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Station  9Antidots

In our dots-and-boxes machines we’ve been working with dots, which we draw as solid dots.

We now need the notion of the opposite of dot.

Like matter and antimatter, which annihilate when brought together, a dot and an antidot should also annihilate – POOF! – when brought together to leave nothing behind.
Let’s draw antidots as hollow circles.

If a dot represents $1$, then an antidot represents $-1$, and bringing one of each together leaves zero.

Question 1

Annihilate the dot and the antidot by dragging them together!

Even without a machine we can conduct basic arithmetic with dots and antidots.

Can you make sense of these pictures?

By the way, some students prefer to call the opposite of a dot a tod. Can you guess what made them think of that name?

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