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:

PDF files of this first chapter

Chapter 6 EXPLODING DOTS (English)

Chapter 6 EXPLODING DOTS Bulgarian (Translated by Stanislav Chobanov)

Chapter 6 EXPLODING DOTS Chinese (Translated by Xinli Wang)


A PDF guide for teaching this experience

Scolab‘s fully interactive web experience

Additional apps by Geogebra, Wolfram, Chee Wei Tan, Ken Wessen, Ulrich Kortenkamp, and more!

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