# The Magic & Joy of Exploding Dots: A revolutionary concept that changes the way we learn and teach mathematics

## byKiran Ananthpur BaccheContribution byJames TantonIntroduction byJames Propp

### Paperback | October 8, 2018

### Pricing and Purchase Info

$32.95

^{®}points

Prices and offers may vary in store

### about

In October 2017, over one million students and teachers from 168 countries and territories were transfixed by a universal story that together, they explored. In Tanzania, a class gathered excitedly around the chalkboard as the teacher began to tell the story. New York City high schoolers drew illustrations on a whiteboard. Ponytailed elementary school girls in Saudi Arabia animatedly explored the key ideas using colorful magnetic dots. In Romania, middle grade students played with the online version on their laptops, exclaiming aloud at each new twist. And in Zimbabwe, students recreated the story for themselves using nothing but pebbles and hollows dug into the ground.

What kind of a story is this that has the power to engage students all over the world, transcending language, borders, and technology? Why, it’s a story of the deeply human endeavor of mathematics!

It’s the mathematics of Exploding Dots!

Comments from participants and teachers around the world:

“Hands up in the air in triumph! Decades of believing I couldn’t do math – poof! Exploded!”

“Exploding Dots has changed my mind, and thus my life! Thank you!”

The following ISBNs are associated with this title:

ISBN - 10:9388459113

ISBN - 13:9789388459112

Look for similar items by category:

#### Educational/Developmental Value:

#### Durability:

#### Hours of Play:

Table of Contents

TABLE OF CONTENTS The Global Math Project – Uplifting Mathematics for All Introduction 1.0 Basic Concepts 1.1 Welcome! 1.2 Other Machines 1.3 Wild Explorations 1.4 Solutions 2.0 Place Value and Base Systems 2.1 What are these machines really doing? 2.2 Wild Explorations 2.3 Solutions 3.0 Standard Arithmetic in a non-Standard Way 3.1 Addition 3.2 Multiplication 3.3 Wild Explorations 3.4 Solutions 4.0 More Standard Arithmetic in an Even More non-Standard Ways 4.1 Negative Numbers 4.2 Subtraction 4.3 The Traditional Subtraction Algorithm 4.4 Division 4.5 Remainders 4.6 The Traditional Division Algorithm 4.7 Wild Explorations 4.8 Solutions 5.0 Polynomial Algebra 5.1 Division in any Base 5.2 A Problem 5.3 Resolution 5.4 Remainders 5.5 The Remainder Theorem 5.6 Multiplying Polynomials 5.7 Adding and Subtracting Polynomials 5.8 Wild Explorations 5.9 Solutions 6.0 Two-Dimensional Exploding Dots 6.1 Exploding Dots in 1-Dimension 6.2 Exploding Dots in 2-Dimensions 6.3 Polynomial Division with 2D Exploding Dots 6.4 More Examples of 2D Exploding Dots 7.0 Interleaved Exploding Dots and Roman Numerals 7.1 Interleaved Exploding Dots Machine 7.2 Interleaved Exploding Dots Machine - Properties 7.3 Roman Numeral Exploding Dots Machine 7.4 Converting Hindu-Arabic numbers into Roman Numbers 7.5 Converting Roman Numbers into Hindu-Arabic Numbers 7.6 Validation of Roman Numbers 7.7 Division with Roman Numbers 8.0 Decimals and Fractions 8.1 Discovering Decimals 8.2 Adding and Subtracting Decimals 8.3 Multiplying and Dividing Decimals 8.4 Converting Fractions into Decimals 8.5 Irrational Numbers 8.6 Decimals in Other Bases 8.7 Wild Explorations 8.8 Solutions 9.0 Playing with Other Bases 9.1 Negative Bases and Negabinary Numbers 9.1.1 Exploding Dots with Intercrossed Rules 9.1.2 Negative Base Number System 9.1.3 Properties of a Negabinary Machine 9.1.4 Negabinary Machines in Action 9.2 Fractional Number Base 140 9.2.1 Base One-and-a-Half 9.3 Circular Exploding Dots and the Imaginary Number System 9.3.1 Imaginary Number System 9.3.2 Circular Exploding Dots 9.3.3 Circular Exploding Dots - Properties 9.3.4 Circular Exploding Dots in Action 9.4 Irrational Number Base and the Pascal Triangle 9.4.1 Exploding Dots Machine with Energized Dots 9.4.2 [1←] Exploding Dots Machine in Action 9.4.3 Number Systems with Base of the form (a+) 9.4.4 The Pascal Diagonal Exploding Dots Machine in Action 9.5 Going Wild with Bases 9.6 Does Order Matter? 10.0 Ten-adic Thinking with Exploding Dots 10.1 A Troubling Number for our Usual Mathematics 10.2 A Troubling Number for our Usual Mathematics Rejects 10.3 Some Unusual Mathematics for Unusual Numbers 10.4 A Serious Flaw of Ten-adic Numbers 10.5 Who really cares about ten-adic and other “adic” number systems? 11.0 Napier’s Checkerboard 11.1 Introduction 11.2 Addition 11.3 Subtraction 11.4 Multiplication 11.5 Division 11.6 Wild Explorations 12.0 Square Root and Squares 12.1 The Four Properties 12.2 Square Root of a Polynomial 12.3 Square Root of another Polynomial 12.4 Square Root of an Integer 12.5 Square of an Integer 12.6 Square of a Polynomial 13.0 Modulo Arithmetic with Exploding Dots 13.1 The Modulo Machine 13.2 A Simple Problem 13.3 The Modulo-5 Machine 13.4 A Modulo-8 Quaternary Machine 13.5 Modulo Machines with Antidots 14.0 Vedic Mathematics and Exploding Dots 14.1 Nikhilam Sutra - Division 14.2 Exploding Dots Division using Nikhilam concept 14.3 Nikhilam Sutra - Multiplication 14.4 Exploding Dots Multiplication using Nikhilam concept 15.0 Infinite Series and Sums 15.1 Some Series 15.2 Should we Believe Infinite Sums? 16.0 Exploding Dots Card Game 17.0 Web Resources