## Exploring Dan Meyer’s Boat Dock with PearDeck

In PreCalculus, I tend to be application heavy whenever possible. This unit, which has focused on analytic trigonometry, has been pretty high on the abstraction ladder. I try to emphasize right triangle trigonometry in nearly everything we do so that students have a way in, but that’s still pretty abstract. I decided it was time to do something more on the application side.

Enter Dan Meyer’s Boat Dock, a makeover concept he put together a year ago on his blog.

I decided to put some of it into Pear Deck to allow for efficient collection of student responses. The start of my activity was the same as what Dan suggested in his blog post:

After collecting the data, I asked students to clarify what they meant by ‘best’ and ‘worst’. Student comments were focused on safety, cost, and limiting the movement of the ramp.

I shared that the maximum safe angle for the ramp was 18˚, and then called upon PearDeck to use one of its best features to see what the class was thinking visually. I asked students to draw the best ramp.

After having them draw it, I had them calculate the length of the best ramp. This is where some of the best conflict arose. Not everyone responded, for a number of reasons, but the spread was pretty awesome in terms of stoking conversation. Check it out:

The source of some of the conflict was this commonly drawn triangle, which prompted lots of productive discussion.

When students built their safest ramp using the Boat Dock simulator, it prompted the modelling cycle to return to the start, which is always great to have the ability to do.

I then asked students to create a tool using a spreadsheet, program, or algorithm by hand for finding the safest ramp of least cost for every random length of the ramp in the simulator. This open-ended request led to a lot of students nodding their heads about concepts learned in their programming classes being applied in a new context. It also lead to a lot of confusion, but productive confusion.

This was a lot of fun – I need to do this more often. I say that a lot about things like this though, so I also hope I follow my own advice.

## Holiday Travel and Exporting PearDeck Data to Desmos

One of the unique phenomena of international schools is the reality that, during a vacation, the school population disperses to locations across the world. I had students do an end of semester reflection through PearDeck, and one of the slides asked students to drag a dot to where they were going to spend the vacation.

PearDeck allowed me to see the individual classes and share these with the students one at a time. I wanted to create a composite of all of the classes together in Desmos to share upon our return to classes, which happens tomorrow. You can find the result of this effort below. This is the combined data for draggable slides from five different sessions of the same deck.

The process of creating this image was a bit of work to figure out, but in the end wasn’t too hard to pull off. Here’s how I did it.

The export function of a completed PearDeck session, among other things, gives the coordinates of each student’s dragged dot in a Draggable slide. I could not use these coordinates as is, as graphing them on top of the map image in Desmos did not actually yield the correct locations. I guessed that these coordinates represented a percentage of the width of the image used for the Draggable background since the images people upload are likely all of different sizes. I did a brief search in the documentation, and couldn’t find official confirmation, but I’m fairly sure this is the case. An additional complication for using these is that the origin is at the upper left hand corner, which is typical for programming pixel art, but not correct for use with a Cartesian system as in Desmos.

This means that an exported data point located at 40, 70 is at 40% of the width of the image, and 70% of the height of the image, measured from the top left corner.

Luckily, Desmos makes it pretty easy to apply a transformation to the data to make it graph correctly. I took all of the data from the PearDeck export, pasted it into a spreadsheet class by class, and then pasted the aggregate data into a Desmos table. Desmos appears to have a 50 point limitation for pasting data this way, which is why the Desmos link below has two separate tables.