## Mathematical Explorations to Support Common Core## ...going beyond numbers to mathematical thinking |

An overarching value that infuses the Common Core Mathematics Standards is to introduce what it means to think like a mathematician. The lessons described below were developed specifically to meet this objective. Each lesson introduces mathematical concepts generally not part of the regular classroom instructional curriculum, but that are ideas young people can explore and develop just as if they were a mathematicians. The focus in each lesson is on the process of discovery vs. the specific mathematical content. While the lessons have math content they are more about thinking processes.

This project is a work-in-progress. Additional lesson will be posted after they are classroom tested. Your feedback, positive and negative, is greatly appreciated. Please feel free to email me.

FILE NAME | QUESTIONS EXPLORED |

big
numbers counting |
How big is a big number? Is there a biggest? What does a million look like? What does a googol look like? |

big
numbers calculating |
How fast is the earth moving? How far does the Earth (with us onboard) travel in a year? How fast is light? |

happy-sad
arithmetic |
What do you get when you add a happy and sad face? A Sappy? Playing with picture numbers (but really an introduction to integers). |

math
art fractals |
How can you construct a
picture of a tree with a mathematics rule? Can
math describe nature? |

math
art polygrams |
What do you get inside a pentagon when you draw some diagonals? Do you always get a star when you draw the diagonals of a polygon? |

patterns in our number system | Patterns, patterns and more
patterns (exploring our fabulous number systems): Can
you find any vertical patterns? Can you find any
diagonal patterns? Can you find any patterns when you add
the digits of a number? |

topology
curves |
Is that an open or close
curve? Are those points inside or out? |

topology traceability | Can you trace that curve without lifting your pencil? What does it mean that the letters A and R are topologically equivalent? |

topology networks | Can you discover a rule for when a curve is traceable? |

topology map problem | What is the smallest number of colors you need to color a map? |

topology Mobius Strip | How can a paper strip have
just one side? |

- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.

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Jason Frand, PhD. Math Olympiad Coach and

Los Angeles County-wide Math Olympiad Tournament Chairperson Linwood Howe Elementary School Culver City Unified School District Adjunct Assistant Professor, Retired Assistant Dean and Director, Retired UCLA Anderson School of Management Created July 20, 2014 Updated May 13, 2015