Comments on: [PS] The Piano Lid

By: Context: The Mathematical Cerberus | Irrational Cube

Context: The Mathematical Cerberus | Irrational Cube — Sat, 06 Nov 2010 18:30:19 +0000

[…] and irrelevant pieces of information.Â These problems scream who cares?!?Â For example, the piano lid problem asks students to find the angle at which the lid of a grand piano is propped up.Â Â This might be […]

By: Ed Geometry

Ed Geometry — Mon, 25 Oct 2010 15:53:39 +0000

I just wanted to pick a bone with Tim (not really, as I think he makes some great points):

“I skipped a problem this lesson that has our hypothetical hero carefully pacing around an entire lake to form a triangle and doing some calculating to determine how long their swim will be. Really? How ’bout Google Maps?”

I actually think indirect measurement problems like this provide real context for right triangle problems ( I realize the piano problem deals with angles, but Tom mentioned a problem computing sides). Indirect measurement is more of a useful and motivating example than most pseudocontext in text problems. Google Maps or not, I think it’s reasonable to think of indirect measurement as motivating context. Heck, if we’re taking into account all the tools/ tech that COULD make math easier, I’d never get off the couch…

By: Steve Phelps

Steve Phelps — Mon, 25 Oct 2010 00:36:22 +0000

There is probably more Geometry in the window and in the stuff seen through the window!

By: Randy

Randy — Sun, 24 Oct 2010 23:59:05 +0000

If this is like the grand pianos I know. The hinge is at the edge. The ray that “makes angle x actually is perpendicular to the two rays making angle y and in line with the hinge. It does not exist in the same plane.

By: Wing

Wing — Sun, 24 Oct 2010 15:49:19 +0000

This discussion here made me realize another frustration I have with problems like this: they essentially state something as a fact (“the longest prop stick makes the angles as shown”) without actually backing it up. What could be an interesting research/exploratory project (more so for middle schoolers) is then reduced to a dead end subtraction problem.

To ponder a little on one of Kate’s questions: I think the general question of whether you need a stick to be perpendicular to a slanted, heavy, hinged surface like this to prop it up is actually a great question to think about and explore and is pretty relevant (like in car hoods, for example).

Also: this post is now number 2 on a Google search for piano prop sticks.

By: Dan Meyer

Dan Meyer — Sun, 24 Oct 2010 15:21:10 +0000

This is my favorite part of these pseudocontext posts, where we try to rehab the pseudo out of the pseudocontext. I’d like to point out (in agreement with several of you) that the person who is most concerned about angles here is the guy making the stick. There are several really good questions to ask there, but unfortunately, I don’t think any of them lead to subtracting 57Â° from 90Â°. Those questions all involve the length of the stick and, consequently, some trigonometry. Which makes me wonder if this problem is beyond rehabilitation.

By: Sue

Sue — Sun, 24 Oct 2010 12:38:10 +0000

I have just recently started reading your blog! I tutor math, and I’ve started removing the psuedocontext for my students struggling with decoding questions. I have found that once they think about, “What do I need to know to figure out the question”, the students immediately know what information to extract from the question! I know it’s not exactly the goal of removing pseudocontext you have, but I have found it’s helpful!

By: Marcie

Marcie — Sun, 24 Oct 2010 12:14:38 +0000

Sound behaves much like light. The angle of reflection of the sound will be congruent about the normal. This could launch into a whole wonderful discussion about acoustics using angles.

By: Michael

Michael — Sun, 24 Oct 2010 05:28:31 +0000

Does the angle of the lid have anything to do with the resonance of the sound? If so, what angle would provide the best resonance? This seems to be a better problem, perhaps worthy of WCYDWT. However, would this be a practical problem for the classroom? I don’t know.

Better yet, why do I care about the angle so much as how long does the prop stick have to be?

I found a good pseudo context the other day that I have to share. I’ll share it as soon as I get it scanned.

By: Tim

Tim — Sun, 24 Oct 2010 00:41:56 +0000

Heh. I teach with this textbook and just finished this chapter. Overall opinion: the explanations of the actual concepts are good; the problems and proofs that test the concepts are good; the “real-world connection” problems are horrendously contrived. I skipped a problem this lesson that has our hypothetical hero carefully pacing around an entire lake to form a triangle and doing some calculating to determine how long their swim will be. Really? How ’bout Google Maps?

Fortunately, I don’t care much. I’ve approached this course as having two meaningful objectives for my students: preparing them for future classes and the SAT, and using geometry as a platform to discuss logic and proof versus intuition. The ideas of postulates versus theorems are great, with ties to so many things, even religion. The “real world” problems might have some fun thinking, but I don’t need them to fake relevance.