How to Write a Number in Expanded Form

Wondering how to write a number in expanded form? Just decompose it by place value. For example, 390,406 = 300,000 + 90,000 + 400 + 6. Let’s take a look at how to teach this process to upper elementary students.

How to Write a Number in Expanded Form

Ms. Sneed Teaches How to Write a Number in Expanded Form

Our favorite fourth grade teacher stood in front of her class. “Today, we’ll continue with our place value unit,” Ms. Sneed said. “Specifically, you’ll be learning how to write a number in expanded form.”

Opening with Anchor Charts

The teacher shifted her position and pointed to the screen. “On this anchor chart, you can see that the number 627 is decomposed by place value. The six in the hundreds place represents six hundred. The two in the tens place stands for twenty. And the seven in the ones is just seven. To write this number in expanded form, we simply write 600 + 20 + 7.”

Quickly, she gave another example. “Since you’ve already learned about the values of digits in different places, as well as how to read multi-digit numbers and write them, you can also see how we’d write this bigger number in expanded. See? 647,208 = 600,000 + 40,000 + 7,000 + 8. We don’t write anything for the tens place because that digit is zero.”

When she changed the image on the screen, Ms. Sneed continued. “As we get started, we’ll use place value charts for support. Without them, kids sometimes forget to pull each place value apart.”

The teacher proceeded to show her students how to drop each non-zero digit straight down and into a its own separate row. Then she modeled how to fill in blank spaces to the right with zeros.

“Again, we use plus signs to show how to write the number in expanded form. 725,092 = 700,000 + 20,000 + 5,000 + 90 + 2.”

When teaching kids how to write a number in expanded form, start with place value charts.
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Continuing with Guided Practice

Next, Ms. Sneed distributed a two-sided worksheet. “As a warm-up, we’ll begin on the side with blank place value charts,” she said.

“At the top of the first chart, write eight hundred four thousand, sixteen.” Ms. Sneed circulated around the room to make sure everyone had written the correct number.

“Now pull each non-zero digit down into its own row.” Again, she circulated.

As she walked, her eyebrow shot up. “Hmm,” she said. “How many digits does the number sixteen have?”

“Two,” came the answer.

“Yes. Although its just one word, sixteen is a two-digit number. And each of those two digits gets its own row.”

After everyone had added zeros to display each decomposed number, Ms. Sneed asked them to write the expanded form. Circulating once again, she was happy to see that almost everyone had written 800,000 + 4,000 + 10 + 6.

Working much more quickly, she asked them to decompose a second number and write it in expanded form.

For support when learning how to write a number in expanded form, let kids use place value charts.

Providing Independent Practice

As the students finished up, their teacher distributed an open-ended worksheet. “Now you’ll practice expanded form without a place value chart,” she said.

Noticing some students’ discomfort, she added, “If you’d like my support, you may come to the side table. Furthermore, if you just want a little crutch, more blank place value charts are available on my desk.”

A handful of students get a place value chart, and several moved to the side table.

Ms. Sneed also grabbed some place value charts and settled in at the help table. As usual, most of the students requesting support were a little shaky, but much of that stemmed from lack of confidence, not inability. In no time, they began moving back to their desks.

Once kids understand how to write a number in expanded form, move to open-ended worksheets.

Trying Some Mixed Practice

The next day, Ms. Sneed reviewed how to write a number in expanded form. Then she distributed another worksheet. “Over the past few days,” she said, “you’ve gained skill and confidence in writing numbers. On this page, you will show me that you can write multi-digit whole numbers in standard form, words, and expanded form. As usual, the help table is open for support.”

From her seat at the table, Ms. Sneed looked out over her students. Without hesitation, they all got busy on the task. She offered a little help here and there. But overall, the kids sailed along on their own. Soon, a satisfied teacher smile appeared on her face.

Give kids opportunities for mixed practice.

Reinforcing with an Expanded Form Game

As the last of the students finished up, Ms. Sneed returned to the front of the classroom. “Who’s ready for a game?”

As expected, a bright chorus of “Me!” rang out.

“This game is called ‘I have, who has?’ Each of you will receive a card. At the top, it says ‘I have’ and a number. That is your number. You will be listening for someone else to express that exact number in a different form. Then you will read the ‘Who has’ question at the bottom of your card.”

Ms. Sneed began the game with her own card. As they played, she kept the answer key handy. And any time someone stumbled, she provided support.

For practice (and fun), play this "I have, who has" game to practice writing numbers in different forms.

Enjoy Teaching How to Write a Number in Expanded Form

As you may have noticed, successful teaching strategies allow Ms. Sneed’s students to thrive. And when they do, she enjoys teaching even more.

Next up for fourth grade mathrounding and comparing numbers.

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