Math Dance Conways Rational Tangles Dave Klanderman Calvin

Math Dance? Conway’s Rational Tangles Dave Klanderman Calvin University 2020 Math in Action Conference

Outline for Session • Context for activity (What is a Math (Teacher) Circle? ) • Showing off your math dance moves • • • The basic moves (with demonstration group) Initial cluster activity (using smaller models) Analysis of the Rotate dance move Advanced dance class The “coolest” tangle • Discussion: How can you implement this in your classroom?

Context Math Teacher Circles Math Circles Michigan Learning Standards for this activity: 6. EE. A 2(a); 7. EE. B 4; 8. F. A 1; HSF. BF. A 1(a, b) (Details on Handout)

The Basic Dance Moves • Volunteers? • Three valid dance moves: Twist, Rotate, (Display)

Small Group Activity • How can you “undo” a single Twist? (Note: you may not “untwist”!) • What about 2 Twists? • 3 Twists? • … • n Twists?

Applying Function Notation • Easy case: Twist • Hard case: Rotate • What do we know already? • What potential functions might work? (How can be decide? )

Advanced Dance Class • “Visible” example (The “Messy” Tangle) • “Hidden” example (The “Coolest” Tangle)

Discussion • How could this activity be used in an Algebra classroom? • What about a Grade 6 or Grade 7 classroom? Modifications? • Other questions?

Thank you! • Resources (available on conference website) • Handout from today’s session • Conway’s Rational Tangles – Teacher notes • For more information, contact dbk 6@calvin. edu