problem solving for place value

Problem Solving with Place Value

February 3, 2021.

Understanding place value provides the essential foundation for so many aspects of mathematics, from multiplying and dividing by powers of ten, understanding the equivalence between fractions, decimals and percentages, and learning how to write and calculate with numbers in standard form.

The videos below show how I use the place value table to teach these topics conceptually.

Writing numbers as words

Multiplying by 10, 100 and 1000

Converting between fractions, decimals and percentages

I designed this problem-solving lesson to deepen students’ understanding of place value to connect it to other aspects of mathematics, including listing permutations, odd and even numbers and money. By linking to these topics, the questions are challenging yet remain accessible to students in key stage 3 and those studying the foundation GCSE course.

The lesson consists of six problem-solving questions, all centred around place value. Here is a sample of three of the questions.

Here is a sample of three of the questions.

Linking place value to arithmetic

In this question, students link their understanding of place value to writing numbers in figures from words. Next, they use column subtraction to find the difference between two numbers.

Linking place value to permutations

In this question, students arrange the four single-digit cards to make the numbers between 230 and 430.

Students link their understanding of place value to listing permutations.

Linking place value to odd and even numbers

To work out the smallest, even number, students need to find two three-digit numbers with the least difference.

To calculate the biggest, odd number, they need to find two numbers with the greatest difference.

Both questions can be completed through a method of trial and improvement. More able students would use:

• odd + odd = even
• odd + even =odd
• even + odd = odd
• even + even = even.

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About Mr Mathematics

My name is Jonathan Robinson and I am passionate about teaching mathematics. I am currently Head of Maths in the South East of England and have been teaching for over 15 years. I am proud to have helped teachers all over the world to continue to engage and inspire their students with my lessons.

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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 Concepts

This page contains resources to support teaching and learning of place-value concepts. Three videos draw on research-based frameworks to illuminate the rich and complex topic of place value and how children come to understand this topic. Additionally an interview protocol for diagnosing student understanding of place value is available along with video examples of students participating in that interview. Finally a list of additional resources is offered for those who wish to go further with study of this topic.

Educator Videos

The following three videos contain a discussion and synthesis of research-based frameworks that can be useful for making sense of student understanding of place-value concepts and an interview protocol in PDF format used to assess students understanding of place value during these interviews.

The Multifaceted Nature of Place Value: It’s About More Than Digit Values

11:56 / View on YouTube / Download Transcript

The Child’s Perspective on Place Value: Five Ways Children Conceptualize Two-Digit Numbers

12:08 / View on YouTube / Download Transcript

Provoking Place-Value Reasoning with Groups of Ten Word Problems: Excerpts from Ms. Brannon’s First Grade Class

14:41 / View on YouTube / Download Transcript

Place-Value Assessment Resources

Click the thumbnails to access resources to support assessment of students’ understanding of place-value in a base-ten number system. The assessment designed to be used in a one-on-one interview setting. Blackline masters are also available in the downloadable file. The downloadable diagram provides a conceptual model for the various components of place-value understanding that occur over a period of several years of school mathematics.

Student Videos

The following three videos show a kindergarten student, a first-grade student, and a second-grade student engaged in the place-value interview.

Kindergarten – Tim

19:51 / View on YouTube / Download Transcript

First Grade – Weston

30:00 / View on YouTube / Download Transcript

Second Grade – Valerie

23:47 / View on YouTube / Download Transcript

Resources for Further Study of Place Value

Click the following titles to access a short list of teacher resource books and journal articles that were reviewed in preparation of these resources.

Teacher Resource Books

• This book details research findings on the development of children’s mathematical thinking in relation to the four operations (addition subtraction multiplication and division) and base-ten number concepts.
• Chapter one of this book includes ideas for teaching and assessing place-value concepts. The book also contains a collection of activities focused on providing children with a variety of experiences generating strategies for organizing large quantities into tens and ones.
• This book includes a collection of ideas for teaching and assessing place-value concepts. Lessons are organized into three main types: Counting and grouping activities number chart activities and activities focused on exchanging ones and tens. The assessments chapter contains suggestions for tasks to use in an individual interview.
• Chapter eleven of this book includes discussion of children’s development of whole-number place-value concepts and ideas for instruction and assessment related to these concepts.
• This article illustrates how contextualized problems involving groups of ten can be used to advance early elementary students’ understanding of place-value concepts.
• This article introduces a set of strategic counting tasks’ to use for the purpose of assessing children’s place-value understanding. The authors discuss the advantages of the strategic counting tasks over other tasks commonly used to assess place-value understanding and detail findings of three research studies that used this set of tasks.
• Drawing on data from four research projects implementing a problem-solving approach to teaching and learning multidigit number concepts and operations this article presents a framework of conceptual structures that articulate different ways children think about multidigit numbers. The article also discusses categories of methods children devise to solve multidigit addition and subtraction problems. The research in this article forms the basis of the ideas presented in  The Child’s Perspective on Place Value: Five Ways Children Conceptualize Two-Digit Numbers (see above).
• This article draws on the work of multiple research projects to identify curricular elements essential for the development of place-value understanding. A framework is suggested for nurturing and assessing place-value understanding in the early elementary grades.
• This article describes findings of two studies utilizing digit-correspondence tasks to explore students’ understanding of the meaning of the digits in two-digit numbers. Implications for the classroom are also discussed.
• This article describes findings from a classroom study that explores the effects of classroom lessons involving digit-correspondence tasks on students’ understanding of the meaning of the digits in two- and three-digit numbers.

