Expanded Form: Lesson for Kids

Instructor: Bethany Calderwood

Bethany has taught special education in grades PK-5 and has a master's degree in special education.

A number can mean more than you'd expect just by looking at it. A good mathematician knows how to unlock this meaning by using expanded form, which we'll cover in this lesson.

A Mathematician's Tools

Alfred the chef just got a new oven. He knows that the oven's name is Fancy Oven 3000, but before he uses it, he needs to know more--like what the parts are and how to turn it on. There are different ways he can learn about the oven, such as reading the instructions or asking someone to show him how to use it.

One of a chef's tools is an oven. A mathematician's tools are numbers. Like the chef, a mathematician should know more than just the name of her tool. One way to find out more about a number is by using expanded form.

Expanded form is a way to look more closely at a number to find out what each digit is worth, then write it as an addition sentence. To help us understand expanded form, we will look at how Alfred packages the cookies he makes in his new oven.

Packaging the Cookies: Place Value

Alfred separates his cookies into bags. He arranges them on the shelf so that the first section has bags with 100 cookies, the next section has bags with 10, and the last section has bags with 1.

Shelf of Cookies
shelf with bags of 100 and 10 and 1

The way Alfred packages his cookies on the shelf is like place value in math. Place value tells how much a digit (or number) is worth based on its position (or place) in the number.

Alfred made 542 cookies. 542 has three digits, or numbers: 5, 4, and 2. In 542, the number 5 is in the hundreds place, which is like the first section of Alfred's shelf, where each bag has 100 cookies. The 5 means there are 5 bags, and each bag has 100 cookies. So the 5 is worth 5 x 100, or 500 cookies.

Place Value of 542
542 with place value labels

The number 4 is in the tens place, which is like the section of the shelf where each bag has 10 cookies. The 4 means there are 4 bags, and each bag has 10 cookies. So the number 4 is worth 4 x 10, or 40 cookies.

The number 2 is in the ones place. Each bag in this section only has 1 cookie, so the 2 is worth 2 x 1, or 2 cookies.

The Cookies
500 cookies and 40 cookies and 2 cookies

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