Thursday, January 30, 2014

Napier bones

Today was a short school day for us because H. had (another) pre-op appointment. (For those of you have never had the joy of a child going through surgery, what you don't realize is that for the two weeks preceeding the surgery your life is filled with innumerable appointments at doctor's offices at the exactly the same time you become obsessed with keeping your child away from germs because if the child has a cold, the surgery will have to be postponed. It makes for parental craziness.) This is why we spent the remaining part of the morning opening up the Multicultural Math learning box which we had checked out of the Field Museum.

Inside the box were the things you would expect to find... abacuses (abici? what is the plural for that noun?) and tangrams. But there was also something I had never heard of: Napier bones. These are the coolest things and I'm sure that someone with a better math brain than mine could figure out how the series of numbers were figured out. Have you ever heard of them? They were invented by a Scotman, John Napier, in the 17th century. They were originally made out of bone or wood and merchants used them to aid in accounting. Really, what they are is a pretty nifty way to multiply.

Here is what they look like:


Each of these are long rods with numbers written on them. It took us a while to figure out how they work, but we managed and have been playing around with them ever since.

How do they work? Let's take the problem 6 x 635 as an example. First, I take the index rod and lay out the rods '6' '3' and '5' to make the larger number. Now, just like in a regular multiplication table, run your finger down to the yellow '6' and read the numbers across.


Here is the row I'm talking about:


To figure out what the answer is, you need to add the numbers in the parallelograms together. So, the first '3' is by itself, the '6' and the '1' will be added together, the '8' and the '3' will be added together and the '0' is by itself. Here I have written it out for you.


Once you have done this you have the answer: 3810. Cool, huh?

4 comments:

Lucy said...

I followed up to the point you went from 3 7 11 0 to 3 8 1 0. So if there is a double digit it's an automatic 'carry the one' situation?

thecurryseven said...

Yes, the double digit needs to carry, just as in regular addition.

e

Kristin Mueller said...

Hey, I think this reminds me of the lattice method of multiplication. Could that be? Do you have any idea what I'm talking about? The boxes look the same to me. I had some students who loved doing their multiplication problems this way!

thecurryseven said...

Yes, it is very, very similar to lattice multiplication. The only differences are that you move the strips around to create your multiplication problem and you must multiply by a single digit.

e

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