Leaking Gasoline Puzzler

by Dan Posted on April 6, 2011

The Last Gasp of the Fiat

“A car travels at a steady speed of 45 mph. Its fuel consumption is 30
miles to the gallon. It has a 15-gallon gas tank, which was full when the car started off. But at the very moment the car begins to move at 45 mph, the gas tank begins to leak fuel.

“After 225 miles, the car stops because it’s got an empty gas tank. And so here’s the question — and you might think you don’t have enough information to answer this but I think you do — How many gallons per hour was the car leaking fuel?”

This is cartalk’s puzzler for this week (April 4th through April 8th, 2011). If you answer on their website, you could be chosen to win a prize!

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Khan Academy and SBG

by Dan Posted on March 30, 2011

@CmonMattTHINK put forth a comment on twitter a couple of mornings ago:

Salman Khan TED-talks about classroom inversion:
http://www.ted.com/talks/salman_khan_let_s_use_video_to_reinvent_education.html Very exciting, yes. But I must be the cranky old man and say..
SO much of this (and SBG) is about skill-mastery. If we let our students believe that math = skill-mastery, we’re doing them a disservice.

I think its an interesting point. And I agree that the Khan Academy is absolutely focused on skill-mastery.

Khan Academy

The Khan Academy videos take any and all “color” out of a subject. I think that is what Matt is getting at with his quote about doing math students a disservice. Take out anything interesting about presenting a subject… and you’ve got the Khan video. Relying on Khan videos for teaching math is relying on saltines and water for your survival. Sure it may work, but who would CHOOSE that path? Rarely are there discussions in Khan videos for the WHY of a subject. Even less so the HOW a subject is used in the real world is totally missing. Replacing a classroom with Khan videos would be a travesty, and I’m not sure that Bill Gates and Sal Khan see this.

That said, I haven’t yet written off Khan videos as a supplement to the classroom for students who get lost in the minutiae of math procedures. Its possible that they’ll dovetail with the classroom, for some students, some of the time.

Standards Based Grades

Almost as a throwaway, Matt throws SBG in with Khan videos as a math = skill-mastery problem. I’m really glad he did, because it made a bunch of things with SBG much more clear to me. For instance:

Stuff SBG is (to me):

  • A more accurate representation of where students’ knowledge is, and where it isn’t. After trying SBG out full time this year, I have a much better idea about specifically what they are having trouble with and what they have down cold. This is my viewpoint as a teacher. I am responsible for getting all of my students to “know geometry”. It is important for me to see the class as a whole, to see what topics need more time, and to see what topics can go quicker.
  • Responsibility for the learning is more clearly on the student. They now know where they stand in geometry much clearer than the did in the past. Before they knew if they were failing, passing, or doing very well. Now each student knows what topics they struggle on, and what topics they kick ass at. If this was it, SBG would be worth it. But the students buy cialis Taiwan also have the ability to “re-learn” and reassess topics. They can now fill in the gaps of their knowledge with no penalty. Some students will not take this responsibility, but I’ve seen many more students strive to fill their gaps in, because they now know where their gaps are. Funny thing.

Stuff SBG is not (to me):

  • A way to teach. In no way do I see SBG influencing how I teach geometry. I’m still giving the students geometer sketchpad investigations. I still give the students actual 3D objects to measure LA,SA, and V. I still utilize group work to allow students to observe and try different learning methods. And yes, I still use “old-school” notes for some topics. SBG did not change the how, it only changed the measuring stick.
  • The end all and be all of motivational techniques. No way. I still am failing to motivate all students to learn geometry. No excuses. I still have students failing to do what is necessary to pass the Regents exam. I still have students that choose not to work. I know that if there is no gas in the tank then the car can’t go, but I too haven’t helped pay the gas bill for some of my students. SBG did not greatly affect this problem.

In the end I’d like some feedback from all of you. How do you view the Khan academy or SBG? Also, much thanks to Matt who pushed me to think about this stuff in more depth.

