## Thursday, April 2, 2009

### They Have Me Totally Figured Out. Must Be Spring.

I, apparently, need a new schtick. Today I was doing the old, "What's the diagonal of a 1x1 square?" Students diligently think about pythagoras for 10 seconds, with a few misguided shouts of "1! 1 and a half! 2!" and settle on the square root of 2. This is right after we talk about what square root means, how it's the opposite of square, how "radical something" is "what times itself is the something".

So I say, "ok so what's the square root of 2? what times itself is 2?" Blank stares. Lunges for calculators. "I SAID NO CALCULATORS," I say.

A few speak before they think and say, "one", "one half", "four halves", but realize those aren't going to work before they get all the words out.

"One and a half?"

"OK", I say, and I diligently write on the board 3/2 times 3/2, which gives us 9/4, which we all see is more than 2.

"Hmmm. Must be less than one and a half."

"One and a quarter!" We figure out that one and a quarter is 5/4, and I write 5/4 times 5/4, which gives us 25/16, which is obviously much less than 2.

"one point four?"

"OK", I say, and start writing, to which the kid says,

"Well obviously that's not right because you wouldn't write it down so quick. When I'm right you always say 'Are you sure?'"

That little snot.

#### 5 comments:

Kathryn J said...

Too funny. It is so hard not to telegraph right and wrong to them. If you had them fooled until April...

Alex said...

So where did you go from there? Did you want them to measure the diagonal of a square - and if so, did they get it?

Kate said...

Kathryn, I don't know if I ever had them fooled! :-) Subterfuge isn't really my forte.

No Alex the point of the exercise wasn't to find the length of the diagonal - measuring or using a calculator wouldn't teach us anything new - it was to see that root 2 can not be written as a fraction. I wanted us to keep looking and looking at more fine grained fractions (7/5 * 7/5, then 145/100, etc etc) until the kids started to think maybe there wasn't one. And yeah, they got it...at the end of class they all successfully sorted 8 expressions as rational or irrational.

jd2718 said...

You know what I do... mix it up. "Are you sure?" goes half the time to right answers, half the time to wrong answers... Boy, do they hate that.

Jonathan

Amanda said...

LOL- I always tell my students that if I ask them, "are we done???" the answer is always "no!"- by this time of year they are shouting the "no" but most of them have already come up with the answer to the next questions, which is "ok, what do we do next?" LOL