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:
- Get a blueprint for your school (I scanned the fire escape map from my wall) and paste it into Geometer’s Sketchpad or Geogebra.
- (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.
- 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:
- 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:
- Repeat steps 3 & 4 until you have a whole bunch of these triangles.
- 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.
- 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.