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Problems Related to Place Value | Tips to Solve Place Value Questions | Place Value Word Problems

Are u seeking homework help to solve the problems on place values? If yes, then this guide is the perfect solution. Here, in the below modules, we have wrapped plenty of problems related to place values. But First and foremost, students should have proper knowledge on what is place value and tips that develop place value. Generally, place values are used to represent the group of digits in the correct position in the place value chart . Let’s have a glance at Problems Related to Place Value for quick & easy solving.

What is Place Value?

Place value can be defined as the value followed by a digit in a given number based on its position in the number. Every digit in a number has a place value. The place value of digits has a position itself such as ones, tens, hundreds, thousands, ten thousand, and so on. Every number has a place value and face value. Place value is nothing but the position of a number whereas the face value is the number itself.

If a number has the same digits twice or more but the place value of a digit is different from one another. For instance, if we have the number 25423, here, 2 is repeated twice but the place value of 2 is different i.e., one place value of number 2 is ten thousand (2×10,000) and another place value of a number 2 is tens (2×10).

Let’s represent the digits with place values using a place value chart. It helps the students to know the correct places of a number and each digit that stands for. The following place value table makes it clear to identify the digits quickly.

Place Value Table Using International System

Here is the table to remember & learn easily about the place value of a given number in the international place value system:

Also Check :

• International Place Value Chart
• Worksheet on International Numbering System
• Worksheet on Indian Numbering System

Place Value Table Using Indian System

Let’s see the same above number in the Indian Place Value system and aware of the difference while solving problems related to place values:

Tips to Solve Place Value Problems

• Take the place values and use blocks to represent them. It helps in reading and writing numbers easily.
• Count the place values by grouping them as 10’s, 100’s, and 1000’s, and so on.
• Practice the place value problems daily to build confidence and to grasp the place values of a number in seconds.
• Place value positions are increased 10 times than the previous place value of a digit.

Problems Related to Place Values

Write the digits in the place value of M, T, H-Th, H for the number 7634562.

Take the given number 7634562. Place the digits with place values using commas i.e., 7,634,562.

A number in place value of Tens (T) is 6.

A number in place value of Hundreds (H) is 5.

A number in place value of Hundred thousand (H-Th) is 6.

A number in place value of Million (M) is 7.

Example 2: 

Write the place values of highlighted digits of given numbers

(i) 2 9 54623

(ii) 1 2 4789

(iii) 32 5 47

(i) Take the given number 2,954,623

The place value of a stressed digit 9 is at a Hundred thousand position i.e., 9×100,000=900,000.

(ii) Take the given number 124,789

The place value of a stressed digit 2 is at Ten thousand position i.e., 2×10,000=20,000.

(iii) Take the given number 32,547

The place value of a stressed digit 5 is at Hundreds place i.e., 5×100=500.

Find the place values of the number 987654321.

The given number is 987654321.

Place the number in the correct position using place values by grouping them with the help of three periods.

Thus, the number is 987,654,321 after grouping the digits.

The place values of digits are

Number 1 is in one’s place 1×1=1, Number 2 is in the tens place 2×10=20, Number 6 is in the hundreds place 3×100=300, Number 4 is in thousands place 4×1000=4000, Number 5 is in ten thousand place 5×10,000=50,000, Number 6 is in hundred thousand place 6×100,000=600,000, Number 7 is in million place 7×1,000,000=7,000,000, Number 8 is in ten million place 8×10,000,000=80,000,000, and Number 9 is in hundred million place 9×100,000,000=900,000,000.

For clear understanding, we have given the representation of the number in an image form as below.

What number has 5 tens and 3 more ones than the tens?

First, we know that we have 5 tens and also have 3 more ones than the tens.

Next, our Tens are 5. We add 3 to 5 for ones i.e., 3+5=8.

Now, there are 8 ones.

Thus, the answer is 58 .

What number has 7 tens and 3 fewer ones than the tens?

We have 7 tens and 3 fewer ones than the tens.

Our tens are 7 and subtract 3 ones from 7 ones i.e., 7-3=4.

Now, there are 4 ones.

Therefore, the answer is  74 .

What number has 7 ten thousand, 1 fewer thousand than ten thousand, 3 more hundreds than thousands, the same number of tens as hundreds, and 2 fewer ones than thousands?

First, the number in ten thousand place value is 7.

There are 7 ten thousand and 1 fewer thousand than ten thousand i.e., 7-1=6 (6 is in thousands place).

3 more hundreds than thousands i.e., 3+6=9 (9 is in hundreds place).

Then the same number of tens as hundreds i.e., 9 is in hundreds place then tens place value is 9.

2 fewer ones than thousands i.e., 6-2=4 (4 is in one’s place).

Thus, the number with the place values is 76,998 .

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