Expanded Notation

Expanded notation is a great tool that we can use to simplify math problems by breaking them down into bite size pieces in order to make more sense of the problem. The way we learned how to do expanded notation is in what we call "Base Ten". Basically, this means that each place value is some exponent of the number 10. The "one's" place is the number times ten to the zero power. The "ten's" place is that number times ten to the first power. The "hundred's" place is ten to the second power, or ten squared. The "thousand's" place is ten to the third power, or ten cubed, and so on.

Lets look at this number to write in expanded form:

7265

Instead of looking at this as one large and complex number, we can break this information down by recognizing place values. We will multiply each place value by the number 10's proper exponent for each place value. Starting with the 7 which will be multiplied by 10 cubed, moving on to the 2 which will be multiplied by 10 squared, and going to 6 which will be multiplied by 10 to the first power, and ending with 5 which will be multiplied by 10 to the zero power. Then we will add all the numbers together at the end. We break will break this number down and build it up to show place value. 

 7 is in the thousand's place 

2 is in the hundred's place

6 is in the ten's place

5 is in the one's place

So when we write this number in expanded notation it will look like this:

7265 = (7x1,000)+(2x100)+(6x10)+(5x1)

This skill is great for kids to learn in math, it helps them take something abstract and give it a foundation to build on. It also helps develop their thinking processes as they solve problems. When they begin to add, subtract, divide or multiply numbers, they can use this tool to solve problems easier and faster. A great tool to use when teaching the foundations of place value to kids is to introduce to them base ten manipulatives. They need to grasp the concept of place value in order to build on it later. Get them familiar with these base ten blocks in order for them to see how big is the number they're working with, which number belongs to which place value and what that really looks like as far as how many hundreds, tens, and ones there are.

Practice place value through a math game
Here you can see a video learning how to use expanded notation in multiplication: