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Lesson 1-2 Place Value Relationships

Mathematics.

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Name the value of the digit 5 in 152,432,962.

In one year, a large airport was used by 5,662,000 passengers. In the number 5,662,000, the value of the 6 in the hundred thousands place is _________ the value of the 6 in the ten thousands place.

Susie says that in the number 55,555,555, all the digits have the same value. Is she correct?

Vin says that in the number 4,346, one 4 is 10 times as great as the other 4. Is he correct?

What is another way of naming 900?

9 thousands

Which of the following shoes 564 in word form?

Five hundred sixty-six

Five hundred sixty-four

Five hundred forty-six

Five hundred sixty

How is 3, 072 written in expanded form?

300 + 70 + 2

3,000 + 70 + 2

3,00 + 700 + 2

3,000 + 700 + 20

Which place has the least value in the number 2,387?

Thousands place

Hundreds place

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Place Value Worksheets

And base 10 blocks.

Our place value worksheets focus on deepening a student's understanding of our base 10 system. In our " base 10 blocks " worksheets, students manipulate blocks (units of 1) and rods (groups of 10) to build, deconstruct or add numbers. Later worksheets focus on building or de-constructing multi-digit numbers.

Choose your grade / topic:

Grade 1: Base 10 blocks worksheets

Grade 1: Place value worksheets

Grade 2: Place value worksheets

Grade 3: Place value worksheets

Grade 4: Place value worksheets

Grade 5: Place value worksheets

Topics include:

Grade 1 base 10 blocks worksheets

• Counting and making 10 with ten frames
• Regrouping unit blocks into blocks of 10 ("rods")
• Counting "tens" and "ones"
• Breaking a number (11-99) into rods ("tens") and  blocks ("ones")
• Adding 2 digit numbers with base 10 blocks

Grade 1 place value worksheets

• Identifying tens and ones from 2 digit numbers
• Combining tens and ones into 2 digit numbers
• Identifying a digit's place value (tens, ones)
• Building a 2 digit number with missing addends
• Write 2 digit numbers in expanded form
• Write 2 digit numbers in normal form

Grade 2 place value worksheets

• Building a 3-digit number from the parts
• Missing place values in 3-digit numbers
• Write 3-digit numbers in expanded form
• Write 3-digit numbers in normal form
• Hundreds, tens & ones - identify the underlined digit
• Comparing and ordering numbers up to 100 and 1,000

Grade 3 place value worksheets

• Building 3, 4 and 5-digit numbers from the parts
• Missing place values in 3 and 4-digit numbers
• Write 4-digit numbers in expanded form
• Write 4-digit numbers in expanded notation
• Write 4-digit numbers in standard form
• Identify the place value of the underlined digit
• Compare and order numbers up to 10,000 and 100,000

Grade 4 place value worksheets

• Building 4, 5 and 6-digit numbers from the parts
• Missing place values in 4, 5 and 6-digit numbers
• Write 5-digit numbers in expanded form
• Write 5 digit numbers in expanded notation
• Write 5-digit numbers in standard form

Grade 5 place value worksheets

• Building 5 and 6-digit numbers from the parts
• Missing place values in 5 and 6-digit numbers
• Build numbers from parts with decimals
• Decimal numbers in expanded form
• Decimal numbers in expanded notation

Related topics

Comparing numbers worksheets

Rounding worksheets

Sample Place Value Worksheet

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Place Value Relationships

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• Content and Standards

This post explains how to teach place value relationships for understanding and offers activity ideas and resources.

You want me to teach . . . place value relationships? What on Earth does that mean? 

It was always the first lesson of the year . . . place value — Ugh! 

I went to my math storage area and pulled out sets of Base 10 Blocks, place value mats, and dry erase materials as I prepared for the next day’s lesson. 

I had done the same lesson at least 20 times. We modeled numbers with Base 10 Blocks to help students “see” the number in a hands-on way. Then we moved to reading and writing numbers in number form, word form, and expanded form. 

Fast forward about 10 years. The standards have changed. 

Now, instead of just teaching students how to read and write numbers, we are required to teach students to recognize a digit in the tens place is ten times greater than the same digit that is one place to its right, the ones place. 

That just sounds complicated, right? 

And now I have to teach it to kids . . . oh my word!

So what does this standard really mean– in simple terms? 

