One of the things I post each day on my "On This Day in Math" blog is something about the number that day of the year is. For instance yesterday was the 71st day of the year. I checked the Prime Curios page and it told me (among a bunch of other stuff that I will mention later) that 712=5041 = 7! +1! ...
As a teacher, I loved that kind of stuff because it was so easy to generalize problems from it. Kids do a lot of simple math exploration looking for patterns like this, and I think a lot more happens when they are doing math that they want to do.
So why mention that now. Well I was just reminded that Chris Caldwell from Tennessee Martin, (just down the road from my home here near Possum Trot, Ky) and his coauthor, G. L. Honaker, Jr. who run the Prime Curios page, also put out a book a couple of years ago (2009) called (wait for it) Prime Curios! The Dictionary of Prime Number Trivia.
So I'm plugging the book because I hack off his page regularly and think every math teacher in the country ought to have a copy on his bookshelf for kids to finger through, "Happy birthday kid, you were born on the XYZ day of the year...did you know...."
Anyway, just to give you a feel for a day, here are some things from the page on the prime number 31, because it has a note about a most unusual speed sign.
"The speed limit in downtown Trenton, a small city in northwestern Tennessee, is 31 miles per hour." They should know about this because Trenton is only a little down the road from Martin, where Chris teaches.
And the little teapot on the sign? Well, Trenton also bills itself as the teapot capital of the nation. The 31 mph road sign seems to come from a conflict between Trenton and a neighboring town which I will not name ,...but I will tell you they think of themselves as the white squirrel capital. Yeah, I know you city folks don't get off the freeway, and think I'm kidding, so here's their "Welcome sign".
Some other good notes from the book on 31:
The sum of the first
31 odd primes is a prime square.
(ask the students to find out that sum and that prime and watch how they attack it to learn a lot about how they attack problems)
The sum of digits of the 31st Fibonacci number is 31.
The big "31" sign made its debut at all Baskin-Robbins
stores in 1953, offering customers a different ice cream for every
day of the month. Note that 31 is the largest prime factor of 1953."
Ok, where else can you find neat details like that... or like these... and remember, these are all on the SAME page:
"There are 31 milligrams of cholesterol in a tablespoon of butter."
"31 and the 31st prime are both Mersenne primes."
"The smallest prime that can be represented as the sum of two
triangular numbers in two different ways (21 + 10 and 28 + 3)"
and that's part of the stuff that's on ONE of the pages... you want this book... it's just a fun book.