Place value is the basis of our entire number system. A place value system is one in which the position of a digit in a number determines its value. In the standard system, called base ten, each place represents ten times the value of the place to its right. You can think of this as making groups of ten of the smaller unit and combining them to make a new unit.
Ten ones make up one of the next larger unit, tens. Ten of those units make up one of the next larger unit, hundreds. This pattern continues for greater values (ten hundreds = one thousand, ten thousands = one ten thousand, etc.), and lesser, decimal values (ten tenths = one one, ten hundredths = one tenth, etc.). At this level, however, your students will be focusing on mastering place value for ones, tens, and hundreds.
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In standard form, the number modeled above is 233.
A place-value chart is a way to make sure digits are in the correct places. A great way to see the place-value relationships in a number is to model the number with actual objects (place-value blocks, bundles of craft sticks, etc.), write the digits in the chart, and then write the number in the usual, or standard form. Place value is vitally important to all later mathematics. Without it, keeping track of greater numbers rapidly becomes impossible. (Can you imagine trying to write 999 with only ones?) A thorough mastery of place value is essential to learning the operations with greater numbers. It is the foundation for regrouping ("borrowing" and "carrying") in addition, subtraction, multiplication, and division.
Understanding place value, however, is much more than knowing how to break numbers into hundreds, tens and ones. Some students who can recite "247 has 2 hundreds, 4 tens, and 7 ones" may have no idea about the relationship of 247 to the number system -- for example, that it is 100 more than 147 and 10 less than 257, that it is almost 250, or that it is about halfway between 200 and 300.
Understanding place value and how it is linked to understanding how a number is composed and to knowing its relationships to many other numbers is crucial for students to master before learning more complex mathematics. For example, understanding the place value of a number like 126 is studied in a larger context that includes exploration of the following questions:
Where is the number in the number system? (Is it bigger than 10, bigger than 50, bigger than 100?)
How can the number be pulled apart into additive components that are easy to work with? (For one problem, it might be convenient to pull 126 apart into 100 and 25 and 1; for another problem, it might be convenient to think of it as 120 and 6.)
What are the factors of the number? (What numbers can you count by to reach the number exactly?)
What are the multiples of the number? (What happens when the number is doubled or multiplied by 10 or by 100?)
What is the relationship of the number to important numbers in our number system, such as multiples of 10, 25, or 100?
Throughout work on the number system and the place value of numbers, the emphasis is on making sense of the structure of the number system and on developing a large repertoire of number relationships that students can build on to solve problems. One focus of this work is on what we have come to call landmarks in the number system -- familiar anchor points in the sequence of numbers, such as 10, 25, 100, 1000, .1, and their multiples. Students study these numbers, their factors and multiples, and their relationships to other numbers. Because operations with numbers such as tens and hundreds make for simple calculations, place value plays a critical role throughout the grades in the development of strategies. Consider the following addition problem and sample strategy:
364 + 347
Break the addends into hundreds, tens, and ones, then combine the parts:
Place Value Overview:
Place value is the basis of our entire number system. A place value system is one in which the position of a digit in a number determines its value. In the standard system, called base ten, each place represents ten times the value of the place to its right. You can think of this as making groups of ten of the smaller unit and combining them to make a new unit.Ten ones make up one of the next larger unit, tens. Ten of those units make up one of the next larger unit, hundreds. This pattern continues for greater values (ten hundreds = one thousand, ten thousands = one ten thousand, etc.), and lesser, decimal values (ten tenths = one one, ten hundredths = one tenth, etc.). At this level, however, your students will be focusing on mastering place value for ones, tens, and hundreds.
In standard form, the number modeled above is 233.
A place-value chart is a way to make sure digits are in the correct places. A great way to see the place-value relationships in a number is to model the number with actual objects (place-value blocks, bundles of craft sticks, etc.), write the digits in the chart, and then write the number in the usual, or standard form.
Place value is vitally important to all later mathematics. Without it, keeping track of greater numbers rapidly becomes impossible. (Can you imagine trying to write 999 with only ones?) A thorough mastery of place value is essential to learning the operations with greater numbers. It is the foundation for regrouping ("borrowing" and "carrying") in addition, subtraction, multiplication, and division.
Source:http://www.eduplace.com/math/mathsteps/2/a/index.html
Why Understanding Place Value is so Important:
Understanding place value, however, is much more than knowing how to break numbers into hundreds, tens and ones. Some students who can recite "247 has 2 hundreds, 4 tens, and 7 ones" may have no idea about the relationship of 247 to the number system -- for example, that it is 100 more than 147 and 10 less than 257, that it is almost 250, or that it is about halfway between 200 and 300.
Understanding place value and how it is linked to understanding how a number is composed and to knowing its relationships to many other numbers is crucial for students to master before learning more complex mathematics. For example, understanding the place value of a number like 126 is studied in a larger context that includes exploration of the following questions:
Where is the number in the number system? (Is it bigger than 10, bigger than 50, bigger than 100?)
How can the number be pulled apart into additive components that are easy to work with? (For one problem, it might be convenient to pull 126 apart into 100 and 25 and 1; for another problem, it might be convenient to think of it as 120 and 6.)
What are the factors of the number? (What numbers can you count by to reach the number exactly?)
What are the multiples of the number? (What happens when the number is doubled or multiplied by 10 or by 100?)
What is the relationship of the number to important numbers in our number system, such as multiples of 10, 25, or 100?
Throughout work on the number system and the place value of numbers, the emphasis is on making sense of the structure of the number system and on developing a large repertoire of number relationships that students can build on to solve problems. One focus of this work is on what we have come to call landmarks in the number system -- familiar anchor points in the sequence of numbers, such as 10, 25, 100, 1000, .1, and their multiples. Students study these numbers, their factors and multiples, and their relationships to other numbers. Because operations with numbers such as tens and hundreds make for simple calculations, place value plays a critical role throughout the grades in the development of strategies. Consider the following addition problem and sample strategy:
364 + 347
Break the addends into hundreds, tens, and ones, then combine the parts:
300 + 300 = 600
60 + 40 = 100
4 + 7 = 11
600 + 100 + 11 = 711
Source: http://investigations.terc.edu/library/curric-math/qa-1ed/place_value.cfm