What is place value and why is it important? Place value is the foundation for understanding numbers. Without a solid understanding of the value of numbers, it’s difficult to learn most math concepts. Let’s take a fresh look at place value, what it is, and how to use place value activities to help your students master this important foundational math skill.
What is Place Value?
In simple terms, place value is the value of each numeral in a number. Place value is determined by the position of the digit in the number. For example, the numeral 3 can represent different values depending on its position within a number. When you write the number 6,375, the number 3 represents 300 because it is located in the hundreds place. However, in the number 735, the number 3 represents 30 because it is located in the tens place.
I like to use a row of houses to depict the value of numbers. In my class, we call this chart “Place Value Street“. Each house on the street holds one period, or group of 3 numbers separated by a comma.
For example, the number 8,249,503,017 has 4 periods. Each period is shown inside a different house on the street and contains hundreds, tens, and ones. The pink “thousands” house (below) has a place for the hundred thousands, ten thousands, and one thousands. Likewise for the other periods. Seeing numbers in this format really helps kids understand the value of each digit within a larger number.
For students to understand our number system, they need to master place value. From being able to hear a number and write it down correctly, to solving addition, subtraction, multiplication, and division problems, students need a strong grasp on place value.
How to Teach Place Value to Upper Elementary Students
When I kick off my place value unit, my upper elementary students often make claims such as “Numbers are easy”, “We did this before” or “I already know place value”. Deep inside, I know they need a deeper understanding. While they have basic knowledge of place value, many students in third, fourth, and even fifth grade haven’t mastered this topic.
My favorite way to illustrate this point is to say, “Okay. Great! Let’s write some numbers!” I hand them each a piece of lined paper and ask them to number it from 1 to 10, leaving space to write an answer on each line. Then I dictate some large numbers for them to write.
I start off easy before increasing the difficulty. “Number One: Please write the number 742 (said out loud as seven hundred forty-two). Number Two: Please write the number 3,563 (said out loud as three thousand, five hundred sixty-three). Then, I gradually increase the size of the numbers and use numbers that have zeros as placeholders.
This is when they start to doubt themselves. “Number Three: Please write the number 18,091 (eighteen thousand, ninety-one). Number Four: Please write the number 503,204 (five hundred three thousand, two hundred four). This continues until we get up to the final number: 1,000,001 (one million, one).
At this point, the class is in an uproar. “I don’t get it! This is hard! That’s not a real number!” Suddenly, they realize that there is indeed more to learn about numbers and place value.
This always leads to the most perfect conversation about the value of digits within a number, related to their location, or place. Opening the unit with this quick activity can help students see the value in studying place value.
Understanding Numbers and Place Value: 3 Ways to Write a Number
One way to help reinforce place value is by writing numbers in different ways. There are three ways to write numbers:
- Standard Form: This is the standard way to write a number with numerals. For example 3,789,341.
- Expanded Form: In this form, students need to show the value of each numeral in the number. The number listed in standard form would be: 3,000,000 + 700,000 + 80,000 + 9,000 + 300 + 40 + 1
- Word Form: In this form, students write out the number in words. This helps students get a sense of place value, as they write out how they would say each number. For example, Three million, seven hundred eighty-nine thousand, three hundred forty-one.
When writing out numbers in these three ways, students need to think through the value of each digit. This reinforces place value. Yet, writing out many numbers like this over and over again can be boring. That’s why I try to bring in fun place value activities to keep the lessons upbeat and engaging.
Fun and Engaging Place Value Activities to Try
There are many place value activities to use in your place value unit. For example, you can make a fun place value teaching tool with Dollar Store pill boxes and dice. With this tool, you can turn place values into an engaging game. They’re easy to make and well worth the effort. Kids love them!
I also created a Place Value Lapbook that provides an engaging format for studying place value. The lapbook includes many different activities that help children master place value. Then, the lapbook challenges students to perform different operations and compare numbers to reinforce their understanding. Plus, it includes an optional decimal insert to the tenths, hundredths, and thousandths, which is perfect for fourth and fifth-grade students.
Alternatively, you might try setting up a Bingo game using large numbers. Students need to hear numbers verbally and identify the matching written numbers on their Bingo cards. You can even use word form or expanded form on the Bingo cards for extra practice.
Place Value Activities for Deepening Understanding
As with many topics, students need lots of practice to achieve a deep understanding of place value. When I teach this unit, I try to use various place value activities to help students get the practice they need. Before long, you’ll find that your students have mastered place value!
I hope you’ve found this overview of teaching place value in your upper elementary classroom useful! Do you have a favorite place value activity that works well for you? I’d love to hear about it. Let us know in the comments below!