Marine Ramp, Part 1

I spent two months thinking about the same math problem. Not the math. But the problem. Now I'm free! https://t.co/jHUwVc1vub

— Dan Meyer (@ddmeyer) January 18, 2016

I didn’t realize I was playing tag. But apparently I was, and I got tagged.

I noticed Dan’s Preview Post right before a long weekend. I spent the weekend thinking on and off about the problem. As promised, Marine Ramp Makeover was published a few days later, just in time for our try-a-bigger-task day in our Right Triangles unit. So we tried it.

Our essential learning for the day:

Level 4: I can use trigonometric ratios to solve non-right triangles in applied problems.

Level 3: I can use trigonometric ratios to solve right triangles in applied problems. 

Level 2: I can use trigonometric ratios to solve right triangles.

Level 1: I can define trigonometric ratios.

We started with the image. What’s wrong with this scenario?

We watched the video, which ends with this image.

Which one is worst? Why?

Which one is best? Why?

[I happened to have recently read Suzanne’s post about #phonespockets, so I turned on the voice recording when our whole class conversation started. Which is one of the only reasons I know exactly how the conversation went, four weeks later.)

Students brought up the need for safety, which led to building codes and minimum standards.

So I told them the standard. The slope of the ramp can’t exceed 34%.

Students thought individually about what that means. We watched the video again. We saw a triangle that we hadn’t all noticed before.

What does it mean for the slope of the ramp to not exceed 34%?

I heard all sorts of things … the angle of the ramp is 34˚. 34% has something to do with 34/90, since the triangle is right, 34% has something to do with 180˚ or 360˚.

How would you get this conversation back on track?

(Or if you’re smart, maybe you follow Dan’s suggested questions, which skipped this part of the problem and gave the maximum ramp angle instead. I included it because I wanted students to have more opportunity to use trigonometric ratios to solve right triangles in applied problems.)

What is slope?

rise/run, rate of change.

I drew a right triangle and labeled the vertical and horizontal legs as 3 and 4. What is the slope of this ramp? What is the slope of this ramp as a %? Would you want to walk down this ramp?

How can you figure out the ramp angle?

What does it mean for the slope of the ramp not to exceed 34%?

So what is the ramp angle?

So the ramp angle has to be 18˚ or less. What other information do we need to know to figure out the length of the ramp? Talk with your team to decide what you want to know.

[#phonespockets note to self: I called on the same two students at least three times during this lesson. I was missing my seating chart clipboard where I usually keep up with whose talking better than that.]

They wanted to know

• Side lengths of the triangle. What side lengths?
• Both legs. Do you need both legs?
• We need the brown thing. Is that enough to figure out the ramp length? What does the brown thing represent?
• The rise. And there literally is some rise here, right? On the water.
• Oh! The rise changes with the tide.

So the distance between low and high tides is 5.0 m. What is the length of the ramp?

As students were working, I noticed one screen in particular. When I asked her why she revised her work, she had noticed that her previous answers weren’t reasonable for the length of the ramp. (Scoff all you want, but as far as I’m concerned context scores one for helping students checking the reasonableness of their results.)

Everyone didn’t pay attention to the reasonableness of their results, of course, as the poll results showed.

Does 55 work for the ramp length?

We went to the Boat Dock Generator to try it.

Maybe not such a good dock.

It’s not wrong. But it’s inconvenient.

Do you really even know it works past the part of the screen we can’t see?

How about 16?

We built it. They were satisfied.

So we generated a new situation.

And I sent a Poll.

And a few students answered before the bell rang.

To be continued, just like class …