Monthly Archives: February 2014

What’s my Rule?

Have you seen this YouTube video?

Watch it, and then tell me . . . how long in to the video before you figured out the rule? For me, it was at 2:01!


Happy Valentine’s Day 143

1 4 5 11

Do you?

It just makes me think of Valentine’s Day.  As a little kid I remember getting them from my parents, in their little cardboard box.  In high school, I used to tell my sweetheart of the month that all I wanted for Valentine’s Day was one of those little boxes . . . forget the flowers and stuffed bears!

What’s that you say?  You don’t know what 1 4 5 11 means?  It’s code.  1 4 5 11 is code for I love Necco Sweethearts.  You know those chalky little hearts with the Valentine sayings on them?  I didn’t make up this code, Necco did.  Have you seen these hearts?

Screen Shot 2014-02-13 at 1.38.46 PM

(Find the top 14 conversation hearts here, including 143).

Do you know what 143 stands for?  I (1) love (4) you (3).  Get?  If not don’t feel bad.  This person Facebooked Necco to find out why in the world she ate a heart with 143 on it!

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Anyway, I think its cute and all but as far as codes go . . . its really not that great.  I mean 143 could stand for lots of things couldn’t it?

But here’s the thing, Necco’s touching on something that mathematicians have used for a long time.  That is, numbers as code for something else.  Try this one:


OK, OK.  So its not that hard, right?

Its either:

IABAEBBEBEAEBA or ILOVEYOU.  I’m not sure that I would want to send some sort of top secret code through cyberspace if my coding technique was A=1, B=2, C=3, etc.  But what about this code?


Do you want a hint?  OK.  It looks like that number might be divisible by 5.  Oh!  It is divisible by 5.  I wonder what you get when you divide the number by 5?

Hmm.  We might be on to something.  It seems to me that a great way to code something might be to do the whole A=1, B=2, C=3 thing and then to multiply it by another number.  If the person I’m sending the code to knows the number to divide my code by, the code is pretty darn easy for the receiver to crack and its fairly difficult for a spy to intercept and figure out what it says, don’t you think?

So, find a sweetheart and send them something in code for tomorrow.  My sweetheart is getting this message.  Can you crack it?


How Tall is That Tree?

One of my most favorite lessons to teach is featured in this month’s issue of NCTM Middle School Mathematics (February, 2014).  If you’re a member of NCTM, click here to check it out and download the handy classroom printables.  If you’re not a member, click here to join NCTM; then click here to read the lesson and download the handy printables (or, you could make friends with someone who is already a member of NCTM . . . like maybe your department head and talk them in to letting you read the lesson!).  However you get your hands on it, I hope you enjoy!

Here’s a little excerpt from the full text:

“The American Forests organization documents the largest trees int he 50 states and the District of Columbia.  Each state, responsible for locating its largest trees to add to the national database, has its own method for measuring and locating tall trees.  Some states rely on amateur tree hunters for nominations.” (MMS pg. 386)

Turn your students into amateur tree hunters in this lesson!

Don’t worry the groundhog isn’t right anyway . . .

This year my two oldest children really got in to the whole Groundhog Day thing . . . so much so that when they heard on the Today Show that Punxsutawney Phil saw his shadow, signaling 6 more weeks of winter the oldest insisted that there be a “redo,” because he was not going to endure 6 more weeks of winter.

See?  They still have fun in the winter!

See? They still have fun in the winter!

“You guys,” I said.  “Just relax.  The groundhog can’t really predict the weather.  It’s just something fun to do on February 2 every year.  It’s just folklore.”  (My son is currently learning about folk stories in 2nd grade, so I thought this might sell my explanation!)

“How do you know mom?”  (that was my kindergartener, not convinced and not happy about the groundhog’s prediction).  “Maybe he’s right and you’re just saying its folklore so we won’t be sad.”

I don’t really remember how the rest of the conversation went, mostly because there wasn’t any use in arguing with either of them and also because by then, they had completely lost interest in the conversation.  But that kindergartener, she got me thinking.  How often is the groundhog right?  Does he predict the end of winter enough that there might actually be something to this whole “groundhog sees his shadow” thing?

U.S.A. Today wrote an article about the groundhog’s predictions and the National Weather Center also has a thing or two to say about how accurate the groundhog actually is; they report the groundhog has been wrong 15 times and right 10 times.  But here’s the thing . . . according to both websites the groundhog either predicts 6 more weeks of winter or an “early spring.”

Who decides if spring has come early?  How do we know if winter has lasted for 6 weeks?  Is this measured by the air temperature?  The amount of snow on the ground?  The vernal equinox is the “official” start of spring, but clearly that’s not what people are talking about when they refer to the groundhog’s prediction . . . otherwise, no prediction would be needed!

I suggest we get a little more precise about what we mean by the groundhog’s prediction, before we decide whether his predictions are accurate or not.  I propose that if the temperature for half or more than half of 6 weeks after February 2 (so that’s the week of 2/2, 2/9, 2/16, 2/23, 3/2, 3/9, 3/16) has an air temperature at or below the national average for the last 100 years that counts as 6 more weeks of winter; otherwise, spring.  According to this definition of an “early spring” Phil has correctly predicted the weather for the next 6 weeks, 11 times over the course of the last 26 years.

But, I agree spring is much, much better!

But, I agree spring is much, much better!

If we recognize this as an example of binomial probably, we know that about 30% of the time we would have been able to be just as accurate as Phil by flipping a coin where “heads” is early spring and “tails” is 6 more weeks of winter.  I’d say that qualifies as a folktale to me, wouldn’t you?