Exploding Dots


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?


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1.0 EXPERIENCE ONE: The Machinesarrow
1.1 Welcomearrow
1.2 The \(1 \leftarrow 2\) Machinearrow
1.3 Other Machinesarrow
1.4 The \(1 \leftarrow 10\) Machinearrow
1.5 Wild Explorationsarrow
1.6 Solutionsarrow
2.0 EXPERIENCE TWO: Insightarrow
2.1 Welcomearrow
2.2 Explaining the \(1 \leftarrow 2\) Machinearrow
2.3 Explaining More Machinesarrow
2.4 We Speak \(1 \leftarrow 10\) Machinearrow
2.5 Wild Explorationsarrow
2.6 Solutionsarrow
3.0 EXPERIENCE THREE: Addition and Multiplicationarrow
3.1 Welcomearrow
3.2 Additionarrow
3.3 (Optional) The Traditional Algorithmarrow
3.4 Multiplicationarrow
3.5 (Optional) Multiplication by 10arrow
3.6 (Optional) Long Multiplicationarrow
3.7 Wild Explorationsarrow
3.8 Solutionsarrow
4.0 EXPERIENCE FOUR: Subtractionarrow
4.1 Welcomearrow
4.2 Piles and Holes; Dots and Antidotsarrow
4.3 Subtractionarrow
4.4 (Optional) The Traditional Algorithmarrow
4.5 Wild Explorationsarrow
4.6 Solutionsarrow
5.0 EXPERIENCE FIVE: Divisionarrow
5.1 Welcomearrow
5.2 Divisionarrow
5.3 (Optional) Division by 10arrow
5.4 Remaindersarrow
5.5 (Optional) Deep Explanationarrow
5.6 (Optional) The Traditional Algorithmarrow
5.7 Wild Explorationsarrow
5.8 Solutionsarrow
6.0 EXPERIENCE SIX: All Bases, All at Once: Polynomialsarrow
6.1 Welcomearrow
6.2 Division in Any Basearrow
6.3 A Problem!arrow
6.4 Resolutionarrow
6.5 (Optional) Remaindersarrow
6.6 (Optional) The Remainder Theoremarrow
6.7 (Optional) Multiplying, Adding, and Subtracting Polynomialsarrow
6.8 Wild Explorationsarrow
6.9 Solutionsarrow
7.0 EXPERIENCE SEVEN: Infinite Sumsarrow
7.1 Welcomearrow
7.2 Infinite Sumsarrow
7.3 (Optional) Should we believe infinite sums?arrow
8.0 EXPERIENCE EIGHT: Decimalsarrow
8.1 Welcomearrow
8.2 Decimalsarrow
8.3 Adding and Subtracting Decimalsarrow
8.4 Multiplying and Dividing Decimalsarrow
8.5 Converting Fractions into Decimalsarrow
8.6 Irrational Numbersarrow
8.7 Decimals in Other Basesarrow
8.8 Wild Explorationsarrow
8.9 Solutionsarrow
9.0 EXPERIENCE NINE: Weird and Wild Machinesarrow
9.1 Welcomearrow
9.2 Base One-and-a-half?arrow
9.3 Does Order Matter?arrow
9.4 Base Two? Base Three?arrow
9.5 Going Really Wildarrow
10.1 Invent. Create. Enjoy!arrow
11.0 Kids Explain the Math to Kidsarrow
11.1 Kid Videos by Kids for Kidsarrow
100.0 Where did these ideas come from?arrow
100.1 To answer …arrow
Return to List of Coursesarrow




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