Finally: A Chance to Merge Math & Physics

Because my students took the statewide End Of Course Test (EOCT) earlier this week, my school allows me to give a final project instead of an exam. This was a big break for me because my kids are tested out and I have no desire to write a 50 question comprehensive multiple guess test that can be graded within mere minutes of it being turned in so that I can close out my gradebook on the insane end-of-semester schedule we all have.

I’ve included the project below for you to enjoy steal. [Galileo’s Ramp (Word, 622kb)]

I start the kids off with understanding position-time and velocity-time graphs

Here’s a little snip:

Later, we move into understanding how quadratic functions can be transformed

There’s more in the full version (I guess that’s kinda obvious). Hit the link above.

I owe a huge debt of gratitude to @occam98, @fnoschese, and @jsb16 for brainstorming with me via Twitter the other night. Y’all were amazing. I opened with, “give me some phenomena that fit a quadratic function.” Also, I would never have finished writing this project tonight if I hadn’t had a horrible day at work. Something about a lousy day makes me want to do better the next.

This project gets students to understand position-time and velocity-time graphs in a rudimentary way, gets them thinking about the quadratic equations that describe those graphs, and helps them begin to understand how to collect data accurately.

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Stuff I’m Doing This Week: Math Taboo

Thanks, Bowman Dickson (@bowmanimal), for Math Taboo! Whenever I tell my kids to give me a definition in their own words, I get some regurgitation of what I already said. No real understanding needed. Enter Math Taboo:

The idea of the real game is to get your partner to guess a word by describing without using any of the five taboo words, which are usually the first words that anyone would go to in a description. So the obvious math equivalent is to pick a term that you are throwing around in your class and get students to describe it without using their go-to math descriptors.

     Please go read the entire original post.

As someone who teaches courses made of 60% English Learners and 40% students who failed math last semester, I’m eager to put this game out there. My students may just enjoy this one.

 

Dude, I love the comment that students make the Taboo cards.

Finding the Best Lock

Can you help me make this into a 3 Acts problem? I was thinking some thing along these lines:

  • Act 1: movie clip of someone trying to crack a combination lock. I want to set up the question “how long will it take?”
  • Act 2: What are the rules for these combination locks? Maybe I could even be so lucky as to find these listed on a website with the number of permutations.
  • Act 3: Which lock will take longer to crack?*
* Interesting factoid: I started this idea with the extension, not the first act. That is, I knew I wanted to present my students with a permutations-of-a-lock problem. I spotted these two locks on a website. Then wondered if kids could tell me which was more secure. For those who have written 3 Acts problems, is this a typical workflow?

Standard schmandard…

Georgia Performance Standards (GPS) for Math: MM1D1b
MM1D1. Students will determine the number of outcomes related to a given event. b. Calculate and use simple permutations and combinations.

Math Question Banks from New York

Recently googled: JMAP ExamView Question Banks of NY Regents math exams…going back to 1890!

Oh, and I go back to work on Tuesday, to a building with 50% more students than in May, to the year my classes’ English Learner population should tip 50%, probably to “float” into other teachers’ classrooms, to teach physics!, to my 8th year in the classroom, and with the best math department in the world. Am I ready? Heck no. Am I excited? Heck yeah!

Polar Clocks

This is the Polar Clock (apparently, it’s soooo 2009). I recommend grabbing the screensaver or smartphone app (Win/Mac/Android/iPhone versions all available). In a pinch, you can watch a video of someone else running the app here.

Polar Clock isn’t precisely a Meyerian[1] What Can You Do With This? creature.  But I do think the Polar Clock falls in the same genus as WCYDWT because it could inspire some pretty cool mathematical investigations.

If you’re a Georgia math teacher, check out standards from Math II, specifically the properties-of-circles stuff under MM2G3.

I ask y’all, what mathy questions does the Polar Clock inspire? Leave ’em in the comments.

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[1] As I understand it, Dan Meyer’s WCYDWT requires that the problem have a hook anyone can guess at, that the math scaffolding can slowly be lowered, and that the photo/video/hologram/whatever look good. I got this based on my reading of http://blog.mrmeyer.com/?cat=70.

Treasure Hunt!

Thanks for the inspiration, Kate Nowak. Your Circumcenters was an amazing lesson that my colleagues and I turned into a full-fledged project.

The day before Thanksgiving break, my students searched for approximately 25 treasures that were hidden inside and out of my school. We secured permission to hide treasures in offices of the most feared administrators, on the doors of teachers the kids love to hate, and on the walls of our halls.

The kids used Geometer’s Sketchpad with an embedded blueprint of our school (upstairs and down) to locate vertices of a triangle as given in a clue, then constructed all 4 points of concurrency. Upon showing me their 4 points, I unlocked a second part of their clue: hints that told them which point of concurrency marks the spot. In a mad dash, the kids grabbed the hall pass, a camera, and embarked on finding the flag. If a teacher or administrator busted them breaking rules or removing the treasure, they forfeited it. Students returned with photographic evidence of them at the site of the treasure flag.

Ignore the Man Behind the Curtain

Or, how this huge project came together

The numbers: Approximately 300 students participating. Three teachers @ 5 hours each to write the project. $400 in treasures and treasure flags.  Seven donors bought some of our supplies through DonorsChoose and we 3 teachers bought the rest.

Here’s how we set the project up:

  1. Get a blueprint for your school (I scanned the fire escape map from my wall) and paste it into Geometer’s Sketchpad or Geogebra.
  2. (In GSP), Right click the image, choose Properties, then uncheck the “Arrow Selectable” checkbox. This way, you and the students can’t move the picture around.
  3. Find a place to hide your treasure! This needs to be at one of the points of concurrency of a triangle. Here’s how we did it: Construct a triangle and all 4 points of concurrency. Get a little GSP help starting on page 22 of “Meet Geometer’s Sketchpad”. Manipulate the triangle by moving vertices until one of the points of concurrency falls in an interesting spot. Here’s one example:Screenshot from GSP showing a triangle and its 4 points of concurrency.
  4. Write a clue to tell students how to place the 3 vertices. Add a second step to the clue that tells them which point of concurrency the need to search out. (That last bit was important as we want students to construct all 4 points of concurrency but only hide treasure beneath one of them.)  In hindsight, I’d spend more time making the clues easy to read and decipher. Clue example:
  5. Repeat steps 3 & 4 until you have a whole bunch of these triangles.
  6. Name each of the treasures, associate prizes with them. Our treasures included: foam airplane toys, playing cards, hand sanitizer, candy, doughnuts for breakfast with a math teacher of your choice, and teacher buys you ice cream with lunch.
  7. Package the clues in interesting envelopes. I found colorful envelopes at a craft supply store.

The project was an amazing success. Kids loved it and were all excited about playing the game — even though we ran it the day before Thanksgiving Break. Teachers: this is completely worth the time to set up for your school. Can’t say enough good about the wonderful donors who helped with $300 worth of goodies, either.

Georgia Performance Standards Alignment:
MM1G3. Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.
e. Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.