## Exploding Dots

## Overview

Here is a story that isn’t true:

*When I was a young child I invented a machine (not true) that was nothing more than a series of boxes that could hold dots. And these dots would, upon certain actions, explode. And with this machine, in this non-true story, I realized I could explain true things! In one fell swoop I explained all the mathematics of arithmetic I learnt in grade school (true), all of the polynomial algebra I was to learn in high-school (true), elements of calculus and number theory I was to learn in university (true), and begin to explore unanswered research questions intriguing mathematicians to this day (also true)!*

Let me share this story with you. See how simple and elegant ideas connect to elegant and profound ideas in mathematics as a whole. **See how these ideas will COMPLETELY REVOLUTIONIZE your thinking of school arithmetic and algebra and beyond!**

This course will knock your socks off!

## Lessons

2.0 Going to Decimals and \(x\)-mals |

2.1 Introducing Decimals |

2.2 Division and Repeating Decimals |

2.3 \(x\)-mals |

2.4 Some Irrational Thoughts |

2.5 ADDENDUM: Some Fun Extra \(1 \leftarrow 10\) Questions |

3.0 Wild and Weird Explorations |

3.1 On Base One-and-a-Half |

3.2 Base Two? Base Three? |

3.3 Changing the Order of Explosions |

3.4 Negative Bases? Irrational Bases? Going Wild! |

4.0 Connections to the COMMON CORE STATE STANDARDS and MATH CIRCLE WORK |

4.1 Common Core State Standards |

4.2 MATH CIRCLES for Students and for Teachers |

5.0 Where did these ideas come from? |

5.1 To answer … |

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## Resources

## Books

Take your understanding to the next level with easy to understand books by James Tanton.

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## Guides & Solutions

Dive deeper into key topics through detailed, easy to follow guides and solution sets.

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