Problem #6: Copper Plate Multiplication

First of all I was confused about the name of this method. I googled copper plates and found no relation between them and what we were doing in this problem and copper plate multiplication yielded no results.

I checked to make sure that the product of the two numbers given was in fact the answer you get from this method using a calculator. My intial response was to multiply these numbers like I was taught in elementary school. I realized in doing this I was breaking up the numbers found in this new method to follow through with the "carrying" process.

I stopped half way through and tried to figure out where the each of the numbers came from in the rombus shaped group. For some reason the middle number group was where I wanted to start. I could easily see that in that row the numbers were the products of each of the numbers in the problem that were on top of each other. I workd my way down from that row to find the pattern in the next 4 rows. They were all two digit products of the diagonals of the numbers.

After I recongnized some sort of a pattern, I tried recreating it in order

to draw more conclusions. I wrote the numbers out huge and tried to use different collors to show where I was getting the numbers from. I started with the biggest diagonal multiplying the bottom 6 by the top 5, then making my diagonals smaller and smaller until they were the numbers directly above each other. Once I got to that point, I switched the direction of the diagonals and ended with finally multiplying the bottom 9 by the top 7. I don't know how clear it will be, but it looks pretty :)

In creating this several questions/assumptions came to mind and I tried a few examples of my own to either prove or disprove them. My inital questions/assumptions are in green and my answers are written in black after I did a few examples:

Here are the examples I did:

Once I got used to this method, I kind of liked it. It took me awhile to be able to do it with out checking the orginial to make sure I was multiplying the right things at the right time. It was neat to see this method broken down and to even start thinking about the place values. It would also be interesting to look at the "standard" method and break that apart as well.