## Thursday, February 02, 2006

### Tutoring

On Wednesday I tutored an Algebra 1 student who was just starting to learn how to solve 2 step equations (solve: 5x + 3 = 13). ... I've taught older kids for so long, and I just daily take it for granted that "my" kids can do that without thinking, that I forget how much they know and how hard it must have been when they first started out learning such things. It was refreshing and a nice reminder that everyone has to start somewhere, and it doesn't just come naturally.

Of course my precalculus kiddies were struggling today with:
Solve sqrt(x-5) - sqrt(x) = 7

Everyone is struggling at a different level. ... except for us perfect people (cough cough).

1. Anonymous5:53 AM

Ok, here's one I'm struggling with: I have a number between 1 and 2147483647.

How do I tell if my number is a power of two. i.e. 65536 = 2^16

Is there an easy way, without just knowing all the powers of two. :)

Owl.

2. Anonymous9:28 PM

Ooh, I like that problem. Do I get to use a calculator or multiple calculations? ....

1st thought: keep dividing your number by 2, and if you ultimately end up at 2, then it's a power of 2.

2nd thought: (though it didn't work on the calculator I'm guessing because of the LARGE number) 2^x = 2147483647 (or whatever the # is, then x*ln(2) = ln(2147483647), and therefore, x = ln(214...)/ln(2), and if that's an integer, then you have your power.

Thanks for the brain teaser.