## Exploding Dots

## Overview

**During October 10 -17, 2017 a global phenomenon occurred. ****It was the world’s inaugural Global Math Week.**

**Over a million students and teachers from 168 different countries and territories experienced the uplifting joy of Exploding Dots. All was grassroots. All was volunteer. And all was propelled by a beautiful global community educators and math lovers simply wanting to share the joy and wonder of meaningful mathematics. **

From our survey:

96.8% of teachers agreed or strongly agreed that *Exploding Dots* helped students see mathematics as more approachable, 96.6% as more enjoyable, 96.1% as making sense, and 93.1% as helping students be more confident in mathematics.

75.5% of teachers said that *Exploding Dots* changed their own perception of mathematics in some way with 97.7% agreeing or strongly agreeing that* Exploding Dots* made mathematics more enjoyable, 97.3% as more approachable, and 96.0% as more understandable.

You too can enjoy the wonders of *Exploding Dots*, here, in this course, or with the web app powered by *Scolab*.

**Scroll down to see and access the Exploding Dots chapters. Play with them at your leisure. **(Warning: When you start one, you won’t want to stop!

It all begins with 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 mathematical story will knock your socks off!

*Scolab’s *The Exploding Dots Experience by The Global Math Project and Buzzmath

On a final note, here’s a fun wordless animation. It’s a teaser for the course. Can you figure out what is going on?

## Lessons

1.0 EXPERIENCE ONE: The Machines |

1.1 Welcome |

1.2 The \(1 \leftarrow 2\) Machine |

1.3 Other Machines |

1.4 The \(1 \leftarrow 10\) Machine |

1.5 Wild Explorations |

1.6 Solutions |

2.0 EXPERIENCE TWO: Insight |

2.1 Welcome |

2.2 Explaining the \(1 \leftarrow 2\) Machine |

2.3 Explaining More Machines |

2.4 We Speak \(1 \leftarrow 10\) Machine |

2.5 Wild Explorations |

2.6 Solutions |

3.0 EXPERIENCE THREE: Addition and Multiplication |

3.1 Welcome |

3.2 Addition |

3.3 (Optional) The Traditional Algorithm |

3.4 Multiplication |

3.5 (Optional) Multiplication by 10 |

3.6 (Optional) Long Multiplication |

3.7 Wild Explorations |

3.8 Solutions |

4.0 EXPERIENCE FOUR: Subtraction |

4.1 Welcome |

4.2 Piles and Holes; Dots and Antidots |

4.3 Subtraction |

4.4 (Optional) The Traditional Algorithm |

4.5 Wild Explorations |

4.6 Solutions |

5.0 EXPERIENCE FIVE: Division |

5.1 Welcome |

5.2 Division |

5.3 (Optional) Division by 10 |

5.4 Remainders |

5.5 (Optional) The Traditional Algorithm |

5.6 Wild Explorations |

5.7 Solutions |

6.0 EXPERIENCE SIX: All Bases, All at Once: Polynomials |

6.1 Welcome |

6.2 Division in Any Base |

6.3 A Problem! |

6.4 Resolution |

6.5 (Optional) Remainders |

6.6 (Optional) The Remainder Theorem |

6.7 (Optional) Multiplying, Adding, and Subtracting Polynomials |

6.8 Wild Explorations |

6.9 Solutions |

7.0 EXPERIENCE SEVEN: Infinite Sums |

7.1 Welcome |

7.2 Infinite Sums |

7.3 (Optional) Should we believe infinite sums? |

9.0 EXPERIENCE NINE: Weird and Wild Machines |

9.1 Welcome |

9.2 Base One-and-a-half? |

9.3 Does Order Matter? |

9.4 Base Two? Base Three? |

9.5 Going Really Wild |

11.0 EXPERIENCE 11: Napier’s \(1 \leftarrow 2\) Machine |

11.1 Napier’s Checkerboard |

11.2 Addition |

11.3 Subtraction |

11.4 Multiplication |

11.5 Division |

11.6 Wild Explorations |

12.0 MAKE SPACE with EXPLODING DOTS |

12.1 Invent. Create. Enjoy! |

13.0 Kids Explain Math to Kids |

13.1 Kid Videos by Kids for Kids |

100.0 Where did these ideas come from? |

100.1 To answer … |

Return to List of Courses |

## 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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