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What is Expanded Form?

Are you teaching expanded form? Do you have a rubber band? Perfect! That’s all you need to introduce expanded form!

As a second grade math nerd, expanded form has been my favorite number form to teach. To begin the lesson, I would use a rubber band and show what expanded means. By placing the rubber band around my hands and pulling them away from each other, it would show them the rubberband expanding, getting longer, and stretching. 

“That is what we are going to do with these numbers today, expand them, make them longer. The number will stay the same, it will just be stretched out!” I say.

What is expanded form?

Expanded form is a number sentence that shows the value of the digits based on its place. Here is an expanded form example: 126=100+20+6. This is expanded form because it is an addition number sentence that shows the value of each digit in 126. The 1 is in the hundreds place so its value is 100, the 2 is in the tens place so its value is 20 and the 6 is in the ones place so its value is 6. 

Why is expanded form so important?

It is key to helping students understand that the value of a digit changes based on its place.

 As a teacher, it is a quick assessment of a student’s place value understanding. If students are able to tell you the value of a digit in a 3-digit number,  you know that they understand the place of the digit  will change its value.

It helps with adding and subtracting  2 and 3-digit numbers. When students are able to pull numbers apart to add and subtract their fluency will increase and will contribute to building stronger mental math strategies.

Expanded form doesn’t stop in 2nd grade! In fourth grade and up they will be using expanded form to understand decimals, to add and subtract them too! Helping them master the concept of expanded form sets them up for success in the years to come. 

After you teach Expanded for it is a good idea to include it in a spiral review to let students continue to practice and gain confidence. Get a free Google Slides Spiral Review HERE!

Ways to Practice Expanded Form

Place Value Cards

My absolute favorite way to have students practice expanded form is number building using Place Value Cards. (You may have heard them called Hide Zero cards or Arrow Cards). 

To use Place Value Cards choose the “places” you want to practice, so for 2nd grade it would be hundreds, tens and ones. 1st grade tens and ones and Kinder just the 10 card  and ones. These cards are printable and students can make their own set. I like to make each “place” a different color. To use these cards layer them starting with the hundreds then find the tens and ones and stack them on top of each other, so the only thing visible is the standard form.

After showing the students how the Place Value Cards work, I have them work in partners at their desks. I display a number in standard form and students must build the number and give me a thumbs up when they are finished. 

When everyone is ready I have them “expand” the number by spreading the cards apart and then we say it in an addition sentence which is expanded form.

There are digital versions of place value cards as well. Check out this blog post all about virtual manipulatives and how to use them in your class!

Digital Centers:

Here are some examples of what a digital center or practice may look like. You can get this Google Slides activity here! There is also a place value bundle that includes practice for all number forms for 2nd grade.

Using number bonds

Students roll a dice to create their 3-digit number. Then they put it into the number bond and show the parts. This is a great option for a center and can be put into a dry erase sleeve. And if you have a 9 sided dice, this is even better practice.

Expanded Form Differentiation

2nd grade students are at grade level when they are able to express a number in expanded form for 3-digit numbers.

If students struggle with the hundreds place have them practice 2 digit numbers and if there is still a struggle, just use the 10 card and ones to practice numbers under 20. 

Extend

If students are already understanding 3-digit numbers, bump them up to practice 4 digit numbers.

Mix the numbers around and have students solve. So instead of the traditional 500+20+4=_____, mix it up. Here is an example 20 +  4+ 500=____.

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