Play Auditorium

This is a really cool game sent to me recently. It is called Auditorium, and is made by a company called Cipher Prime. The goal is to move around the circular pucks on the board and change their radius to control the flow that is coming into the screen. When the flow enters the circular puck, it changes direction depending on the circle's symbol direction, position and size. If you can move the flow to hit the things that look like meters, they will start playing music.

Your goal, or problem, for each level is to light all of the meters up at once by directing the flow through them all at the same time. It is really, really fun and visually beautiful. I have been using it with some of my students, and it definitely tests their logical reasoning, problem solving and visual reasoning skills, while engaging them visually, tactially and aurally. From a teaching vantage point, the fact that there are many ways to solve a problem is great for mimicking real world problem solving, and could be used as a way to identify different learning styles across student populations by analyzing a student's solution paths.

In addition, one of the most interesting and useful areas of applied mathematics is that of DYNAMICAL SYSTEMS, which often deals with the behavior of fields and flows like we see in this game. This game setting offers a setting to introduce the idea of Curl (in two-dimensions at least), which can be one of the most difficult in multivariable calculus and dynamical systems. The puck pieces in Level 2 (Spring) with the crescent on them are actually curl creators -- they cause the flow to curl into a vortex, depending on the radius of the puck.

Writing an equation for how to control the degree of curling in the flow is an important part of understanding a number of physical systems, like fluid dynamics (Wikipedia) and bird flocking:



Check it out here . . . It is really fun.

Play Auditorium

Games that Teach: Algebra v. Cockroaches

THE EQUATION OF A LINE

If you ask most people who have been through high school mathematics what the equation of a line is, a surprising number can spit out "Y equals m x plus b", or y = mx + b. Many of them can even tell you that the "m" stands for the SLOPE, and the "b" stands for the Y-INTERCEPT, and that the number that we pick for each of these parameters controls the appearance of the graph of the line that we get.

But I also don't think many people understand why this equation is so important. Part of the answer is that this particular equation ISN'T that important. Though there are many examples of processes that behave like a line, most often we need much more complicated equations or functions to describe real world phenomena. But what IS important about the equation of the line are the techniques we will use to analyze equations of polynomials of which "mx + b" is an example. In fact, analyzing y = mx + b is one of the simplest cases of a function that we can analyze, which is why it is discussed so often.

To understand how to analyze our equation of a line, and how changing the values of m and b affect the shape of our line, I have been using the game below called Algebra v. Cockroaches, where students need to fill in the equation of the line that the cockroaches are traveling on to be able to exterminate them.

y = mx + b