Thursday, December 25, 2008

Get Ready for Happy 41*7^2

Let the amusement begin with all of the cutesy questions and math contest problems involving our new calendar year, 2009.

Shall we begin, looking for curiosities. Perhaps our students in grades 4-8 can discover their own. Why not post their best ideas or perhaps I may create a contest right here at MathNotations! Hmmm...

Ok, let's get started:

1) The difference of the units' digit and thousands' digit is 7, the smallest prime factor of 2009.

NOTE: An important benefit of these kinds of observations is that it helps students learn how to formulate and express their ideas using correct mathematical language. This is as hard for many high schoolers as it is for middle schoolers!

2) Who actually knows a divisibility rule for 7? (Proving it is another matter).
How about 200 - 18 = 182, then 18 - 4 = 14 which is divisible by 7, so 2009 is also!
No idea what I just did? You'll just have to research it, boys and girls! Ok, an excellent resource is the Math Forum of course. Look here.

3) When 2009 is divided by its units' digit, 9, the remainder is 2, the thousands' digit. Not surprising if you know about remainders when dividing by 9.

4) The product of the distinct prime factors of 2009 is 41x7 = 287, my favorite highway in NJ. This is probably not the curiosity I would be looking for from my students!!

Ok, enuf' of this silliness. I'll leave it to my astute readers to bring in the New Year in their own unique fashion. BTW, a useful site for a list of primes is here. Keep it handy and enjoy!

HAPPY 2009 (a bit early!)


pat ballew said...

The divisibility by seven is one of my favorites..I wrote about it a while back..and you can make similar rules for 13, 17, 19 etc ...kind of a neat idea

Dave Marain said...

One of my favorites, too, Pat and Happy New year! Of course, if such notions are among our most favorite things it does say something about us, doesn't it!

Seriously, students enjoy such divisibility tests and I believe they have value as more than just curiosities in the age of the calculator. An understanding of the derivation of any of these is a challenging but wonderful investigation.

Dave Marain said...

At least I didn't mentioned that 41 backwards is 14 and 14 is divisible by 7!! Uh oh, I just did...

Mike Croucher said...


I've not seen that divisibility rule before - thanks :)

We have been discussing interesting facts about 2009 over at Walking Randomly. Feel free to pop over and join in.

Best Wishes,

Dave Marain said...

Thanks, Mike, and Happy "sums of cubes"!
I did check out your post and you've definitely gone way beyond my few observations. I think we will not be the only bloggers/math enthusiasts or educators who will mention the year 2009 in their blogs or classrooms. I definitely think this is both instructive and fun for students and we can safely say that the list will be endless! Anytime students experiment with numbers they are developing their number sense and deepening their understanding of patterns. Most importantly, their fascination with mathematics will grow.

This all reminds me of the classic Ramanujan story about the number 1729. When the famous British mathematician Hardy commented that there was nothing particularly interesting about that number, Ramanujan immediately replied that 1729 is the smallest positive integer which could be written as a sum of two cubes in 2 distinct ways! Imagine that, he did it without a calculator! If you haven't heard that story, it's a nice little exercise for students to solve. Of course, they WILL use their calculator. God forbid they should "know" that 9^3 = 729, etc...

rgetzel86 said...

The rule for seven is great. When I learned divisibility rules we were generally told that there is no shortcut to seven. 11 and 13 are a bit involved, but cool to know as well. Is anyone aware of an effective way of teaching divisibility rules? I am a first-year teacher and I had a rough time of it. Everyday Mathematics has really taken its toll on students' number sense.