Comments on: The Frozen Code

By: Shernell Mabien

Shernell Mabien — Mon, 13 Apr 2015 03:15:08 +0000

Hi, I am a student at the University of South Alabama and each week are comment on different blogs. I think it is interesting to do research like you have done. I think the Frozen code would be very helpful.

By: Dan Anderson

Dan Anderson — Mon, 12 Jan 2015 16:04:37 +0000

@Bowen
I’d bet that the person who wrote that formula has taken some programming classes. It’s the exact code that I’d write to update the price variable with the new price (the old price info would be overwritten). Ugly though.

By: Mark P

Mark P — Sat, 10 Jan 2015 20:53:14 +0000

I see some of the suggestions above as mathematical social studies. It is interesting to consider alternative strategies etc, but at the end of the period you’ve advanced their maths very little, if at all, by talking about things without doing the maths.

I also have a dislike of unchecked answers. They are the best way to embed incorrect techniques, because if students don’t know their working has flaws they will continue to make those mistakes, and indeed embed them deeper. (It’s why I distrust homework that is not marked as it is done.)

I would suggest

1) setting the scene pretty quickly

2) propose the “solution” come to by Gelato Fiasco

3) ask them to write that solution in words

4) ask them to convert words into variables (specifically not giving them letters to use as the variables, as they need the skill of picking their own).

5) ask for student answers as they come in, put on the board, in words and equations (allowing the slower ones to keep on going, but letting the fast having something to look at). We go through them seeing if they work or not. Explain that any that work are acceptable, no matter how ugly they look.

6) Correct any misconceptions, such as the price = price – discount. Quickly explain the mental process of writing equations. (It is important to discuss it as soon after they did it as you can — talking at the end of the period about what they did 20 minutes ago and since moved on from is not helpful.)

7) explain that the US uses Fahrenheit, not Celsius, so we’re going to have to change our zero point to be 32 and see if they can rewrite a correct equation in degrees F.

8) work through suggested solutions — inserting them into the previous correct ones on the board where possible, to mimic the process a skilled person uses.

I know this sounds very traditional, but it need not be if you pace it right, with engagement and discussion about the alternative correct answers. Some might allow students to come up and write their equations on the board, although I wouldn’t.

What I find most disconcerting about discovery and investigative learning is just how little gets done in a period. They may love it, but if you spend 30 minutes writing one equation then you’re selling them short.

By: Bowen Kerins

Bowen Kerins — Sat, 10 Jan 2015 03:07:34 +0000

Their formula is terrible! Price = Price – [Price * (…)]

Or is it…? Subtract Price from both sides…

0 = -Price * (something nonzero)

Therefore 0 = Price! It’s free, and there’s proof! QED

By: John

John — Fri, 09 Jan 2015 13:50:05 +0000

With the clear correlation between temperature and number of chain gelato shops, CLEARLY the temperature causes more gelato shops to be built…or does the number of gelato shops cause the temperature to decrease…am i right?

By: Pam Rawson

Pam Rawson — Fri, 09 Jan 2015 12:58:22 +0000

With a lunchtime temp of 5 degrees here in Portland, Maine, yesterday was a perfect day to take advantage of the Frozen Code. Not sure too many of my students did, though. I can’t believe that I forgot about this marketing scheme. Thanks for the reminder, Dan. I’ll be using some form of this with my students next week. Perfect timing – seasonally and curriculum-wise.

By: Dan Anderson

Dan Anderson — Fri, 09 Jan 2015 02:20:35 +0000

Extension 2: If they decided to institute demand pricing (ala uber surge pricing), how would you (the student) price the froyo based on temperatures greater than 72?

By: Nic Paolini

Nic Paolini — Thu, 08 Jan 2015 22:30:45 +0000

Dan Anderson’s comment inspired this thought in me for an extension: What if they used Celsius instead of Fahrenheit? How about Kelvins? Which is the better deal?

By: Jeff Morrison

Jeff Morrison — Thu, 08 Jan 2015 17:33:12 +0000

I would even start by identifying the problem (Drop in Sales of Gelato when the temperature is colder).
Ask how to solve the problem – they may come up with creative ideas of their own.
Then offer Gelato Fiasco’s solution – discounts based on how cold it is. Each degree below freezing is a percent off (simple language, not too “mathy”)
Have students try to encode that mathematically, and derive an equation. Maybe by doing tables, etc.

Could also include a discussion about the difference between percent, and percentage point. A drop by 1 degree, then another degree sums, to add a second percentage point off. If the discount is 1%, then it drops another 1 degree, the phrase “another 1% off” is (technically speaking) inaccurate.
Maybe not the time for that though?

By: Dan Anderson

Dan Anderson — Thu, 08 Jan 2015 17:30:05 +0000

Extension: How would your equation have to change to account for windchill temperatures? What if they used the old formula? Better discount?
Formulas: http://www.onlineconversion.com/windchill.htm
Desmos interactive of windchill temp: https://www.desmos.com/calculator/fvjycjwdcy