According to Gojak and Miles (2016), this standard

• Relates the relationship of the values of the digits in a number to multiplication and division
• Connects to multiplying and dividing by multiples of 10

Relationship Between The Places: Moving To The Left

Notice the value of the Base 10 Blocks on the far right have a value of 3. Observe what happens each time we move to the left. 

The value of the blocks is 10 times greater than the previous set of blocks. Thus, the value of the 3 is 10 times greater as well.

• When we move one place to the left from the ones place (3), the tens place (30) is 10 times greater than the ones place. 
• Moving one place to the left from the tens place (30), the hundreds place (300) is 10 times greater than the tens place.
• When we move one place to the left from the hundreds place (300), the thousands place (3,000) is 10 times greater than the hundreds place.  

Relationship Between The Places: Moving To The Right

Now, notice the value of the Base 10 Blocks on the far left have a value of 3,000. 

Each time we move to the right, the value of the blocks is one-tenth of the previous set of blocks. Thus, the value of the 3 is one-tenth of the previous value.

• When we move one place to the right from the thousands place (3,000), the hundreds place (300) is one-tenth of the thousands place. Think: 3,000 ÷ 10 = 300.  
• Moving one place to the right from the hundreds place (300), the tens place (30) is one-tenth of the hundreds place. Think: 300 ÷ 10 = 30.  
• When we move one place to the right from the tens place (30), the ones place (3) is one-tenth of the tens place. Think: 30 ÷ 10 = 3.  

How Do Decimals Fit Into The Picture?

Using Base 10 Blocks to represent the relationship between decimal values requires a bit of a shift in thinking. 

The relationships follow the same rules from left to right and right to left; however, more attention is needed to ensure decimal values are represented correctly. 

Ways To Help Students Understand Place Value Relationships

Students need many opportunities to explore this concept and explain the relationship between the same digits in different numbers. 

Follow-up activities:

• Have students compare the value of the same digit in different numbers. For example, ask students, “How does the value of the 7 in 10,749 compare with the 7 in 8,567?” Then have students use mathematical language to explain the comparison.
• Look at patterns of numbers such as 4, 40, 400, 4,000, and 40,000 and have students extend the pattern and explain what happens to the value of the four as you move from left to right or right to left. 
• Give students a number and ask them to record a number which includes a specific digit that has a value related to the original number. For example, say, “Write a number where the nine has a value that is 100 times greater than the value of the nine in 911.” Or, say, “Write a number where the two has a value which is one-tenth of the value of the two in 2.56.” Students can then record their responses on a dry erase board and share/justify them to a partner. 

Communicating About Place Value Relationships

Providing a variety of place value activities and games to reinforce this concept is essential to student mastery. Students should also be encouraged to identify the relationship between places in numbers as “_____ times greater” or ______ (fraction) of the value of the [insert digit] in the [insert previous place].” 

Making connections to multiplying by multiples of 10 (moving from right to left) or dividing by multiples of 10 (moving from left to right) can be reinforced at this time as well. 

Final Thoughts

For many students, the abstractness of understanding place value relationships is confusing. Using manipulatives, such as Base 10 Blocks, to model numbers and make visual connections help students understand the skill. 

Recognizing a digit in the tens place is ten times greater than the same digit that is one place to its right, in the ones place, doesn’t have to be complicated. With manipulatives, standards-based activities , and opportunities to explain their thinking, students will be able to articulate the relationship between place values. 

Ready to jump in? Grab my free place value dice game using the form below.  

What strategies do you use to help your students understand place value relationships?

Gojak, L. M. & Miles, R. H. (2016). The Common Core Mathematics Companion: The Standards Decoded. Thousand Oaks, California: Corwin.

Shametria Routt Banks

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Place Value Worksheets Hub Page

Welcome to our Place Value Worksheets area.

Here you will find a wide range of place value activites and worksheets which will help your child gain a better understanding of how our number system and place value works.

You can also take a look at our printable place value charts or our place value sheets with decimals or BIG numbers over a million!

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Place Value Worksheets and Resources

On this page you will find link to our range of place value resources, including online practice, charts and worksheets.

Quicklinks to Place Value ...

• Online Place Value Practice
• Place Value Charts and Number Grids
• Place Value Tens and Ones

Place Value up to Hundreds

Place value up to thousands.

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Place Value Games

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Definition of Place Value

So what exactly is place value?

