Coskey, Samuel. Ellish, Paul. Wood, Japheth (2020). Touching Infinity. In S. Bowen (Ed.), Math Circle Activity Database. American Institute of Mathematics. https://mathcircles.org/activity/touching-inifity

Touching Infinity: Hyperbinary Numbers and Fraction Trees

Contributor(s): Japheth Wood, Paul Ellis, Samuel Coskey

Math Circles: MTC Network

Activity Description
Topics Covered
Session Styles
Mathematical Practices

Are there more fractions than counting numbers? Surprisingly, an investigation into binary notation can help us answer this question! This session explores the binary number system. Participants will investigate Hyperbinary numbers, create a Fraction Tree, and discover connections between them.

Number Theory

Manipulatives
Multiple Representations
Try a Smaller Problem

MP1 - Make sense of problems and persevere in solving them.
MP2 - Reason abstractly and quantitatively.
MP3 - Construct viable arguments and critique others' reasoning.
MP5 - Use appropriate tools strategically.
MP6 - Attend to precision.
MP7 - Look for and make use of structure.