.

I did a very rough estimate:
The outher ring took 4.06s, which means the the middle ring should take 2.03s. I reacon this is the average time pr. lap. There are between 19 and 20 circles. 2.03 * 19,5 = 39,6s (pretty close!)

Aften spending nearly 30 minutes my students where actually a bit disappointed when they saw my "easy" solution.

Domino Spiral

Act 1 - The Spiral

Act 2 - Dimensions and Time Measurements

Act 3 - The Reveal

Sequels and Extensions

Guiding Questions

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