Exploding Dots

Overview

A global phenomenon is underway. Pure math joy is sweeping the planet!

Learn about the phenomenon here.

Over a 7.4 million students and teachers from 170 different countries and territories have experienced the uplifting joy of Exploding Dots

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!

 

HOW TO ENJOY EXPLODING DOTS: Three Ways

1. BRAND NEW:  A teacher/student classroom guide chock full of new material and new videos! 

Watch a short video explaining what’s in the guide. 

Download the guide and/or watch all the videos in a new PlayList.

EXTRA: Here’s the description of a great Mind-Reading Trick that serves as super fun motivation for the Exploding Dots story.

Our deepest thanks to the MARY P. DOLCIANI-HALLORAN FOUNDATION for supporting this work. 

 

2. The GLOBAL MATH PROJECT website 

Learn about the GLOBAL MATH PROJECT and all the math joy we offer the world.

See Exploding Dots there too in multiple formats.

 

LOW TECH: Share our videos and use our written materials.

NO TECH: Download our teaching guides and use them to give no-tech lessons.

HIGH TECH: Enjoy the wildly popular Exploding Dots WEB APP powered by Scolab. Count classroom KAPOWS!

 

3. View the lessons on this site

Just work your way through what you see. Enjoy! 

 

 

 

Early support for the development of this work was graciously given by the Edward  E. Ford Foundation.

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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 Can One Do Explosions in Any Order?arrow
9.4 Base Two in Disguise? 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 Jim Propp’s CHIP-CHIP Game (Powered by HAPPY NUMBERS)arrow
16.0 PUZZLES EXPLAINED WITH EXPLODING DOTSarrow
16.1 Puzzles Explained with Exploding Dotsarrow
17.0 Adventures in Exploding Dots: SIX-EIGHT LESSONSarrow
Protected: 17.1 The Lessonsarrow
Protected: 17.2 Workbooks for Downloadarrow
100.0 Where did these ideas come from?arrow
100.1 To answer …arrow
Return to List of Coursesarrow

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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