# Multi-Digit Whole Numbers – Place Value for Fourth Graders

Place value for fourth graders involves multi-digit whole numbers. Kids need to fully conceptualize the value of a digit, read, write, compare, and round. Are you ready to have some fun with this?

## Place Value & More

Our favorite elementary school teacher sat at the side table with her student teacher. “Let’s get ready to teach place value in fourth grade math, ” Ms. Sneed said. “We always multi-digit whole numbers at the beginning of the year. After all, it’s the basis of many other concepts we’ll teach.”

“You mean writing big numbers?” Mr. Grow asked.

“Yes, that and more.” She slid a copy of the standards toward him and read aloud:

• “Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
• “Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
• Use place value understanding to round multi-digit whole numbers to any place.

Then she pointed to the tiny lettering at the bottom of the page and continued, “Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.”

“So,” said Mr. Grow, “in addition to place value, we’ll also work on comparing and rounding numbers up to one million.”

“True.” his mentor replied, “In past years, however, I’ve found that the advanced students already know how to work with numbers that big. Therefore, in our place value unit, students who have mastered most or all of the numeration skills will work with numbers up to one billion.”

Ms. Sneed pulled a file folder from her bag. She pulled out the top page and handed it to Mr. Grow. “From this schedule, you can see that we’ll begin with a pretest. From the results, we’ll place kids in two groups. We’ll teach the same skill to both groups each day. However, worksheets and activities for the advanced group are differentiated with bigger numbers.”

### Begin Teaching Multi-Digit Whole Numbers by Building Them

Next, Ms. Sneed pulled out a long place value chart and some number cards. “On the first day of instruction, you’ll review place value. Then you’ll orally prompt them to build a number.”

Pulling out another page, she read the first prompt aloud:

• “Put a seven in the ten thousands place.
• “Put a four in the hundreds place.
• “Put a six in the ones place.”

As she read, Mr. Grow manipulated the numbers. Now he had seven – blank – four – blank – one on the place value chart.

Ms. Sneed continued reading: “What number do you have?”

“Seventy thousand, four hundred six,” Mr. Grow responded.

“Correct! Why isn’t it 746?”

The student teacher sat silently for a moment. Then he picked up some zeros and filled in the blank spaces. Finally, he responded, “Because these zeros have been added to hold the place values.”

Ms. Sneed nodded. “Right. Although it seems like a no-brainer to us, this is a huge misconception for kids. Often, they let the number collapse because they don’t use zero as a placeholder. That’s why we need to work on it right away.”

### Teaching Multi-Digit Numbers with the Same Number in Different Places

As Ms. Sneed pulled out the next activity, she asked Mr. Grow to clear the place value chart.

“For the next activity, we’ll work on teaching multi-digit numbers with whole numbers in different places. Let’s try it out. First, grab a non-zero number.”

Mr. Grow picked up a nine.

“Now place it in the tens place and fill in zeros as necessary.”

The student teacher did so, with 90 now on the board.

“After this, you’ll move the non-zero number to make it ten times larger.”

Mr. Grow glanced sideways at his mentor. “Hey, this is nothing like any math learning I ever did in school.”

With a smile, Ms. Sneed nodded. “Yes, but you’ll soon see the method to the madness.”

Now Mr. Grow slid the nine to the left and added another zero. “Nine hundred,” he said.

Then his eyes opened a little wider. “Ah, I see. This addresses that standard about a digit in one place representing ten times what it represented in the place to its right.”

### To the Left, to the Left – Place Value for Fourth Graders

Ms. Sneed’s eyes twinkled. “Right. And it’s the perfect time for a song:

To the left, to the left,

Everything’s ten times in the place to the left!

In the ones place,

That’s single stuff, yes

If you move it, baby

It’s ten times as much.

At that, Mr. Grow burst out laughing. “Hey! Isn’t that a Beyoncé song?”

“It sure is! ‘Irreplaceable.’ Now how ironic is that? I like to use this song to remind kids of the concept.”

Once again, she pulled a worksheet from her file. “After introducing the song, kids will work on this. All they have to do is write the value of the underlined digit in a multi-digit number. And, if you want, they can rewrite the remainder of the song’s lyrics to fit with what they’re learning.”

### Teaching Kids to Read Multi-Digit Whole Numbers

Pulling an anchor chart from the file, Ms. Sneed continued. “Next, you’ll teach kids how to read large numbers out loud. As you can see, you begin with a three digit number, like six hundred fourteen. Then you show them how those three digits are read exactly the same regardless of the period they’re in. See? Six hundred fourteen million, six hundred fourteen thousand, six hundred fourteen.”

“Wow, no one ever taught it to me that way,” said Mr. Grow. “That makes it easy.”

“Sure does.” She slid two pages of typed numbers to him.

Looking at the worksheets, Mr. Grow nodded. “And next, we’ll practice by reading these numbers.”

### Teaching Kids to Write Multi-Digit Whole Numbers

“Teaching multi-digit numbers in writing is next,” said Ms. Sneed as she pulled out more anchor charts and worksheets.

#### Writing Numbers in Words

“To me, it makes sense to start with writing numbers in words. After reading them aloud, it’s not difficult. Kids just need to remember a few things:

• “Don’t use and. That word is only used when you encounter a decimal point.
• “Add a comma after the period name.
• “Place a hyphen between two-digit numbers greater than twenty.”

She picked up a spelling list and slid it over to Mr. Grow. “Number words will make up our spelling list that week. Fourteen, forty, and ninety are particularly tricky.”

#### Writing Numbers in Standard Form

“Yes, they need to practice that too. Even after all the earlier practice with zero as a placeholder, they forget.” She slid some printable place value charts toward him.

#### Writing Numbers in Expanded Form

“Next, kids will work on writing multi-digit numbers in expanded form. In most cases, they find this relatively easy. However, for those who don’t we’ll use a chart like this.”

### Comparing with Place Value for Fourth Graders

Next, Ms. Sneed felt around in her teacher bag. “Here they are.” She pulled out a handful of dice.

“To make comparing multi-digit whole numbers fun, we’ll play this game. They roll some dice and record the numbers here. Then they rearrange the digits to form different numbers. From there, they order and compare them.”

“That’s fun,” Mr. Grow commented. I know that this game will shake things up.”

Ms. Sneed smiled mischievously. “Well then, I know you’ll like the ‘I have, who has’ game that wraps up the sequence.”

### Rounding

With a sigh, Ms. Sneed sat back in her chair and looked at Mr. Grow. “Last,” she said, “we’ll tackle rounding. Unfortunately, it can really challenge our fourth graders.”

As she spoke, she pulled out more anchor charts. “Using number lines doesn’t make it easier. However, it does make them understand. Therefore, we can’t cut any corners.”

She pointed to the first anchor chart. “When rounding to the nearest ten, kids identify multiples of ten that surround the number. Then they mark those on a number line. After that, they mark where the number falls. Finally, they determine which multiple of ten is closest. And that’s rounding.

“We’ll ask our kids to round the same number to the nearest ten, thousand, and ten thousand. At first, they will likely struggle. But you just have to keep at it. In time, it gets easier for them.”

### The Importance of Teaching Multi-Digit Whole Numbers

“Our math book only touches on place value for fourth graders,” Ms. Sneed said. “But kids need deep understanding of multi-digit whole numbers. After all, if they don’t understand numeration, how can they understand addition, subtraction, multiplication and division? Taking the time to teach for understanding is worth it!”