Exploding Dots

Overview

ACCESS TO ALL LESSONS AND VIDEOS LIE AT THE BOTTOM OF THIS SCREEN  

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. (And it has since grown to well over 4 million!) 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.

By popular demand we are doing it again! Join us as we reach 10 million students across the globe!

GLOBAL MATH WEEK 2018

October 10-17

 

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

A one-hour Exploding Dots video of a lecture at Scottsdale Community College is here.

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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Lessons

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) The Traditional Algorithmarrow
5.6 Wild Explorationsarrow
5.7 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
10.0 EXPERIENCE TEN: Unusual Mathematics for Unusual Numbersarrow
10.1 A Troubling Number for our Usual Mathematicsarrow
10.2 A Troubling Number our Usual Mathematics Rejectsarrow
10.3 Some Unusual Mathematics for Unusual Numbersarrow
10.4 A Serious Flaw of Our Ten-adic Numbersarrow
10.5 Who Really Cares about Ten-adic and other “adic” Number Systems?arrow
11.0 EXPERIENCE 11: Grape Codes & Napier’s Checkerboardarrow
11.1 Grape Codesarrow
11.2 Napier’s Checkerboardarrow
11.3 Additionarrow
11.4 Subtractionarrow
11.5 Multiplicationarrow
11.6 Divisionarrow
11.7 Wild Explorationsarrow
12.0 MAKE SPACE with EXPLODING DOTSarrow
12.1 Invent. Create. Enjoy!arrow
12.2 Funville Adventure: A story by A.O. Fradkin and A.B. Bishoparrow
13.0 Kids Explain Math to Kidsarrow
13.1 Kid Videos by Kids for Kidsarrow
14.0 Web Apps and Tools: Where to Play with Machines Onlinearrow
14.1 The Official Scolab.com Suitearrow
15.0 ChipChip: A Game Invented by Jim Propp and powered by Happy Numbersarrow
15.1 The Game: STAGE 1arrow
15.2 The Game: STAGE 2arrow
15.3 The Game: STAGE 3arrow
15.4 The Game: STAGE 4arrow
15.5 The Game: STAGE 5arrow
15.6 The Game: STAGE 6arrow
100.0 Where did these ideas come from?arrow
100.1 To answer …arrow
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Resources

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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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