Japanese multiplication method

There is a bunch of videos going around lately that seem to be very popular, which demonstrate a style of Japanese multiplication.  It is quite visual, and I would argue that more complicated products could require even more work than traditional (at least, what I consider traditional) methods.  In any case, it is a very interesting process that you could use to impress your friends and family, or even use it as a math trick.  Here's the gist of how the Japanese multiplication method works.

Let's try a simple example.  Find the product of 12 x 31.

Essentially, you denote the digits as groups of lines, and then you count the intersections to arrive at your result.  So, in this case, the 12 is represented by a group of 1 line and a group of 2 lines, and the 31 is represented by a group of 3 lines and a group of 1 line.  We'll draw the "12" lines slanting up in blue, and the "31" lines slanting down in orange.

Now, imagine that these lines and their intersections can be divided into columns.  You get the left point of the diamond in the first column, the top and bottom of the diamond together in the second column, and the right point of the diamond in the third column.  Now, to find the product of these two numbers, all you do is count the intersections in each column and write that number down.  These numbers will be the digits in the final answer.

Check with your calculator and you can verify that 12 x 31 = 372!  It takes a bit of work, but it's a pretty cool method of multiplying numbers together!  This works really easily when you are multiplying a pair of two digit numbers together.  When you have three digits numbers, or more, you simply add another group of lines, and then you will wind up with more columns to tally the intersections.  Also, in any one column, if you count more than 9 intersections, you simply carry the tens digit of your intersections over one column to the left and add to that total.  So, if you count 12 intersections in a column, the value you keep is the 2, and you add the 1 to whatever is in the column to the left.

If nothing else, I think this method is a really cool demonstration for a cool math trick, though I don't think that I would use it to replace the style of multiplication that I learned in school.  However, that's not to say that it won't be more appealing or useful to you!  Do you use this method in your studies?  Let me know in the comments, and don't forget to hit the Facebook Like button at the start of the post to support my site!

20+ Free Math Worksheet Sites for Teachers

In a recent blog post, I put out a call for recommendations of sites to include in my resource for math worksheets that I hoped to create.  I had several people respond to me, either by commenting here on my blog, through my new Facebook site, or through Twitter.  Thank you to everyone who contributed!  I don't know if this will ever be known as "THE math worksheets site," (though that would be nice!) but if anyone gains any benefit from it whatsoever in the months and years ahead, I will consider this a successful project.  I will certainly be monitoring its popularity and traffic to see how it goes!

What follows is a compilation of sites that I feel are a good resource that can be used by teachers, parents, students and homeschooler alike to help teach and practice math concepts.  None of them are my sites, though some have been kind enough to link back to me!  If anyone objects to any sites that I've included, please don't hesitate to contact me and I will remove it from my database.  READ MORE...

Math Worksheet Database

Several months ago, I posted an article about free printable math worksheets.  I created a couple of basics problem sets that could be printed off, and I also mentioned a couple of other websites that admittedly did a lot better at providing practice worksheets.  I quickly fell behind in keeping my selection of questions up to date, as I instead focused on keeping my blog active with new concept lessons.  Now, I want to do something a bit better and more productive.  

Instead of me having to create sheets that teachers and students can download to practice their math with, I am putting out a request to all of my readers for your help.  

Let me know in the comments below some of the sites that you know about and use where you find good practice math worksheets.  When I have a sufficient number, I will redo or add to my original worksheets blog post, but instead of providing (and having to make) the actual practice questions, I will make the page into a repository of links to other websites that all specialize in providing free math sheets.

I think that this is a way better plan that what I originally envisioned.  As much as I'd love to create all of my own work to share and make freely available to distribute, I unfortunately don't have the time necessary to dedicate to that project.  However, by making use of the power of social networking, I hopefully can put together a database of sites that are all relevant and useful, because they will already have been recommended by some of my readers!

Help me to get this database of math sites off the ground!  Leave me a note in the comments below, or on my new Facebook page, and I will compile them all and make a great resource of free practice materials for students and teachers to use.  I will also be sure to acknowledge everyone who suggests sites!  Thanks in advance for everyone's help!

Be sure to click the +1 button below, or my new Facebook Like button at the start of this post to help me get the word out!

My Facebook site is finally LIVE!

Hello and Happy New Year to all of my readers!

I'm starting the new year off on the right foot by finally getting my Math Concepts Explained Facebook site up and running!  I'll be updating that site as I add information to this blog, but I also welcome my visitors and followers to comment and ask me questions there whenever they'd like.  I will do my best to provide whatever math help I can!  Please visit and Like my Facebook page and add me to your Friends list!

Perfect Christmas Tree Math

Here's a fun little post for the holidays!  It's not going to teach any new math concepts, though it is a neat demonstration of an out of the ordinary use for mathematics.  It describes mathematically how to decorate the perfectly proportioned Christmas tree.  I can't honestly say that I have tried it myself, though I don't doubt that it might be useful!

A department store in the United Kingdom by the name of Debenhams issued a challenge to the University of Sheffield math students to devise a mathematical algorithm to determine the optimum number of ornaments, tinsel, and lights in relation to the size of the tree, as well as the perfect size of the star for the top of the tree.  Members of the University's SUMS Math group were able to come up with a set of equations that described precisely what the challenge required:

Courtesy of http://www.shef.ac.uk/polopoly_fs/1.227830!/image/formulaslarge.jpg

The students say that the calculation took about two hours to design, though to actually compute the equations is as simple as entering numbers into a calculator.  The stated purpose of the formula is to help holiday shoppers to be smarter when purchasing decorations for their tree, as with this knowledge they will be able to buy the precise number of baubels and lights rather than have a box of extras leftover once the tree is done, or else not have enough and so have to go and fight through the mall crowds to get more.  It also means that people can find the right size angel or star for their tree, rather than guessing and then potentially being way off when they actually get home.  They say that the formulas are versatile enough to apply to large trees suitable for the Royal Family, right down to smaller trees that are more common.  You can check out the original news release here.

It's probably a stretch to think that this set of equations will make it into widespread use, as decorating for the holidays is way more about spending time with friends and family and having good times, rather than looking for mathematical precision in a Christmas tradition.  However, it's a fun exercise to show young math students that demonstrates yet another useful and unexpected use of math in everyday life.

Happy Holidays to all of my followers, and all the best in the New Year!