My principal has agreed, in theory, for me to teach an elective next year entirely dedicated to exploratory math. I am absolutely thrilled, of course! I am also trying to put together a pitch for the class that will excite the administration and get middle school kids interested in taking the class.
For context, this would be either a semester-long or year-long math course for 7th/8th graders in my school. I want the stuff we do to be accessible to kids who aren't traditionally successful in math class, although I am going to assume some familiarity with any concepts up through 6th grade.
Here is a rough breakdown of the categories I am interested in developing.Note that this isn't the sequence I'll teach any of these. In fact, I'll probably mix puzzles, patterns and art in the fall and more puzzles, patterns, and games in the spring. But I need categories in order to properly brainstorm.:
Math Art (9 Weeks)
MC Escher and Tessellations
Fractals such as the Sierpinski Triangle and the Koch Snowflake
Curve Stitching (making curved shapes from straight lines)
Building the Platonic Solids and a stellated dodecahedrons
The Four-Color Theorem
Perspective, the Vanishing Point, and Dilations
Impossible Triangles and Stars
Megan Schmidt's Spiral investigations
Math Games (9 Weeks)
Solved Games
-Tic Tac Toe
-The 100 Game
-Nim
Rigged Games
-Even/Odd with Dice (sum vs product)
-Roulette
Probability and Odds
-Geometric Probability
-Expected Value
Combinatorics
Designing Our Own Game
Math Puzzles and Patterns (18 Weeks)
This section is the broadest, but I consider it a whirlwind tour through all the classic cool math stuff like Fibonacci, Golden Ratio, etc, along with lots of non-routine problems to solve.
The Fibonacci Sequence and the Golden Ratio
The Bridges of Konigsberg and Graph Theory
Growing, Shrinking, and the Square-Cube Law (Why is Ant Man Impossible?)
Exploding Dots and the base system
Prime Numbers (so much to do with prime numbers!)
The Moscow Puzzles
Martin Gardner’s books
PLEASE help me with other suggestions! I especially need ideas for the back half of the class. I know there is a ton of stuff out there, so give me everything you love to do on special days in class. Thanks in advance for helping to create the greatest math class of all time (I hope)!