Place value refers to the value of the digits in any given number. In the number 482 for example, the value of the digit '8' is 80 and the value of the digit '4' is 400.

At a more advanced level, in the number 36.57, the value of the digit '5' is 0.5 and the value of the digit '7' is 0.07.

In our number system, each time you move a place to the right, the value of the digit gets ten times bigger. Each time you move a place to the left, the value of the digit gets ten times smaller.

• Definition of Place Value Sheet
• PDF version

Place Value Learning

Children start their learning journey in Math when they start to count. When they are confindent counting small groups of objects and getting beyond 10, they then begin to develop their understanding of place value up to 100 and beyond.

When they have understood how place value with whole numbers works, they can start learning about place value with decimals.

Our selection of free math place value worksheets has been split into different areas below so that you can more easily find the right sheet for your child.

Online Place Value Practice Zone

In our Math Place Value Practice area, you can practice your place value skills, adding thousands, hundreds, tens and ones. You can even use this area for adding on decimals: tenths and hundredths.

You can select the numbers you want to practice with, and print out your results when you have finished.

You can also use the practice zone for benchmarking your performance, or using it with a group of children to gauge progress.

• Free Place Value Practice Zone 1 - Digit Values
• Math Place Value Practice Zone 2 - Combining

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Place Value Charts & Number Grids

Place value charts.

We have a selection of place value charts which are great for helping to develop understanding of place value.

The charts cover a range of numbers from billions to millionths.

They are a good supporting resource for children who are finding place value difficult.

We also have place value grids to help children convert to and from expanded form to support place value learning.

They are also a good way to get children to become familiar with how the number system works.

• Place Value Charts (whole numbers)
• Decimal Place Value Charts
• Place Value Grids

Number Grids

These printable grids will help your child learn to read and write numbers and learn the number sequence.

Some of the charts are partially filled to help your child learn their place value.

Using these sheets will help your child to:

• learn to count in tens and ones;
• learn to read and write numbers.

1st Grade Place Value Charts

• Free Number Chart 1-30
• Number Chart to 50
• Printable Number Charts 0-99
• Hundred Number Charts (100 Squares)
• Missing Number Chart 1-100
• Number Grid up to 200
• Number Grid up to 300

Here you will find our selection of place value games.

We have a range of different games for helping to teach place value from 2-digit games up to decimal place value games.

There are a range of games are suitable for all ages, from kindergarten and upwards.

• Games to teach Place Value

Place Value and Number Sense Tens and Ones

Here you will find our selection of 2 digit Place Value worksheets.

Using these Math Worksheets Place Value will help your child to:

• learn their place value to 100;
• understand the value of each digit in a 2 digit number;
• Round numbers up to 100 to the nearest 10
• learn to read and write numbers to 100.
• Place Value Worksheets for Kindergarten
• Place Value to 20 Worksheets
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• Basic Math Worksheets - Ordering numbers 2 Digits
• Rounding to the nearest 10 Worksheets
• Add and Subtract 10 Worksheets

Here you will find our selection of 3 digit Place Value worksheets.

• learn their place value with 3 digit numbers;
• understand the value of each digit in a 3 digit number;
• learn to read and write numbers up to 999.
• 2nd Grade Place Value Models up to hundreds
• Second Grade Place Value Worksheets 3 Digits
• Ordering numbers worksheets up to 999

Here you will find our selection of Place Value up to 4 Digits worksheets.

Using these sheets will help your child learn to:

• learn their place value with 4 digit numbers;
• use place value models to understand how to combine thousands, hundreds, tens and ones;
• understand the value of each digit in a 4 digit number;
• learn to use standard and expanded form with 4 digit numbers.
• Place Value Models 4 Digits
• Place Value 4 Digit Numbers Worksheets (conversion)
• Ordering Numbers up to Thousands Sheets

Place Value BIG Numbers

Welcome to our BIG Number Place Value area.

Here you will find sheets to help your child learn their place value to 10 million.

• Know how to read and write numbers to 10 million;
• Understand place value to 10 million.
• Solve place value problems.

All the 4th grade math worksheets in this section support elementary math benchmarks.

• 4th Grade Place Value up to 6 digits
• 5th Grade Place Value Worksheets to 10 million
• 5th Grade Ordering Large Numbers up to 100 million

Place Value Negative Numbers

• learn to order negative numbers;
• learn to position numbers from -10 to 10 on a number line.
• ordering and comparing rational numbers
• Ordering Negative Numbers -10 to 10
• Ordering and Comparing Rational Numbers

Place Value Decimals

Here you will find our selection of Place Value involving Decimals with up to 2 decimal places (2dp).

