The Value of a Digit in a Number

Do your kids really understand the value of a digit in a number? Use these strategies to help fourth grade students conceptualize zero as a placeholder, as well as how a digit’s value changes when moved to the left. It will pay off!

Ms. Sneed Teaches the Value of a Digit in a Number

Our favorite fourth grade teacher sat at the side table with her student teacher. “Today,” she said, “we’ll plan lessons on the value of a digit in a number. It’s the first part of our unit on multi-digit whole numbers – and integral to much of what we teach in fourth grade math.”

Opening with a Chart

Without a pause, Ms. Sneed opened her laptop and clicked on the file. “First, you’ll introduce periods. As you can see from this anchor chart, they’re arranged as a series of three numbers. Each has a ones, tens, and hundreds place.”

“Hmm, I never thought of it that way,” Mr. Grow responded. “It really simplifies the concept for me.”

Ms. Sneed smiled. “For the kids too. When it’s presented in this straightforward way, they understand it so much better.”

Begin teaching the value of a digit in a number with a chart. Kids learn the how periods are organized in series of three.
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Building Numbers to Demonstrate the Value of a Digit in a Number

“Next,” Ms. Sneed continued, “kids will build numbers. For this activity, they’ll use scissors and glue (or tape). Each of them will put together a place value chart and cut out numbers.”

She turned the laptop toward her student teacher so he could study the next page a little better. “You will guide the activity with this script. Let’s go over the first one:

  • Put a seven in the ten thousands place.
  • Put a four in the hundreds place.
  • Put a six in the ones place.
  • What number do you have?
  • Why isn’t it 746?”

“Ah, I see,” said Mr. Grow. “They’ll place the numbers on the chart. That will help them establish the value of a digit in a number. But then they must add zeros as placeholders.”

“Exactly. Fourth graders often forget the zeros. Then their numbers collapse and end up with a totally different value.”

Continue teaching the value of a digit in a number with a place value chart and moveable numbers.

Quickly, she scrolled to the next page. “After you practice together, kids will complete this worksheet independently. The activity won’t take long, but it offers powerful opportunities for conceptualization.”

Ask kids to build numbers by placing digits in the appropriate place and adding zero as a placeholder.

Ms. Sneed reached into her teaching bag and pulled out a set of printable place value charts. “At this point, kids need plenty of practice. You can use these pages for more oral practice. Furthermore, they work well with writing large numbers. You say it; they write it.”

Comparing the Value of a Digit in the Place to the Left

As she scrolled to the next section of the resource, Ms. Sneed continued. “Next, our class will explore how the value of a digit in a number changes when it’s moved. The kids will use the same charts and numbers. Once again, they’ll build a number. But this time, they’ll slide the number to the left to discover it’s ten times larger.”

Mr. Grow studied the pages and nodded. “This practice is new to me, but I get it. Actually, I can see the benefit.”

“I have a little trick to help them remember too.” The mentor began to sing, “To the left, to the left. Everything’s ten times in the place to the left.”

“Ah ha! Beyoncé! I love it.”

Now kids consider the value of a digit when it's moved one place to the left.

Ms. Sneed scrolled to the related worksheet. “After the activity, they’ll be ready for this. It asks them to find the value of a digit in a number. First, they write it. Then they decompose it.”

On this worksheet, kids find the value of an underlined digit.

Multiplying and Dividing by 10, 100, and 1000

Finally, they came to the culminating activity. “Our math textbook jumps right to this page,” Ms. Sneed said, “but I think kids need more. Anyway, this part of our place value unit asks kids to multiply and divide by 10, 100, and 1000.”

Finally, students practice multiplying and dividing by 10 and 100.

After You Teach the Value of a Digit in a Number

“Before we leave for the day, let’s take a look what comes next. After learning about the value of a digit in a number, kids are ready to read big numbers out loud. After that, they write them in standard form and words, as well as expanded form. But there’s more! You’ll teach kids to order and compare, as well as round.”

“Looks like I’ve got my work cut out for me,” said Mr. Grow. “Thank goodness I have strong resources – and you – to support me!”

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