Exploding Dots
Overview
A global phenomenon is underway. Pure math joy is sweeping the planet!
Learn about the phenomenon here.
Over a 7.8 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 thatExploding 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. GUIDEBOOK, VIDEO PLAYLIST, INTERACTIVE WIDGET
Download the Exploding Dots Guidebook and/or watch all the videos in a PlayList.
Play with an interactive version of the workbook and Exploding Dots widget.
EXTRA: Here’s a great Mind-Reading Trick that serves as extra 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.
3. View the lessons on this site
Just work your way through what you see here.
Enjoy!
Early support for the development of this work was graciously given by the Edward E. Ford Foundation.
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 Can One Do Explosions in Any Order? |
| 9.4 Base Two in Disguise? Base Three? |
| 9.5 Going Really Wild |
| 11.0 EXPERIENCE 11: Grape Codes & Napier’s Checkerboard |
| 11.1 Grape Codes |
| 11.2 Napier’s Checkerboard |
| 11.3 Addition |
| 11.4 Subtraction |
| 11.5 Multiplication |
| 11.6 Division |
| 11.7 Wild Explorations |
| 12.0 MAKE SPACE with EXPLODING DOTS |
| 12.1 Invent. Create. Enjoy! |
| 12.2 Funville Adventure: A story by A.O. Fradkin and A.B. Bishop |
| 13.0 Kids Explain Math to Kids |
| 13.1 Kid Videos by Kids for Kids |
| 14.0 Web Apps and Tools: Where to Play with Machines Online |
| 14.1 The Official Scolab.com Suite |
| 15.0 ChipChip: A Game Invented by Jim Propp and powered by Happy Numbers |
| 15.1 Jim Propp’s CHIP-CHIP Game (Powered by HAPPY NUMBERS) |
| 16.0 PUZZLES EXPLAINED WITH EXPLODING DOTS |
| 16.1 Puzzles Explained with Exploding Dots |
| 17.0 Adventures in Exploding Dots: SIX-EIGHT LESSONS |
| Protected: 17.1 The Lessons |
| Protected: 17.2 Workbooks for Download |
| 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.
BROWSE BOOKS
Guides & Solutions
Dive deeper into key topics through detailed, easy to follow guides and solution sets.
BROWSE GUIDES