ADVENTURES IN EXPLODING DOTS Exploration 4 SUBTRACTION An

ADVENTURES IN EXPLODING DOTS: Exploration 4 SUBTRACTION An astonishing way to make sense of long subtraction

Subtraction is the addition of the opposite!

Subtraction

Antidots (tods) Dots and Antidots

Long Subtraction Consider Going left to right we get: How could we convert this answer to one that society expects? 512 + -347

Long Subtraction Unexplosions make the answer 165 appear.

Long Subtraction What is the straightforward answer without regard to what society thinks? Can you fix up your answer to one that society would accept? Try this one too! First, what does your calculator should be the answer? Do you get that answer too?

Long Subtraction

Long Subtraction Challenge: How might you handle and interpret this subtraction problem?

The Standard Algorithm What is the standard way to compute the following? Is it fundamentally different from the Exploding Dots way?

Web App Here’s a web app that allows you to play with all the machines. https: //www. explodingdots. org/station/Open. Machines. Antidotia

Something Wild Fill in each and every box with either one dot or one tod. The picture shows the number 16 + (-8) + (-4) + 2 + (-1), which is 5. a) Show that the number 17 can be represented in the same way, with each box containing either one dot or one tod (and with no box empty). b) Show that the number -17 can also be represented this way. c) Find all the numbers that can be formed by placing single dots and tods in the five rightmost boxes of this machine. How do you know your list is complete?