Comments on: [Makeover] Shipping Routes

By: Kevin Hall

Kevin Hall — Sun, 11 May 2014 21:32:01 +0000

Here's a 2-post discussion of Shipping Routes in light of research on inquiry learning, with some commentary by Dan and replies by me. The first post is at this link.

By: Kim Haber

Kim Haber — Sun, 29 Sep 2013 16:40:15 +0000

Not sure the simulator is working. It was working for me the other day. Can you help?

By: Cynthia Nicolson

Cynthia Nicolson — Tue, 13 Aug 2013 17:45:57 +0000

As an island dweller who rides ferries all the time, I was intrigued with this makeover challenge and the ideas for helping students visualize this situation. A few of the earlier comments touched on the important idea that ferries need to spend time loading and unloading each time they berth, i.e. no instantaneous turnarounds. Previous discussions on this blog have helped me see the need to be clear about the varying levels of abstraction at which a problematic real world situation matches or does not match introduced examples and representations – and the dangers of jumping up the “ladder of abstraction” too quickly. To prompt a discussion and make these ideas more explicit in this case, I’m wondering if it would be useful to give a quick pendulum demo and then ask something along these lines – Is a swinging pendulum a good analogy for the ferry situation? Why or why not? Some students would probably focus on similarities and differences in the concrete physical situations while others would (we hope!) recognize and share their thoughts about the common characteristic of periodicity that makes the math applicable here.

By: Jim Hays

Jim Hays — Tue, 13 Aug 2013 17:01:53 +0000

While the constraint built into the simulator that the times must be multiples of .1 is practical, it is misleading as far as the extension: “Could you create two boat times so that the boats would never return to shore at the same time? Prove it.”

Take for example, a boat that takes pi minutes and a boat that takes 1 minute. The pi minute boat will never return at an integer interval.

I realize this is getting beyond the Middle School expectations surrounding irrationals, but perhaps worth noting.

By: Monica C

Monica C — Tue, 13 Aug 2013 16:23:38 +0000

(Elementary school perspective) Love the video simulation and the additional depth to the problem provided by your question: “Could you create two boat times so that the boats would never return to shore at the same time? Prove it.” I’d also provide “first departure”/”last arrival” times so the kids wouldn’t try to take the “never” into infinity.

By: l hodge

l hodge — Tue, 13 Aug 2013 02:27:27 +0000

Same idea, but with a car crash simulator:

http://www.geogebratube.org/student/m46112?mobile=true

I like your question that asks students if they can pick times so the boats never return at the same time. I think you can push a lot on having the students find time intervals that produce a requested result (asking the original question backwards basically):

1) Can you set the time intervals so that the boats arrive simultaneously every 42 seconds? Can you do it with the time interval for one boat less than 10 and the other between 10 & 20? If so, can you find a second way to make it happen? A third? Is there a largest time interval you can use for a boat and still make this happen? Is there a smallest? Etc. etc.

2) Is it possible to set the time intervals so that every 3rd boat on the left arrives simultaneously and every 5th boat on the right arrives simultaneously (yes).

The boat and the car crash simulator clarify the task and provide a means for experimenting. But, they really do not provide intuition for the answer or the role of the least common multiple. Anyone got an idea on how to do a better job of that?

@wwndtd, that pendulum video is terrific.

By: wwndtd

wwndtd — Mon, 12 Aug 2013 17:33:38 +0000

Does it matter which shore they go to? What about the other one?

Similar patterns:
— Turn-signals of cars waiting for the stop light
— “Beats” when turning musical instruments (and waves in general)
— Pendula (this is a current favorite: http://www.youtube.com/watch?v=yVkdfJ9PkRQ)

Maybe take several different examples and find a general way of determining the “match point” instead of a single instance.

By: Jan Fabry

Jan Fabry — Mon, 12 Aug 2013 17:20:59 +0000

The link to the shipping route simulator misses the initial http://, sending you back to the front page of your blog.

By: Chris

Chris — Mon, 12 Aug 2013 17:12:00 +0000

Don’t really like the original question. The makeover only slightly better. Sorry, the question ‘when return at same time’ doesn’t do it for me, dare I say it even has s.t. pseudocontextual (which, as you pointed out earlier, doesn’t mean the context can’t be imaginary, after all ‘realistic’ doesn’t come from ‘realistic’ but ‘to realize’). Compared to some great 3act movie the animation here, in my opinion, is less convincing, as well as the simulator.

Wrt the topic. How about connecting the topic to LCM and gcd? Or jumping kids on a trampoline :-)