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Toilet Paper Tubes and the Empire State Building #wcydwt

by Dan Posted on March 29, 2011

So I’m watching the idiot tube the other day and I saw a commercial by Scott Paper Company that claimed that if everyone in America used their tubeless toilet paper product, then we would save two Empire State buildings of toilet paper rolls every year.

Two Empire State buildings of toilet paper tubes? Ok, here we go.

Information provided:

That’s it. Asked the geometry students what information they needed. They drove everything after. It was amazing luck to be right in the middle of the 3D, volume unit.
They asked for the following:

  • Height of empire state building? (you want that in ft or meters? they went for meters, thanks science class.)
  • Width of the empire state building? (also asked what shape the base was, yes!)
  • Diameter of toilet paper tube? (in inches or cm? They went for cm, and I was nice enough to encourage them to convert to meters first)
  • Height of toilet paper tube? (likewise in cm)

The talked about which was best for approximating the volume of the empire state building, they threw out a rectangular prism, and went with a square based prism.

… Yada, yada, yada.

They measured the volume of the empire state building to be 1,007,000 m^3 (google says the volume is 1,048,000 m^3)
WOW! Close.

And they also confirmed that it would take just over 2 empire state buildings to hold all the toilet paper tubes! Neat, so Scott’s marketing did their homework.

Side note, I am lucky enough to be friends with a Jim in a local paper company. He claims that the tubeless process cannot work with 100% recycled content, so this product is not a green as they claim. FYI.

Update (8/10/11): Found the following image on their website:

Censored Image for class:

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The Cosmonaut: An Economic Experiment

by Dan Posted on March 28, 2011

So the guys who made the glif with much success, are now introducing another product on kickstarter.

The Cosmonaut. Its a wide-grip capacitive stylus for tablets.

The interesting thing is their pricing model. They are selling 3,000 of them, and they need to raise $50,000 to make that possible. But they are allowing the users to pay what they want for it, as long as they raise the $50,000 by the end of the month long, it’ll go through. If everyone pays $1, then the whole thing wouldn’t be funded ($3,000 < $50,000).

On average people should give 50,000 / 3000 = $16.6666666… dollars and it would just barely be funded. As of this morning:

Currently the average price is: $4,392/303 = $14.50. So people have to start increasing what they offer otherwise the final amount won’t be enough.

Interesting economic twist on the Radiohead model.

Sidenote, as a irrational person, I offered $16.67. A rational human would pay $1 and screw over everyone else. Oh well, lets see how rational people will be.

Update: At 4:46pm on 3/28/11, $20,895 raised and 1,325, so $15.77 each. price is rising.

Update 2: 3/30/11 This is from an email from the guys who put up the auction:
“This has ended up being a fascinating case study in game theory. We are looking forward to analyzing the backer breakdown and seeing how the pledge amounts were distributed. As of this writing, the pledge average came to $14.85, just shy of the $16.67 we needed to reach the goal.

So, we have decided to add two more tiers, which are both unlimited. One for $25, which will get you a Cosmonaut, and another for $50, which will get you 2. You are of course more buy tadalafil UK reviews than welcome to switch to either of those tiers if you so choose, but there is no need to. All current backers will be getting Cosmonauts. The advantage you all gained by being one of the first backers is you could set your own price, and will still be able to do so up until the campaign ends.”

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Why Teachers Like Me Support Unions.

by Dan Posted on March 22, 2011

edusolidarityBADGE

Why do I support teacher unions?

Because the quality of education is better. Yes it is. (note: I worked in a private boarding school for two years before moving to public schools). We want our students taught by teachers who focus on the students learning.

