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Math for Kids23 chapters | 325 lessons

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.

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.

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.

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.

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.

To write the number 542 in expanded form, we use what we just learned and write it as an addition sentence. The 5 means 500 cookies, the 4 means 40 cookies, and the 2 means 2 cookies.

Alfred has 500 + 40 + 2 cookies. 500 + 40 + 2 is the expanded form of 542.

We wrote that the expanded form of 542 is 500 + 40 + 2. To check our work, we do the addition: 500 + 40 + 2. That equals 542, which was our original number. So our expanded form is correct.

In expanded form, we use place value to tell us how much each digit is worth. Remember how Alfred stacked his cookies on the shelf, in bags of 100, 10, and 1. We then write an addition sentence adding the value (or worth) of each digit. Expanded form is a longer way of writing a number that helps us know more about the number.

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Math for Kids23 chapters | 325 lessons

- Subtraction: Lesson for Kids
- Expanded Form: Lesson for Kids
- How to Do Long Multiplication: Lesson for Kids
- What is Multiplication? - Lesson for Kids
- Addition: Lesson for Kids
- Multiplication Properties Lesson for Kids
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- Lattice Method of Multiplication
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- What is a Theorem? - Definition & Examples 3:11
- What is Subtraction with Regrouping?
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- Metric System vs. Imperial System
- History of the Metric System: Lesson for Kids
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- How to Write Numbers in Expanded Form 3:58
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- How to Write Decimals in Expanded Form 3:30
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- 4 Digit by 1 Digit Multiplication
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- The Box Method for Multiplication 2:29
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