In math class, place value 2 digits practice builds the foundation for our number system. We rely on patterns to help us make sense of our numerical world. The foundation of our entire number system is place value, which is based on a pattern of tens. Learning the place value of numbers will help your student understand the value of the numbers. So, how can we help students understand our place value system?
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As I work with my first graders, we are focusing on building our teen numbers with a ten and some more. Then, we will move on to understanding place values 2 digits up to 99. I like to use unifix cubes so the students can see how we made a ten. Eventually, we will begin to use our base ten blocks. We have been building the number with our blocks, then drawing our blocks to represent the number, and finally identifying how many tens and ones are in each number. I want the students to have a solid foundation before they move into 2nd grade, where they will explore the place value of 3-digit numbers.
Building Place Value Number Sense
In math, every digit in a number has a place value. Place value can be defined as the value represented by a digit in a number based on its position in the number.
For example, the place value of 7 in 743 is 7 hundred or 700. However, the place value of 7 in 472 is 7 tens or 70. Here, we can see that even though the digits are the same in both numbers, their place value changes with the change in their position.
Understanding the Place Value of a Number
Every digit in a number is assigned a place value. Place values determine the worth of digits in a particular number. Since our single-digit numbers are only 1-9, we need place values to show numbers 10 and higher. Each place represents ten times the value of the position to the right.
To better understand place value, let’s look at examples with two numbers: 356 and 630.
The place value of 3 in the number 356 is 300. However, the place value of 3 in the number 630 is 30. In both numbers, the digit 3 is the same–but its value changes because of its position (or place) in the number.
Place value is also called a base ten system or a decimal system.
Understanding Place Value with Tens and Ones
Place value helps us determine the value of numbers. Our (base-10) number system contains numerals (or digits) only from 0 through 9, but we often need to use numbers greater than 9. We show numbers greater than 9 by using place value, which means that the value of a digit is determined by its place in the entire number.
In the base-10 number system, each place has a value that’s 10 times the value of the place immediately to its right.
- For example, numbers between zero and nine are represented by 1-digit numbers — 8.
- For example, numbers between ten and ninety-nine are represented by 2-digit numbers — 58.
Place Value 2 Digits Progression of the Standard
Kindergarten
The work in kindergarten forms the foundation for students to develop an understanding of the base ten system. Special attention is focused on 10 and connections to the meaning of numbers from 11 to 19. Students begin to see those numbers as a ten and some ones.
Work with numbers 11-19 to gain a foundation for place value.
Try Numbers to 20 Activities in Math or Represent a Number to get kids to understand the value of the digits in numbers to 20.
First Grade
First graders begin to think of ten ones as a unit called a ten. They use place value blocks and unifix cubes, then move to symbolic notation. In addition, they begin using the greater than, less than, and equal to symbols. They will find sums and differences to 100 using their tens and ones.
Use place value understanding and properties to add and subtract to 100. This is where students really explore place value 2 digits.
Try out Place Value with Tens and Ones to build numbers with digital place value blocks.
Second Grade
Second graders extend their understanding of place value to 10 tens, which is equal to 100. Using place value and the properties of addition and subtraction, students become fluent with two-digit addition and subtraction to 1,000. Students begin by using concrete representations of the numbers, then move on to pictorial representations, and finally to working with abstract representations.
Use place value understanding and properties to add and subtract to 1,000.
Using Place Value Blocks
The place value of digits in numbers can also be represented using base-ten blocks and can help us write numbers in their expanded form.
Base Ten Blocks provide a spatial model of our base ten number system. They typically consist of four different concrete representations, which are introduced in elementary math and utilized well into middle school.
- Units = Ones; Measure 1 cm x 1 cm x 1 cm
- Rods = Tens; Measure 1 cm x 1 cm x 10 cm
- Flats = Hundreds; Measure 1 cm x 10 cm x 10 cm
- Cubes = Thousands; Measure 10 cm x 10 cm x 10 cm
Providing names based on the shape rather than the value allows the pieces to be renamed when necessary. For example, when studying decimals, a class can use the flat to represent a unit and establish the value of the other pieces from there.
How to Use Place Value Blocks
Fundamentally, children understand place value to access the rest of the mathematics curriculum. Place value ideas are explored extensively throughout elementary school and are the foundation of students’ understanding of numbers as quantities and their operations.
- Base Ten Blocks are proportionally correct. Unlike place value counters or Cuisenaire rods, They are proportionally correct. This means ten ‘ones’ cubes are the same size as one ‘ten’ rod, and this continues with each larger piece. This allows children to understand the relationship between the different columns on a place value grid.
