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!
Posted by Dave Marain at 7:58 AM 6 comments
Labels: fun problems, investigations, middle school, primes