• learn their place value with decimals up to 2dp;
• understand the value of each digit in a decimal number;
• learn to read and write numbers with up to 2dp.
• Decimal Place Value Worksheets to 2dp
• Place Value to 3dp
• Ordering Decimals Worksheets

Rounding Numbers Worsheets

As well as our random number worksheet generator, we have a wide range of graded rounding worsheets.

These sheets are great for supporting less able students, or for giving an extra challenge to more able students.

Using the link below will take you to our Rounding numbers hub page where you will find links to all our rounding numbers worksheets.

• Rounding Numbers Hub page

Place Value Random Worksheet Generator

Here is our generator for generating your own place value worksheets.

Our generator will create the following worksheets:

• digit values
• comparing numbers
• converting between standard and expanded form

These sheets involve saying the value of the underlined digit.

• Digit Place Value Worksheets
• Standard Form to Expanded Form Worksheets
• Expanded Form to Standard Form Worksheets
• Rounding Off Numbers Worksheets
• Greater Than Less Than Worksheets

We have a selection of worksheets designed to help students learn about asbolute value.

Topics covered include:

• absolute value and opposite numbers
• comparing absolute values
• absolute value arithmetic
• solving absolute value equations

Our Convert to scientific notation calculator will take a number and convert it to scientific notation and e-notation.

It shows you all the working out along the way too.

• Convert to Scientific Notation Calculator
• Standard Notation to Scientific Notation Support page
• Scientific Notation to Standard Notation support page

Online Place Value Quiz Page

Here you will find our selection of place value quizzes.

We have a wide range of different quizzes which support the worksheets that we produce.

There are a range of place value and number sense quizzes suitable for all ages, from kindergarten and upwards.

• Online Place Value Quiz

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Place Value Worksheets

A vast compilation of printable worksheets on place value can be instantly downloaded from this page. You can find multiple place value activities, charts, posters and practice worksheets to reinforce your place value skills. Abacus and Base Ten Blocks are excellent teaching tools to review the key concepts of place value. Students also learn to represent whole numbers and decimals in the standard and expanded form.

List of Place Value Worksheets

Abacus Worksheets

Bundles of Tens and Ones Worksheets

Base Ten Blocks Worksheets

Number Names Worksheets

Place Value Charts

Place Value - Ones, Tens, Hundreds

Place Value - Thousands

Place Value - Large Numbers

Place Value Activities

Place Value - Decimals

Standard and Expanded Form Worksheets

Explore the Place Value Worksheets in Detail

One of the best instructional aids to help kids count and learn place value of numbers is the Abacus method. All worksheets presented here employ the abacus model to represent place values up to 4-digits.

Impart foundational knowledge of place value among early learners with these bundles of tens and ones worksheets. They count the objects, sticks, and shapes, and discern tens as a group of ten ones.

These worksheets reinforce knowledge in place values up to thousands with the use of base ten blocks. A perfect visual aid to learn place value of digits.

This exclusive page contains 400+ worksheets on Number Names ranging up to billions. Guide young learners to convert whole numbers to number names and vice versa.

Download and print place value posters and charts from this page. The charts are illustrated with vibrant pictures and are classified into place values ranging from tens to billions.

This array of worksheets comprises a wide range of exercises like identify the place value of digits up to hundreds, write equivalent place values, MCQ's, 'What number am I' and a lot more!

Download our worksheets and get students to determine the place value of the specified digit up to thousands. Exercises like frame the smallest and largest number and much more are up for grabs!

Access our worksheets to learn place value of large numbers up to 12-digits. Activities like insert commas, write the place value of the underlined digit, word problems and more are included here.

Use this set of interactive worksheets to learn subtraction the fun way! Find the place value of the specified digit with a variety of coloring and cut-and-glue activities that will also enhance a child's fine motor skills.

Assist students to understand the place value of digits in a decimal with this batch of ready-to-print worksheets. Well-researched word problems are also incorporated to grasp the concept better.

Select from a wide range of resources on standard and expanded form for whole numbers and decimals. Exclusive worksheets are included for word form, product form and exponential form.

