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Arithmos
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Arithmos

Station  F
The Traditional Addition Algorithm 

How does this dots-and-boxes approach to addition compare to the standard algorithm most people know?

Question 1

Let’s go back to the example 358+287358 + 287. Most people are surprised by the straightforward left-to-right answer
513155|13|15.

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Write on a piece of paper the traditional way to perform this addition problem.
Did you perform an explosion? First with 1515 or with 1313?
Did you perform a second explosion?
Play with the machine to see if you can make sense of matters for yourself, or read my thoughts below.

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The traditional algorithm has us work from right to left, looking at 8+78 + 7 first.

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But in the algorithm we don’t write down the answer 1515. Instead, we explode ten dots right away and write on paper a 55 in the answer line together with a small 11 tacked on to the middle column. People call this carrying the one and it – correctly – corresponds to adding an extra dot in the tens position.
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Now we attend to the middle boxes. Adding gives 1414 dots in the tens box (5+85 + 8 gives thirteen dots, plus the extra dot from the previous explosion).

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Now we perform another explosion.
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On paper, one writes 44 in the answer line, in the tens position, with another little 11 placed in the next column over. This matches the idea of the dots-and-boxes picture precisely.

And now we finish the problem by adding the dots in the hundreds position.

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So the traditional algorithm works right to left and does explosions (“carries”) as one goes along. On paper it is swift and compact and this might be why it has been the favored way of doing long addition for centuries.

The Exploding Dots approach works left to right, just as we are taught to read in English, and leaves all the explosions to the end. It is easy to understand and kind of fun.

Both approaches, of course, are good and correct. It is just a matter of taste and personal style which one you choose to do. (But feel free to come up with your own new, and correct, approach!)

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