Mathematical Bakery

Working with generalized proofs today, we ran into a problem that said (a+b)(a+b)...we were using the distance formula. Oh the crazy answers I heard from my Geometry students!! Sure, we haven't done a lot of multiplying of binomials this year, but still....I was a bit frightened. I explained to them that at the end of this year we're going to do a pretty hefty Algebra review to make sure they're in shape to take Algebra 2 next year. I told them "factoring is cake compared to what you'll see there!" The following conversation ensued:

Student 1: "So....you're saying Algebra 2 is like a scone?"

Me: "What??"

Student 1:" Well if factoring is cake, Algebra 2 is a scone....it's a little harder."

Student 2: "Pre-Calculus must be like a stale scone!"

Student 3 (from across the room): "And Calculus is like a really hard loaf of bread!"

Student 1: "Good thing we have studying...that's our coffee! We can dip our scones into it and it will soften them and make them taste better."

Student 3: "I don't think I'm going to study in Calculus."

Me: "Why not?"

Student 3: "Because....old bread dipped in coffee? Gross."

Groups of kids like that remind me why I love my job, especially on the days when you're ready to hide under your desk.

Proofs by David Bowie

When I was in college, I felt like proofs had personality. I have no doubt this came from years of pouring over them- from intrigued amusement to hopeless despair (I'm talking to you, hyperbolic planes). They joined the list of mathematical characters friends and I would create to numb some of the mathematical stress: the Jacobian who liked going on African safaries, the data my professor loved to put in the freezer, the triangles evil cousin Cryangle. And proofs? These were just some:

• The cute little ones which were made you giggle....toddlers, anyone?
• The elegant ones which so effortlessly seemed to make such a profound impact. These were definitely always wearing elbow length ladies gloves and pearls.
• The beastly ones that took up a lot of space without really saying anything. Any Planet Fitness members out there? These made my inner lunk alarm go off. I usually walked away going..."Well that's just dumb!"
• The ones with a trick up their sleeves. These always struck me as the salesmen of the group.
• The wise old grandfathers....proofs by induction. Figuring out what we definitely know is true. Building on that experience. These always seemed so reasonable to me. 
• The ones that are just really, really, really annoying. 

Then there was my favorite type...the smart, sassy, sarcastic ones....indirect proofs. The let you think something was true until BAM...they proved you wrong. They had attitude. They were the Real Housewives of my mathematical world. 

My students have not spent the endless hours pouring over proofs that I have and they also haven't needed such a mental break from the stress of a 500 level math class that they would begin to understand these characters. However, I wanted to do my favorite proofs some justice and let the kids do some exploring.

I set up 2 stations:

1) A set of sudoku puzzles 

2) This video from the 1980's movie The Labyrinth

1, 2, 3....

DEBATE! CONJECTURE! CONTRADICTION! 

All of this, of course, after the debate and conjecture about Jim Henson and David Bowie. Middle schoolers of 2012 cannot fathom the 1980's.

 

Great first day of the lesson. Wrapping it up tomorrow with discussing how we gave hypothetical conjectures, then tested them to try to see if there was a problem with them.