Thursday, September 8, 2016

Magic Doesn't Always Happen in my Classroom, but When it Does...

I used an activity this week where I introduce the method of using Lowest Common Denominators to eliminate fractions and decimals in 'tricky' equations. On the activity page, I refer to this trick as a 'good idea,' but in class I said, "It's like a magic trick: I wave my LCD wand and presto, no more fractions!" They laughed, so I kept it up.

"Ack. This one looks yucky. I need some magic." Snicker.
"See, here's where the magic happened." Chuckle.

At one point, a student raises his hand and says "You know Mrs. Allman, it's not really magic, it's just logic."

Nice. But aloud I said, "You know what you are? A muggle."

Jaws dropped. Did she really just call him a muggle? Putty in my hands now.

The next equation had some decimal coefficients: 
1.2x + 0.4 = 7.6

I asked, "What's the LCD?"

Someone said, "There aren't even any fractions." (I swear, he wasn't a plant.)

I spun around and looked again, "There AREN'T?"
So I waved my hands and said, "What's this number?"
"One point two."
"Didn't your 5th grade teacher tell you never to say the word 'point' in math class? How are you supposed to say it?"
"One and two tenths."

There was an audible gasp from the class. I cannot make this up.

So now they're fighting over whether 5 or 10 is the LCD of this group (cool) and whether it even matters, and which is more magical, and I could NOT have planned this better. At one point, a student shows me his work "Mrs. Allman, I used a different number to multiply both sides and I still got the right answer. It doesn't matter what you use."

"Ah," I said, "And that's a beautiful thing. You've confirmed one of the properties of equality: that you can always multiply both sides of an equation by ANYTHING, and it will not change the solution. The magic comes from knowing which numbers will make the decimals (or fractions) disappear, and (hopefully) make your life a little easier."

There might still be pixie dust on the floor.