My son had two problems from his Mathcounts practice that puzzled him last night. I thought it was best that he puzzled through one of the questions – what is 47 * 53. His question about this problem was simple – why would they even ask this question?
The other question required a little more review since we’ve not talked about exponents in a while:
Evaluate:
Unlike the first problem which really just involves learning a difference of squares trick, this problem actually connects to an interesting puzzle (and one that we’ve studied before):
Can an irrational number to an irrational power be rational?
I didn’t go all the way to exploring that connection last night, but instead we had a nice 10 minute review about exponents.
By luck, today he was working through a few problems from the 2010 AMC 8 and came across this problem:
Problem #24 from the 20010 AMC 8
The problem asks you to arrange these three numbers in increasing order – 
Here’s how he approached it:
After he worked through the problem I wanted to do a quick review just to give a little extra emphasis to last night’s review.
So, a happy coincidence running into this problem today. Nice to be able to put our little exponent review from last night to work today!
Comments
” what is 47 * 53. His question about this problem was simple – why would they even ask this question?”
I guess, the question is to check if students can come out a quick method:
47*53=(50-3)*(50+3)=2500-9=2491
maybe it is too easy for American kids 🙂