Just a 'little' last-minute challenge before Turkey Day -- similar to many you've seen before on this blog and elsewhere...

Determine the exact digits of 100^{2008} - 100^{1004}.

Comments:

Students in middle school or higher will often (or should) employ the "make it simpler and look for a pattern" strategy. Some students will be able to apply algebraic reasoning (factoring, laws of exponents, etc.) to evaluate. It's worth letting students, working in pairs, 'play' with this for awhile, followed by a discussion of various methods. Then challenge them to write their own BIG exponent problem!

## Tuesday, November 25, 2008

### A "VERY BIG" Pre-Turkey Day Math Challenge for Middle or HS

HAPPY THANKSGIVING!

Posted by Dave Marain at 6:56 PM

Labels: algebra, exponents, math challenge, middle school, patterns

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## 4 comments:

Nice. I wish I had seen this yesterday - I would have run it.

Jonathan

thanks, jonathan--

I wish I had posted it earlier! Even with the late posting it got a lot of last minute views from educators who were looking for that 11th hour challenge!

Actually, I've been busy with the calculus videos, particularly re-doing the last one that had an error in it. I had to fix that! No one is commenting on those but I suspect some Calc I students are looking for help with those 'fun' application problems at this time of year. I've been viewing other calc tutorial videos online. Some are ok, but there's not a lot to pick from (unless you buy the DVD series or a subscription!). I'd be interested in how some hs AP students would feel about these. The writing is too small on my board, the audio is tinny but I am trying to combine rigor with clarity, a difficult combination, not to mention demonstrating some instructional techniques. I have a long way to go with these but any reactions would be nice...

Happy Thanksgiving to you and your family!

10^(1004) (10^(1004) -1)

which is equal to 1004 of nines follows by 1004 of zeros.

Thanks, Watch Math--

Be careful, though, the bases are 100, not 10, so all your exponents need to be doubled.

Do you think most students would consider factoring? What I've observed is that some will look for a pattern:

100^2 - 100^1 = 10000 - 100 = 9900

100^4 - 100^2 = 99990000

etc...

"Making it simpler" requires that the student recognize that the ratio, 2:1, of the exponents must be preserved. This approach has value too!

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