I have been rolling the same math problem around in my head for the last two months. Here is a link and a PDF.

“Obsessed” wouldn’t be too sharp a description. Not with the math, which isn’t more advanced than high school trigonometry. Rather with the problem itself, and the opportunities it offers students to think mathematically.

In its current form, those opportunities are limited. In its current form, the problem asks students to read given information (and a lot of it), recall a formula, and calculate the result. That’s important mathematical thinking but hardly the most important kind of mathematical thinking (a statement of opinion) and not the *only* kind of mathematical thinking the context offers us (a statement of fact). There are *more* mathematical opportunities, and more *interesting* ones, than the problem offers in its current form.

So change that! How would you makeover this problem and help students experience all those interesting opportunities to learn mathematics?

On Monday, I’ll offer my own thoughts, along with a collaboration with Chris Lusto.

## 12 Comments

## Dawn Burgess

January 14, 2016 - 3:47 am -I have also been rolling this same problem in my head, but I didn’t know about the Vancouver version. I teach on an island in Maine, where the tide swings are larger, and these kinds of contraptions are everywhere. I’ve thought about making a three-act type problem, but can’t wrap my head around the best application. I was thinking of doing it for more advanced trig in precalculus: Here’s the ramp, here’s the dock, and for what portion of the day will the ramp be usable? For walking up and down? For hauling a hand-truck? For a wheel-chair? How could you change it to make it usable for more of the day? How might the harbormaster foil your plans? This is a great problem for my context, because many of my less mathy students know more about harbor restrictions and practical “dockery” than I do.

## Justin Brennan

January 14, 2016 - 7:41 am -Practical “dockery”… Is there any other kind?

After spending 8 years as an engineer prior to teaching, I always felt that I’d include all kinds of stuff from my engineering life into teaching. However, now that I am slightly wiser and more humbled, that stuff is too specialized, only interesting to me and maybe 2 other kids on a good day.

Universal understanding of the nature of a problem allows for so much more learning opportunities, especially on the downstream end like checking appropriateness of work.

## Shauna Sheridan

January 14, 2016 - 6:08 pm -This doesn’t correspond great to the problem above, but reminds me of great “3 act” type problem I use in my classroom. We walk down to the section in our school that has a great wide ramp. I show them the car that accelerates down the ramp, then I show them the car that has a constant velocity going sideways across the ramp. What do they hopefully wonder? When they are going to crash. I run them separately as many times as they need, and then they have to find when and where they collide. Of course we run the cars at the end of the class as see just when and where they collide. Great fun!

## Jonathan Newman

January 14, 2016 - 10:28 pm -Made a quick Desmos Activity, complete with lots of open-ended questions, a ramp of adjustable length, and a tide that you can move in and out.

https://teacher.desmos.com/activitybuilder/custom/56987bde42ea0aaf382ff727

Help me improve it!

## Karim

January 15, 2016 - 1:57 pm -Put a mother on the ramp with a baby in her arms.

Steel costs $100/foot.

Submit your bid.

## Dan Meyer

January 15, 2016 - 5:27 pm -Jonathan, strong activity building! Sadly, I think your activity needs a number of elements that our activity builder can’t (yet) provide. Like numeric labels on the graph, for one. Not on you, in other words. This has been helpful feedback in its own way.Karim, can you rework that into a makeover haiku?Justin:Helpful perspective here. What’s interesting to me is that the same application from the world of work (say, this marine ramp) can be imported by math classes in 100 different ways, some more interesting and successful than others. I don’t think the format chosen by BCIT â€“ a page-long word problem, essentially â€“ sets students up for interest or success. What other formats exist?

## Chester Draws

January 16, 2016 - 2:39 pm -Put a mother on the ramp with a baby in her arms.Steel costs $100/foot.

Submit your bid.

An open-ended question like that is how we would normally assess a trigonometric topic in New Zealand.

The top kids would have to cost the ramp too, which is composed of its own little trig problems. Steel is $10 a metre, and you need to order the right amount to make the ramp.

The problem is that it is a total pain to mark. Every question has to be scanned thoroughly for correctness at every point, because there is no “correct” answer. So setting your problem for my class would take them maybe 20 minutes, and my whole evening marking it. (No, they can’t check their neighbour’s — if nothing else they are very poor judges of what “sufficient” working is, and they will reinforce each other’s desire to do as little working as possible.)

That means the problem is good, and I can imagine using some version of it when I teach trig this year, but it can’t be a question I give every day.

If Desmos or the like can check all the parts on the way, then it becomes possible.

## Karim

January 17, 2016 - 9:49 am -“Marina Sabina”

Steel tri rolls the tide.

CampeÃ³n of ramp we’re on:

Cheap, no fumbled babe.

## l hodge

January 17, 2016 - 2:33 pm -Perhaps the main assignment could be to animate the situation in Desmos.

The static situation could be modeled easily enough with three lines and domain restrictions. Next, using a slider for tide level, model the situation dynamically. Finally, adjust the model to fit some constraints as mentioned in the original questions. Perhaps even develop a model with additional slider(s) for dock length, max angle, etc.

Of course, this has turned a homework problem into an activity, so not really a makeover.

## Dan Meyer

January 17, 2016 - 3:56 pm -l hodge:Please see Jonathan Newman’s Desmos animation above.

I wouldn’t disqualify that as a makeover, personally.