When I was a kid, we had this super high-tech board game called Stop Thief!. The gist was this: someone committed a crime somewhere on the game board, which was rife with jewelry displays, unattended cash registers and safes. Your job as the detective was to identify where the thief was. The location of the thief was tracked by a phone looking device that calls to mind those old Radio Shack commercials with car phones. After each turn, the invisible thief would move some number of spaces away from the crime scene. The phone made these noises indicating where he could be – opening a door, climbing through a window, breaking glass. Based on these clues and the number of turns that elapse, you’d try to identify where he was.
Fast-forward a few years. We all remember this scene from The Fugitive:
These are the artifacts that were going through my head as I designed this lesson, linking the pythagorean theorem and equations of circles. In it, students must overlay a circle to establish a “perimeter” (side note: shouldn’t Tommy Lee Jones have used the term “circumference?”).
While this task only starts from the origin, you could quickly modify it to have other starting points, which would allow students to explore what the equation of a circle looks like when you center it wound non-origin points. I’d expect that to occur the next day or later in the lesson as part of the debrief.
Feel free to tweak it to make it better. The desmos graph is linked below, along with a couple word handouts.
(Note: a version of this task will appear in my forthcoming book from Stenhouse Publishers, Necessary Conditions.)
The set-up: a crime has been committed and it’s up to the students to establish a perimeter based on how much time has elapsed. After using the pythagorean theorem a few times to identify buildings the thief could be hiding in.
Given the time that’s passed and typical footspeed, the criminal could be anywhere up to 5 kilometers from the crime scene.
Which of the buildings above could he be in?