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engaging printable & digital math lessons for upper elementary teachers

2.1 Place Value Relationships

Objective: Students will identify the value of each place as 10 times greater than the place to its right and 10 times less than the place to its left, while interpreting questions to identify the unknown.

• How do we know the value relationship between the places?
• What is the value of each place compared to 2 places to its right?
• What is the value of each place compared to 2 places to its left?

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Place Value Relationships

Understanding place value is an important Math skill for elementary students.  One of the objectives is for students to describe the relationship between places in a base ten system.  Although this may seem difficult at first, starting with concrete manipulatives can really help students gain a deeper understanding.

I like to start by letting students “play” with the blocks for a few minutes.  Then I will ask specific questions and have them use the blocks to work out answers.  One such example is “How many ones do you need to equal a ten?” or “How many tens can you use to make one hundred?”  Give students time to work together or independently with the blocks to answer the question, then discuss.  I also like to write the questions/answers on the board or have a record sheet for them to work along with.

After students have a lot of practice discussing and writing the relationships with place value blocks, a place value chart will come in handy.  I like to use different colors and draw arrows on the place value chart to show the students the patterns on the chart.

I also teach students how to draw their own place value charts.  When working word problems with relationships, I have my students draw and label place value charts.

If you are looking for resources to help your students master this objective, I have two great resources in my TpT store:

Place Value Relationships Task Cards:

Place Value Relationships Notes and Practice:

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6 thoughts on “ place value relationships ”.

I love how you color code and and draw arrows to help your students see the patterns on the place value chart. Great idea!

Thanks for sharing these great activities. I need all the help with Math that I can get!

Wow! Our school has just been discussing the importance of place value! Great ideas 👍🏼

I really, REALLY appreciate all the images in this post. For those who are a little slow catching on in understanding what you are teaching and how you go about it, (myself included) the photos are so helpful. Excellent resource on Place Value!

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Place Value Relationship

Jonalyn Dela Fuente

Recognizing the relationship of digits using place value

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Homework 1 2 Place Value Relationships

Homework 1 2 Place Value Relationships - Displaying top 8 worksheets found for this concept.

Some of the worksheets for this concept are Lesson name model place value relationships number and, Homework practice and problem solving practice workbook, Place value work, Place value activity package, Name reteaching 3 2, Chapter 1 place value, Teksstaar based lessons, Value of the digit 1.

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1. Lesson 1.1 Name Model Place Value Relationships Number and ...

2. homework practice and problem-solving practice workbook, 3. place value worksheets -, 4. place value activity package, 5. name reteaching 3-2 -, 6. chapter 1 place value, 7. teks/staar-based lessons, 8. value of the digit sheet 1.

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Place value relationship

Ten Times Greater Place Value Relationships Packet, Power of 10 Worksheets

Place Value Task Cards - Base 10 Relationships to the Millions Place - 4th Grade

Place Value Relationships Interactive Notebook Activity & Quick Check TEKS 3.2B

Place Value Charts to Support Expanded Notation and Place Value Relationships

Ten Times Greater Place Value Relationships Google Slides Place Value 4th Grade

Place Value Relationships in Base 10 Digital Boom Cards - 4th Grade Math

Place Value Patterns Worksheets 10 to 1 Relationships

Place Value Chart to Millions Notes Vocabulary Place Value Relationships Quiz

Place Value Relationships 10x Cards Activity

4th Grade 10x Rule Place Value Relationships

Place Value Relationships Guided Notes & Practice

Place Value Relationships Interactive Notebook Activity & Quick Check TEKS 4.2A

Ten Times Greater Place Value Relationships Task Cards with Decimals 5th Grade

From Place to Place place value relationships task cards + printables (set a)

Place Value Relationships 10x Arcade Task Cards

Multiplying and Dividing by Powers of 10 Math Tool Kit Place Value Relationships

Place Value Relationships in Base 10 Editable PowerPoint and Activities

Digital Game - Ten Times Place Value Relationships - Digital Math Stations

Place Value Relationships Special Education Place Value to 1000 Expanded Form

Place Value Relationships Task Cards Review SCOOT to Hundred Thousands Millions

3rd Grade Math Centers: Review Place Value Relationships Interactive Math Sorts

Place Value Relationships Multiplying and Dividing by Powers of 10 Google Slides

"I Have Who Has" Place Value Relationships Game (10 Times and One-Tenth Of)

Fourth Grade Digital Place Value Slides - Number Patterns and Relationships

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