## Tuesday, December 2, 2008

### The Product of a 40-Digit Integer and a 60-Digit Integer has ___ or ___ Digits. A Problem for the Calculating Middle School Mind!

Too ambitious as a WarmUp for the 6th or 7th grader? Would they immediately employ the "Make it simpler and look for a pattern" strategy? Is the calculator appropriate for this activity? Is this really an activity/investigation?

Since I'm already regarded as an anachronism, I guess it wouldn't hurt to play word games here:

Is this problem un'characteristic' of MathNotations!?!

Hey, there's a whole generation (or more) who may have no idea what that means! If you do know, you can always say you heard about it from your great-grandfather who carried around his slide rule! Hey, anyone have their Keuffel & Esser handy?

Pat B said...

Dave,
You may get a LOG-jam of bad puns now.... (side-bar,.. funny how things line up.... I was just this weekend up to Napier's home in Edinburgh)
Pat

Dave Marain said...

Pat,
Did you find any old BONES lying around! Seriously, it might be worth having students rediscover Napier's Bones just to see that lattice multiplication wasn't invented by Everyday Math! The excellent Wikipedia article actually demonstrates how his invention (similar to an abacus) was used for products, quotients and even square roots - fascinating stuff...
Thanks for reminding me of that!

Anonymous said...

I don't know what this says about my age :-), but my reaction to Dave's "characteristic" comment was to think of characteristic functions, and how I could express the two numbers as polynomials in x, and what the coefficient of the highest degree in the product would be ...

TC

Dave Marain said...

Yup, I'm a lot older than you. TC!! Characteristic polynomials and linear algebra are interesting connections, but I'm reaching even further back!

Look here!
Now to really get punny we should bring Lincoln into this -- the great "LOG" splitter. Ugh...