- Base Ten Blocks can assist with regrouping and exchanging in addition and subtraction.
- Base Ten Blocks are easy for children to use pictorially. They can quickly and neatly draw them to help them calculate answers or prove their work.
Where to Find Place Value Virtual Manipulatives
- Try out Place Value with Tens and Ones to build numbers with digital place value blocks.
- Compare Numbers 1st Grade Students build the number with the place value blocks. Then, they drag the greater than or less than blocks to compare the numbers. Then, they can use the greater than or less than symbols. The last ten slides have comparison word problems. Students explain using tens and ones that have more or less.
- Number Pieces by The Math Learning Center– This site is great because you can create problems and send them to students to solve with the virtual base ten blocks.
Using a Place Value Chart
A place Value Chart is a very useful table format that helps us find the place value of each digit based on its position in a number.
The place value of a digit increases by ten times as we move left on the place value chart and decreases by ten times as we move right.
Understanding the place value of digits in numbers helps compare numbers and write numbers in their expanded form. For instance, the expanded form of the number 548, is 500 + 40 + 8.
Students learn place value much easier when they use a place value chart. This helpful table helps find place values for each digit in a number. As students practice identifying place value using a place value chart, they’ll develop stronger number sense. Eventually, students will be able to look at a number and quickly determine the place value of each digit.
Great Place Value Read Alouds
Zero the Hero by Joan Holub and Tom Lichtenheld is a fun story about zero. Each number in the story is a character. The other numbers in the story aren’t a big fan of zero. He doesn’t add anything in addition. He’s of no use in division. And don’t even ask what he does to you in multiplication. But Zero knows he’s worth a lot, and when the other numbers get into trouble, he swoops in to prove his talents are innumerable.
How Much Is a Million? by David M. Schwartz is an excellent story about large numbers. Ever wonder just what a million of something means? How about a billion? Or a trillion? Marvelosissimo, the mathematical magician, can teach you! How Much is a Million? Knocks complex numbers down to size in a fun, humorous way, helping children conceptualize a difficult mathematical concept.
A Million Dots by Andrew Clements is a unique story that shows your students what 1 million dots can look like when put together. I loved this book because of its fun pictures and fascinating facts. This book could be used to practice reading large numbers or rewrite each number in standard, expanded, and word forms. You could also have your students build these large numbers using base ten blocks.
Earth Day–Hooray! by Stuart Murphy is a story about Ryan, Luke, and Carly. They must collect and recycle 5,000 cans to make enough money to plant flowers in Gilroy Park. This story is a lesson about recycling and the math skill of place value.
Place Value by David Adler is a story about monkeys. As they bake the biggest banana cupcake ever, they need to correct the amounts in the recipe. There’s a big difference between 216 eggs and 621 eggs. Place value is the key to keeping the numbers straight. Using humorous art, easy-to-follow charts, and clear explanations, this book presents the basic facts about place value while inserting some amusing monkey business.
Place Value Anchor Chart
I like to have an anchor chart with a place value chart with the values listed on my wall. This way, students can refer to it whenever they need to.
Check out the Compare Numbers Anchor Charts. The Google Slides version has movable counters and place value blocks.
Ideas for a Place Value Anchor Chart Kindergarten
In kindergarten I would have the teen numbers showing a ten, and then some more. For example, for 11, I would have a ten-rod, then one more.
Using Place Value Language
- Value
- Place Value
- Digit
- Tens
- Ones
- Place Value Chart
Getting Started with Numbers to 20 Activities in Math
Try Numbers to 20 Activities in Math or Represent a Number to get kids to understand the value of the digits in numbers to 20.
Videos about Place Value
- Place Value for Kids | What Is Place Value? Place Value for 1st Graders
- Place Value Song For Kids | Ones, Tens, & Hundreds | 1st – 3rd Grade
Place Value Math Lessons
If you ask a student how many tens are in 67, they may say 6 in the tens place because they simply name the position with little understanding. However, they may not understand that 6 represents 6 groups of ten or 60, and 7 represents 7 single units.
- ☀Download this BONUS Guide with everything you need to cultivate a positive classroom community.
- ➕Includes definitions, lesson ideas, mindset surveys for students and teachers, and printable posters.
- 🧠💪Research shows a link between a growth mindset and math success. Kids with a growth mindset about their abilities perform better and are more engaged in the classroom.
- 👉Includes everything you need to start cultivating a more positive math classroom and students who love math. Download and get started today! Click here to download the Mindset Guide & Survey.
This is why students need time to practice and build numbers to understand the value of each of the digits. Starting in Kindergarten with understanding teen numbers and progressing to place value 2 digits builds the foundation for more complex place value work.
