Matthias Kawski and Michael Hall took the lead in developing this circle session on Tiling and induction for the 2011 Circle on the Road workshop.

**Apprentices:** Linda Green, Martin Montgomery, Nina Otterson

**Target audience:** Advanced middle school and high school students (teachers welcome)

Given a set of bricks of whatever shape and a box of whatever

shape, every child knows what to do: Start packing the bricks

into the box. Sometimes it does not work without leaving empty

spaces, sometimes an elaborate strategy is needed.

This session focuses on planar problems: Use a set of flat

tiles of rectangular, triangular and other shapes to tile

the floor of a more or less odd shaped bathroom (without

cutting any tiles, without any gaps or overlays).

Mathematically, sometimes impossibility can be established using

some kind of parity argument parity. As the rooms get larger (or

the tiles get smaller) it becomes natural to use solutions of

smaller problems. This naturally suggests and leads to formal

induction arguments.

A lesson plan is attached below. In addition templates for five different

triangular grids are attached, a copy of the student hand out, and a proof are attached.

Attachments | |
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tiling.pdf | |

Triangle 1.pdf | |

Triangle 2.pdf | |

Triangle 3.pdf | |

Triangle 4.pdf | |

Triangle 5.pdf | |

Tiling-handout.pdf | |

Triominos1.pdf |