Activity Database

Search
Activity Authors
Activity Circles
Click To Sort By
Grade
Audience
  • 1st - 2nd (12)
  • 3rd - 5th (30)
  • 6th - 8th (83)
  • 9th - 12th (85)
  • College Level (72)
  • For Teachers (81)
Topics
Topics
  • Mathematical Modeling (15)
  • Number Theory (25)
  • Parity / Invariants (2)
  • Problem Solving / General (39)
  • Probability and Statistics (3)
  • Social Justice Mathematics (5)
  • Algebra / Arithmetic (33)
  • Combinatorics (31)
  • Geometry (36)
  • Mathematical Games (26)
Supporting Materials
Supporting Materials
  • Facilitator Guides (88)
  • Handouts (38)
  • Lesson Plan (10)
  • Photos & Videos (28)
  • References (36)
  • Virtual Tools (17)
Session Styles
Session Styles
  • Integrates Technology (17)
  • Kinesthetic Element (11)
  • Manipulatives (33)
  • Multiple Representations (33)
  • Problem Posing (45)
  • Problem Sets (51)
  • Try a Smaller Problem (40)
  • Work Backwards (21)
Mathematical Practices
Mathematical Practices
  • MP1 - Make sense of problems and persevere in solving them. (83)
  • MP2 - Reason abstractly and quantitatively. (53)
  • MP3 - Construct viable arguments and critique others' reasoning. (58)
  • MP4 - Model with mathematics. (58)
  • MP5 - Use appropriate tools strategically. (40)
  • MP6 - Attend to precision. (40)
  • MP7 - Look for and make use of structure. (72)
  • MP8 - Look for and express regularity in repeated reasoning. (61)

Tiling With Pentagons

By:


A pentagonal tiling is a tiling of the plane where each individual piece is in the shape of a pentagon. The plane cannot be tiled with regular pentagons. However, are there any convex pentagons that can tile the plane? This session explores various pentagons and their tiling abilities. From 1918 to 1985, fourteen irregular pentagons that would tile the plane were discovered. On August 14, 2015, Casey Mann, Jennifer McLoud, and David Von Derau of the University of Washington Bothell announced that they discovered a fifteenth pentagon. Interestingly, in 2017, Michaël Rao proved that there were no more than these...