Expanded Notation for Multiplying Whole Numbers

Using Expanded Notation has got to be the best way I have seen for solving multiplication problems! It is so easy and simple to use, and you can solve your problems faster and with accuracy. Below are some pictures of what large numbers look like in  Expanded Notation. (I like the idea of using expanded notation for large number multiplication; makes it much less confusing and time consuming)

I find this to be a very clever way to be teaching students place value, by breaking down the numbers into their respective parts (hundreds, tens, and ones). 

Now when multiplying, lets say with a problem like 8x469, you would first start with converting 469 into Expanded Notation which would look like so:

400+60+9=469

Now that we know what 469 looks like in Expanded Notation we can move onto our next step of the problem. We need to now multiply our 469 by 8, and to do this we would put our Expanded 469 into parenthesis and write 8 before it like so:

8x(400+60+9)

From here the next step is to distribute the 8 through the parenthesis, and would look like this:

8x400+8x60+8x9

From here you would solve each multiplication problem, looking like this:

3,200+480+72

To finish you just go through and add up everything giving you your answer of:  3,752

I personally have used this method while helping the school-aged children at my place of employment, and with much success. At first, it is overwhelming, but after a couple of days they no longer need my help (which makes me kind of sad). I wish that when I was younger I could have been taught this way to do multiplication problems. I am stuck in the long-hand way of doing multiplication, so doing this at first was very hard for me to get used to. But, through using this method with the students I tutor at work, I have come to always use this method for multiplying. Study Jams is a wonderful website that offers students training, and testing on expanded notation I myself have used this website many times in helping my step-son practice writing numbers in expanded notation for many math assignments.