In this post, we'll explain what a place value is, what it means, and ask some questions to test your child's skills!
- What is a place value?
- When will my child learn the value in school?
- Schools that follow the Common Core:
- Other schools:
- How does my child learn about value in elementary school?
- Base ten blocks
- ten marks
- How does place value relate to other areas of mathematics?
- Place value and other areas of mathematics within each grade level
- Schools that follow the Common Core:
- Other schools:
- Asking practical questions that are of value to elementary school children
- related posts
What is a place value?
Place value is the basis of our entire number system. It is the value of each digit in a number. In other words, a digit's position in a number determines its value.
For example, the 5 in 350 represents 5 tens or 50; However, the 5 in 5006 stands for 5000 or 5000.
It's important for children to understand that while a digit can be the same, its value depends on where it is in the number.
Children are likely to learn the value of place through aGraphic as follows:
Often they appear with only letters to represent each position:METROMillions,Hno redºMiles,TSheºMiles,ºMiles,HWunder,TSo,ÖSimulator,Tones,Hundredths, and so on.
For example, in 27.435 the number 2 is in the ten thousand's place and represents 2 ten thousand or 20,000; the number 7 is in the thousands place and represents 7,000 or 7,000; the number 4 is in the hundreds place and represents 4 hundreds or 400, the number 3 is in the tens place and represents 3 tens or 30; and the number 5 is in the ones place and represents 5 ones or 5.
You can download yoursplace value chartand activity here. This is done in a snap and you can then physically manipulate the numbers to show their place value. That makes a big difference when working with children.
When will my child learn the value in school?
Place value is arguably one of the most important areas of the elementary school mathematics curriculum.
Each grade level has a set of goals that specifically focus on number and place value. At the beginning of each elementary school year, your child will likely be repeating previous place value work and expanding with larger numbers (or smaller in the case of decimals).
Schools that follow the Common Core:
emKindergarten, The pupils have to:
- Count in increments of one and ten to 100.
- Count forward from any number.
- Write numbers up to 20 in digits.
Students can also begin to recognize the place value in numbers above 20 by reading, writing, counting and comparing numbers to 100, aided by objects and visual representations.
em1st again, The pupils have to:
- Recognize the place value of each digit in a two-digit number (tens, ones).
- Read and write numbers up to at least 100 in numbers and spelling.
By the end of 1st grade, students should know that the number is related to 20 and use and understand the place value accurately.
em2. Grad, The pupils have to:
- Recognize the place value of each digit in a three-digit number (hundreds, tens, ones).
- Count to 1000; Jump count in 5s, 10s and 100s.
- Read and write numbers up to 1000 using digits, number names and extended form.
em3rd class, The pupils have to:
- Use place value understanding to round whole numbers to the nearest 10 or 100.
emFourth grade, The pupils have to:
- Realize that in a multi-digit integer, a digit in one position represents ten times what it represents in the position to its right.
- Read and write multi-digit integers using base ten, number names, and extended form.
- Use place value understanding to round multi-digit integers to arbitrary digits.
em5th grade, The pupils have to:
- Recognizes that in a multi-digit number, a digit in one position represents 10 times what it represents in the right position and 1/10 of what it represents in the left position.
- Read, write, and compare decimals to thousandths.
- Use place value comprehension to round decimals to arbitrary digits.
Other non-common-core schools follow the same sequence of concepts for teaching place values as shown above, although some individual standards may vary slightly.
How does my child learn about value in elementary school?
Two in elementary schoolConcrete Mathematical Resourcesare used to make the place value more understandable for children. The next two help with that by rendering it visually.
Base ten blocks
Base ten blocks (aka "base 10 blocks") are dice used to represent ones/ones, tens, hundreds, and thousands.
These cubes are an easy way for kids to form different numbers. To make number 174 they would need to make a set of 100, 7 sets of 10 and four individual dice.
Ten frames are rectangular grids with two rows of five cells. They are often used in elementary school classes to represent numbers related to "ten". This helps students develop a strong sense of numbers by providing simple visual representations of ones and tens.
To use a ten-board, students are given counters that they can manipulate within the ten-board to create different numbers and learn about place value. You can also use two tens frames (a full tens frame to show a ten, then a second tens frame to show the ones) to form numbers 11 through 20. Frames of ten are also used when students are just beginning to learn, and to add and subtract.
Understanding place value is crucial for children before they can add and subtract two-digit numbers.
If you're interested in delving deeper into this topic, we encourage you to keep reading this in-depth guideteach valueand test some of themPriority games.
How does place value relate to other areas of mathematics?
Place value is inseparable from many other areas of mathematics; A solid understanding of this is essential for children to be proficient at adding, subtracting, multiplying and dividing, among other things.
Place value and other areas of mathematics within each grade level
Schools that follow the Common Core:
emKindergarten, students will assemble (make) and decompose (dissect) numbers from 11 to 19 into tens and ones using objects or drawings.
in the 1st classstudents use place values and numbers to add and subtract up to 100.
in the 2nd year,Students will add and subtract within 1000 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction and explain why these strategies work.
In the third rowPlace value is used in addition and multiplication. Students add and subtract within 1000 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
Students will also multiply single digit integers by multiples of 10 in the range 10 to 90 using strategies based on place values and properties of operations.
In measurement, third grade students develop their understanding of place value by relating addition and multiplication to the concepts of area and perimeter.
In the fourth grade,Students add and subtract multi-digit integers using the standard algorithm.
Students will also multiply a four-digit integer by a one-digit integer, multiply two two-digit numbers, and divide up to four-digit dividends and single-digit divisors, all using place-value based strategies.
In measuring, students will apply their knowledge of place value and the four operations to solve problems involving distance, time interval, volume of liquid, mass of object, and money. You will also use multiplication and division to convert between units like meters and kilometers.
in the 5th grade,Students will multiply multi-digit integers using the standard algorithm and will divide integers using up to four-digit dividends and two-digit divisors
Students will use their understanding of place value to add, subtract, multiply and divide decimals up to hundredths.
When measuring, students convert between standard units of measurement of different sizes within a given measurement system.
Other schools that do not follow the Common Core still follow the same sequence of concepts shown above; Students begin forming and decomposing tens and ones in kindergarten and progress through all four operations until finally using all four operations with decimal numbers in fifth grade. Some rules may vary by state.
Asking practical questions that are of value to elementary school children
Try this to get an idea of how comfortable your child is with the place value system.
1) What is the value of the digit 7 in the following numbers? a) 405.7 b) 30,070
2) Jack has four number cards: 2, 3, 4, and 7. Use each card once to form a four-digit number. He writes 4 in the tens column; 2 to have a higher value than all other digits and the remaining digits to make 7 the highest value. What number did Jack do?
3) Look at this number: 23,451.96. Write the number in a) the hundreds place b) the hundredths place.
4) Write the number 402,037 in words.
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This blog is part of our blog series aimed at teachers, schools and supportive parentslearning at home.
On the other handmathematical terminology, take a look at ourElementary mathematical dictionary for childrenIt includes parent and child definitions of all important math vocabulary.
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The content of this article was originally written by elementary school teacher Sophie Bartlett and has since been revised and adapted for schools in the United States by elementary school math teacher Katie Keeton.