Exploding Dots

6.1 Welcome

Lesson materials located below the video overview.

The first chapters of this story have taken us through much of grade school mathematics. Let’s now head on to advanced high school algebra. Whoa!


But here’s the thing: there is nothing to it. We’ve already done all the work.


The only thing we have to realize is that there is nothing special about a \(1 \leftarrow 10\) machine. We could do all of grade school arithmetic in a \(1 \leftarrow 2\) machine if we wanted to, or a \(1 \leftarrow 5\) machine, or even a \(1 \leftarrow 37\) machine. The math doesn’t care in which machine we do it. It is only us humans with a predilection for the number ten that draws us to the \(1 \leftarrow 10\) machine.


Let’s now go through much of what we’ve done. But let’s now do it in all possible machines, all at once!

Sounds crazy. But it is surprisingly straightforward


Supplementary Content for this Experience:

The overall Teacher’s guide: Teaching_Guide_GETTING STARTED

Teacher’s Guide for this Experience: Teaching_Guide_EXPERIENCE_6

Accompanying Student handouts: Handouts_EXPERIENCE_6

Sprinkled throughout these lessons are kid videos, from Goldfish & Robin and friends, explaining the math for kids too. Here is their vision statement.

BOOK CHAPTERS (The on-screen text as a book to download.)

Chapter 6 EXPLODING DOTS (English)

Chapter 6 EXPLODING DOTS Bulgarian (Translated by Stanislav Chobanov)

Chapter 6 EXPLODING DOTS Chinese (Translated by Xinli Wang)

Chapter 6 EXPLODING DOTS Serbian (Translated by Aleksandra Ravas)

Chapter 6 EXPLODING DOTS Spanish (Translated by Cindy Weitzman)


The Global Math Project is honoured to have a number of its partner organizations provide the means to play with and learn about Exploding Dots with newly developed apps, products, and pages especially designed for the project. Click here.  Of course, Scolab (Buzzmath) has the full Exploding Dots story here.


Please join the conversation on Facebook and Twitter and kindly share this page using the buttons below.
Share on Facebook
Tweet about this on Twitter




Take your understanding to the next level with easy to understand books by James Tanton.



Guides & Solutions

Dive deeper into key topics through detailed, easy to follow guides and solution sets.


light bulb


Consider supporting G'Day Math! with a donation, of any amount.

Your support is so much appreciated and enables the continued creation of great course content. Thanks!


Ready to Help?

Donations can be made via PayPal and major credit cards. A PayPal account is not required. Many thanks!