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Question

Dear Mitch,

I have been a middle school mathematics teacher in Oakland, California, for the past nine years. Every year at Halloween I've managed to come up with something the students found engaging to connect the holiday season with a math concept included in their curriculum. I just spent an hour or more looking for something new on the Internet, but neither my usual favorite sites nor the bunch of new ones I read seemed to excite me in the way that gets me ready to teach the way I Like. Then one of my colleagues mentioned an article you wrote years ago in some teaching journal (at least that's how she recalls coming across it), and she still recalled several of the Halloween ideas you described. I liked them and may use one almost exactly as she described it, but I was wondering if you still have a copy of that article in your files or if you even recall it. If so, would you post it again here on your website? Alternatively, if you have new thoughts on Halloween math for middle school students, do you think you could post your thoughts here? In fact, another colleague, looking over my shoulder right now, remarked that he too recalled your article and also would appreciate either a reprint or something similar before it's ghost and goblin time.

So, if you wouldn't mind...

Thank you,

Mr. B

Answer

Dear Mr. B,

Your letter is one of the eight I've read so far today asking for something relating to teaching math at Halloween and/or mathematical Halloween costumes, and I see an almost daunting number of others underneath it. So, here is an excerpt from my answer to a letter I received many months ago. A woman wrote in on behalf of her brother who was about to begin his career as a teacher of mathematics and wanted to surprise him by making him the best Halloween costume she could. Following that, I'll share an idea that I have enjoyed with students, and it remains one of my favorite Halloween ideas for math. Here goes:

During my years teaching and directing departments in schools as 'the math guy', I always enjoyed coming up with Halloween costumes that make people think, wonder, and (hopefully) laugh!

So here are some of the characters and items I've been for Halloween:

  1. Wearing all black -- except for a large, white, cardboard #1 standing up on the top of my shoulder, I was... the invisible guy or force that 'carries the one' in borrowing and regrouping...
  2. I dressed as a large wild cat with a mane, and had students write numbers all over me (I was... the "number lion")
  3. (This one I would not do again and would not be thrilled to see others do it... I was younger and had not yet learned to be sensitive to issues that once just seemed so removed from my world that they seemed fair game for jokes. I wore a straight jacket, unmatched shoes, my pants backwards, and had numerals written all over me. I was, of course, a 'set of irrational numbers') Well, you asked.
  4. One year when I just wanted to be as downright silly as I knew how to be, I actually bought a huge round pumpkin costume. It was, of course, bright orange. I spray-painted it black. And I wore black everywhere else. (I was a decimal point).
  5. One year I wore my regular clothes except for a hat. (It was a baseball cap). And I made what looked like a plant growing out of the top of the hat. (Geometry..."gee-I'm-a-tree?!)

For a school that has a whole math department, I always thought it would be fun to come up with something that everyone in the department could wear and it would work together, like a number line, with each person a different number and little horizontal lines sticking out from their sides in each direction, so that when they line up...

But, somehow, we never got to that one.

OKAY, NOW, FOR AN ACTIVITY I'VE ENJOYED WITH STUDENTS AND WHICH I BELIEVE ENGAGED THEM IN THE LEARNING AND DISCOVERY AS AUTHENTICALLY AS I EVER COULD HAVE HOPED:

Preparation before students arrive:

This could be presented in a classroom, in an open place in the school, such as on a table near the administrative office, etc. or any area you wish to have a fun display for the holiday season that will get people to think mathematically.

Obtain a few different sized pumpkins, the more spherical the better (so that the volume of a sphere formula helps get students so close that it's SPOOKY...)

It's easiest if some of the pumpkins have a diameter of ten inches or less, but large pumpkins work perfectly well also.

Obtain some rulers, perhaps some metric and some imperial (or what we call in the U.S. "Standard" or "Customary"), and obtain some yardsticks and meter sticks.

The yardsticks and the meter sticks are for the larger pumpkins.

Obtain a tube of fake Halloween blood, only if it is convenient. If not, any red paint or permanent marker works well enough.

Before students arrive (long before, to avoid rushing, such as a couple of hours before or the evening before), stab each pumpkin with a separate ruler. And push each ruler all the way through the pumpkin so that it emerges from the other side. Try to get the "stab" as close as you can through the pumpkin's center point, so that it forms a diameter, albeit one that is hidden inside the pumpkin. So, for example, one ruler might have one inch exposed on one end, two inches exposed where it made its exit, and the rest hidden inside the holiday pumpkin. AND LEAVE IT THERE. You need to leave one ruler going through each pumpkin. (Don't worry about sacrificing the rulers; I found that they eventually can be washed off and continue functioning with their drawer-mates).

***NOTE***: IT is EXTREMELY difficult to 'stab' a ruler through a pumpkin, and though I was excited to try, I found it impossible. The flexible wooden rulers I used would have died trying. SO what you need to do is cut a slit with a sharp knife for the ruler to enter the pumpkin, and cut another slit with a sharp knife for the ruler's exit. (But that's our secret!)

Then smear a bit of fake blood or red paint around the ruler's entrance and exit point.

Do the same with the yardsticks/meter sticks and the larger pumpkins.

And, in your own way, of course, when the students approach the strange display and become silent, you explain that a bunch of "EVIL RULERS" came in the middle of the night and attacked these poor pumpkins. There are detectives working away on the case, and everything can be solved -- as soon as the students do a few things to help.

In groups, they are to figure out the circumference, diameter, volume, and estimated weight of various pumpkins assigned to their group. All, of course, based upon how much of each measuring stick is immersed in the gourd.

The only other thing to include is a weighing of some other pumpkins and the measurements of those with known weights -- thereby setting up the necessary ingredients for a ratio situation once the students figure out the appropriate parameters for the "attacked" pumpkins at their table. And, after all is said and done, let each group check another group's work and present its findings and reasons and calculations. Then, if all goes well, cook them up! (Oh, and then, of course, cook the pumpkins for yourself).

Happy Holiday!

Hope this helps,

Mitch