Without unions, teachers also have to worry about the following non-education worries:

  • Does this administrator like me? I’d like to think that all the administrators that I’ve worked for, 7 different people in my building over the past 5 years (not even counting higher ups), liked me and the job that I was doing. But teacher unions force the evaluation process to remain professional. Because humans are humans, and if any one person can derail you, then eventually, they will.
  • Am I being paid in a fair manner? Unions allow for teachers not to have to worry about fairness in compensation. I don’t need to worry about the teacher next to me getting a raise because the administrator’s kid is in their class (I’ve seen it happen in the private system). Say what you want about every teacher at every level at every subject matter making the same despite different qualifications (I would, but not today), the system is still better then the alternative.
  • Am I going to be fired because of a crazy parent? Yes they exist, and yes I’ve seen this happen in the private system. I’m not worried about a single biased observer affecting my livelihood.

I really could keep going, but instead, I’ll link to the excellent list of posts by other teachers on the same matter. http://edusolidarity.us/ Go there. Read. Straight from the horses (ouch) mouths. Follow #EDUSolidarity on Twitter.

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No Homework Grade! No Way!

by Dan Posted on March 11, 2011

In concert with the Standards Based Grading, I’ve also changed my homework policy. In the past I would check homework completion levels every day from every student. They would have a grade out of 4; 4 fully done, 2 half done or late, 0 not done.

http://www.icanhazgeekpet.com/index.php/dog-eats-homework/
From : http://www.icanhazgeekpet.com/index.php/dog-eats-homework/

But in Geometry R this year, I haven’t been counting homework as part of the grade. It’s been going rather nicely. I check and record their completion level every time I assign homework, but it never gets turned into a grade.

Pros

  • I think their grade more accurately gauges where they are in class.
  • Smart kids who “get it” right away aren’t being affected if they don’t do the practice on the stuff that they already know how to do.
  • Kids who struggle, aren’t being buoyed to a passing level just because they are putting a minimal effort towards the homework. They are now doing both;seeking help after school, AND doing their homework.
  • I don’t have to worry about kids copying other’s homework, the payoff isn’t worth it for them.
  • I post the answers on the website (nearly) every time I assign homework. I don’t really care if they copy the key.
  • So much time gained from not entering 90 grades a year for each student.

Cons

  • If I stop checking and marking, most of them stop doing the homework. It has to “feel” like a grade.
  • Rationally, many of them have a dilemma at home,”If I only have time for homework from one class tonight, then I’m going to do the one that is worth points.”
  • The completion rate hasn’t gone down, but it hasn’t gone up either.

To put a bit more pressure on them, I’ve starting putting their homework record on the webpage, so parents can check to see if their child has their homework done. I don’t have any stats about how many parents are using the homework chart to check up on their kids.

Have you found the same to be true with your classes? Have any of you eliminated homework altogether?

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Three Slips of Paper – Car Talk Puzzler

by Dan Posted on February 20, 2011

Excellent probability (ish) puzzler from Car Talk:

Three Slips of Paper
RAY: This is from Norm Leyden from Franktown, Colorado. The date on it is 1974–I’m a little behind.

Three different numbers are chosen at random, and one is written on each of three slips of paper. The slips are then placed face down on the table. The objective is to choose the slip upon which is written the largest number.

Here are the rules: You can turn over any slip of paper and look at the amount written on it. If for any reason you think this is the largest, you’re done; you keep it. Otherwise you discard it and turn over a second slip.

Again, if you think this is the one with the biggest number, you keep that one and the game is over. If you don’t, you discard that one too.

TOM: And you’re stuck with the third. I get it.

RAY: The chance of getting the highest number is one in three. Or is it? Is there a strategy by which you can improve the odds?

Found here.

SPOILER: Answer found here, with an excellent illustration of the solution.

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“Skinny” Diet Pepsi Can WCYDWT

by Dan Posted on February 10, 2011

Diet Pepsi will soon be available in a “taller, sassier new Skinny Can” that the company says is a “celebration of beautiful, confident women.”

(Article linked by @21stcenturychem and found here.)

I’ll table the discussion on whether or not this can is “sassier”, but if the can is 6 inches tall, how wide must it be to hold the same volume as the can that doesn’t feature a “celebration of beautiful, confident women.” ?

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