Expanded Notation

Students entering fifth grade math need to take what they learned in 4th grade math and expand upon it.

5th grade math expanded notation compared to 4th grade math expanded notation

Basically what we are trying to accomplish is grasp place value or base ten concepts. When students see expanded notation for the first time they get a little scared. It looks intimidating!

Expanded notation is described as a number represented as the sum of the product of each digit within a number multiplied by the value of each digit’s place value position [e.g., 58.049 as (5 x 10) + (8 x 1) + (7 x .0.01) + (9 x 0.001)]

But it doesn’t have to be intimidating if they learn the base ten or place value of each number. If we think this is a problem for 4th graders or even 5th graders I have seen six graders struggle with place value. Especially when it comes to decimals.

So in fourth grade we learn that 125 is represented in expanded notation as this.

(1×100) + (2×10) + (5×1) = 125

When we know that the one is in the 100 place, 2 is in the tens place, and 5 is the ones place. We can move onto writing any number in expanded notation.

Expanded notation compared to place value
Expanded notation compared to place value

One Example of a question of expanded notation without a decimal.

Example of expanded notation without a decimal
Example question of a non-decimal expanded notation

As you can see by the above example. This is modeled through base ten blocks. You can use these blocks in a variety of ways. You can use them for place value. You can use them to write questions. I even use fraction base ten blocks to represent decimals.

Below I will use base ten blocks with fractions as a way to see expanded notation.

Example question of expanded notation with decimal.

expanded notation with decimal
Expanded Notation with decimal

Like anything in math, expanded notation takes practice. The more you practice it the better you understand it.

The more they work on it in fourth grade the easier it will be for them in the fifth grade. The more they do it in the fifth grade the better understanding they will have in sixth grade math when it comes to place value.


If you need a resource to help you teach and practice this concept you can see my unit on Ordering Comparing Rounding Decimals.

Base ten blocks Clip Art Provided by A Hughes Design

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