One of Those Days...

I've been watching way too much Keeping Up With The Kardashians in an effort to numb my brain during end of quarter grading, so here it is, the peak and the pit of today.

Pit: The server goes down. In the middle of 5th period. For 2 periods. When I have tablet and Smart Board activities planned for all! Coworkers lost all files. Thank you, Dropbox, for saving my life. 

Peak: My Geometry class bringing a staples "easy" button to class and it exclaiming "That was easy!" every time we successfully finish a tough problem. Special right triangles ain't never been so much fun. 

Notice...the peak is the kids. The pit is all the other nonsense. 

A Geometric Valentine's Day

We're just digging into geometric mean in Geometry and the inevitable question of "Why are there 2 types of means?" always arises. 

Here's a timely explanation of one way math & geometric mean are used in real life....just in time for Valentine's Day!

Happy Valentine's Day to all of you!

Update: Discussed this with my class last period...they immediately wanted to know if I used eHarmony or Match.com (despite the fact that they know I'm in a long term relationship) and which was better. They decided they should probably test both to figure out which one worked better.  I guess I'm glad they're trying to test their conjectures? Scientific thinking at its finest. 

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. 

Word of the Week: Centroids

Each week I have my students for a Math Lab. This was supposed to be an extra enrichment or intervention period, but it's turned into organized chaos. I have 20-30 students in 3 different courses all vying for help and attention. It's that class that I dread leaving for a sub....chaos. 

My Geometry students are at the top of the food chain and it breaks my heart to give these critical thinkers "drill" practice when they could be exploring. Today was one of those days when you're not sure if an activity it will bomb or fly. And this one? It flew!

We have been studying centers of triangles (orthocenters, incenters, centroids, and circumcenter). This has had 2 highlights for the kids: a foldable that they used to keep them all straight and giggles when one student kept slipping and saying "circumcision" during an oral presentation. They are always cooperative and brilliant, but I wanted to give them some reference into why this stuff might matter. Good thing I spent 3 semesters of college teaching physics! Centroids.....centers of gravity....suspending random objects around the classroom? Sounds like it's worth a try. 

I used this video on center of gravity to introduce the topic. One their interest was piqued, this video related the information to our chapter. I had each student design a triangle out of cardboard and find its centroid, then suspend it. Then they had to find some weird shape other than a triangle and try to find its center of gravity. Can you find a centroid for that? How is it alike and different? All questions to be examined! 

Anytime you get to hear "whoa!" and "that's so cool" is a good day in my book. I had to shoo students out of the room when the bell rang and we spent the first minute of class later that day balancing our triangles on smaller and smaller points around the room. One student got it balance on the head of a pin....he took it home because he just HAD to show his parents. Here's a great activity that I wish I had thought of before today....could have been integrated nicely. 

The only problem? The 20 Algebra students I had in the class found it nearly impossible to focus on their linear equations project with all excitement! They wanted to build their own centroids and were even starting to use the vocabulary. I love when, at the end of class, I catch students who aren't even in the course watching videos I've posted for other classes (also a problem with Vi Hart's videos!). As I was walking out to my car I found 3 triangles, centroids labelled, that had been made by students outside my class. Love when math leaves the 4 walls of my room! 

Any other ideas for integrating more physics into high school math? Obviously with calculus, but with lower level? Share share share!

The Wonderful World of....Foldables?

I am like my middle schoolers in some sense....there are "cool kids" in the "class" with whom I really, really want to hang out. Go to the mall, braid each other's hair, share secrets....you know? I just haven't quite figured out how to infiltrate their world yet. Obviously, I am talking about foldables. I see teachers who do these elaborate interactive notebooks and I think....those are SO COOL!!! But do I have time for them? Will they be helpful or are they just a bigger waste of time? How do I get a class of 28 to listen to elaborate directions for a foldable without wanting to pull my hair out? 

So today, I decided to go over to the cool kids lunch table and sit right down. We tried a (very simple) foldable for slope intercept form in Algebra. My students spent extensive time last year studying the topic, so I'm not dwelling on it for long. A foldable seemed like a good way to re-establish our relationship with good old m & b, then do some practice. Thanks to Sarah at Math=Love for the idea!

The kids LOVED it. To some extent, it was the "anything different than what we normally do is AWESOME" syndrome. But I genuinely think the found it informative and useful. 

My geometry class recently finished their own "foldables" project....making pop-up cards using triangle vocabulary. We established what an altitude is and what properties it has without even cracking a textbook. It was a nice transition to a really dense chapter (Euler line project, anyone?). 

Came out pretty cute, right?

The turkey card was from a pattern the students followed.  The Easter card was one the student designed on their own, then wrote out directions using chapter vocab.

I've seen tons of foldable ideas, but anyone have any that really hit the ball out of the park for Pre-Algebra, Algebra, and Geometry? 

Anyone have any tips on how to make and use them most effectively in class?

In the meantime, I'm going to keep creeping on their lunch table. Cool kids, here I come!