Caroline asked me for help with her math homework this afternoon. She's in the advanced math group in her class, and had a worksheet involving equations involving exponents. I know. SIXTH grade.
Well, it's been quite a while since I've done this sort of math, but I was a good student and figured I could sort it out. Plus, the worksheet had cute little fishies swimming all over it, so it looked like it was within my math range.
Here's a sample equation:
1.5^x + 8^y = 633
(That's 1.5 to the x power plus 8 to the y power ... so the challenge is to figure out which exponents fit. And it was in the instruction that it would be a whole number between 0 and 9.)
Yikes. Decimals and exponents? I don't remember encountering that. And for the life of me, I couldn't figure out how you could take any exponent of 1.5 and add it to a whole number to get a whole number.
Caroline had struggled until she was in tears, and after working on this, I felt similarly frustrated. I kept concluding that the worksheet HAD to be wrong. But every other problem had a decimal in the equation, too.
You should have seen the various ways I yanked algebra out of my ancient brain. We multiplied and divided and tried all sort of rearrangements of the equations. Yikes. And I simply couldn't figure it out. I was becoming alarmed, not just at my own inability to do the worksheet, but also realizing that Caroline will be shooting past me intellectually and it's starting NOW, apparently.
Caroline was beside herself at not being able to finish the homework. Finally, I figured I'd see if there was a simple instructional aide on the internet (Yay, internet!) and failing that, I'd write a note to the teacher reporting how hard we'd all worked.
The only thing I could find on the internet that showed how to do problems that looked like Caroline's involved logarithms. Yes, you read that right. LOGARITHMS. And, as advanced as Caroline is, I don't think her teacher is throwing those at her yet. Not with little fishie drawings, anyway.
While Caroline and I were continuing our calculations, Roger arrived home from work and jumped in to show us how to do these. He worked through the same steps I'd tried, coming to the same conclusions. "This has got to be wrong!" So, I wrote a note to the teacher and convinced Caroline that it'd be okay for her not to struggle any further.
We set the paper aside, down at the end of the table, to eat dinner. And while we were eating, I glanced over at it and realized.... Those weren't decimals. They were the problem numbers. So what we'd read as 1.5 in the first equation was, in effect, Problem #1: 5^x = 8^y = 633. And sure enough, once we looked we saw that they were the problem NUMBERS.
NOT DECIMALS. You think they could have made that spacing a bit more obvious, eh?
So... the math was still tricky but back down to reasonable advanced-sixth-grade level.
I'm leaving the note attached for the teacher, because I'm sure she'll get a laugh over all of us working so hard with all of those decimals. I wonder if anyone else did what we did.
And while I'm sure that Caroline's school work will exceed my ability to help her do it sometime soon, I'm breathing a sigh of relief that I have a bit of a reprieve.