Our number system is based on 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), thus giving it the name "Base-ten." Most often though, we need to work with numbers greater than these digits. This is accomplished through using place value. We use place value to help us make daily decisions, such as using money.
A visual representation of a mathematical concept is known to be an essential tool for helping children to develop a solid understanding of basic ideas. Base Ten Blocks are a very useful tool for teaching place value. The units represent 1, the longs represent the regrouping of 10 units for one 10, the flats represent the regrouping of 10 longs for 100, and the cubes represent the regrouping of 10 flats for 1000.
Be sure to teach the links between numbers, symbols and models. Some children have faulty number conceptual understanding and fail to make the relationship between a model and the actual numbers.
Place value is defined as a positional system of notation in which the position of a number with respect to a point determines its value (4). It took humans, specifically the Babylonians, nearly 28,000 years to come up with the idea of place value. Before place value, symbols were repeated in order to represent a number (5). Think about Roman Numerals. There is no easy way to add them, which is what people experienced before place value was established. Many children have difficulty when learning and applying place value concepts (1). Unfortunately, research has not determined the most effective way to teach place value, so textbooks remain the same.
How Do Children Build An Understanding of Place Value?
To understand place value is to understand the structure and sequence of our base ten number system. As students count, interpret the values of written and spoken numbers, decide which number is larger or smaller, and explore relationships among numbers, they are developing a picture of our number system.
At first this picture is a single sequence of counting numbers: 1, 2, 3, 4, 5 ... Young children become familiar with this sequence, and through many experiences with quantities, they gradually come to see that each number in the sequence represents an amount that is one more than the previous counting number. Even before students can count very high themselves, they begin to appreciate that the numbers can go on forever, with each number representing "one more."
In our base ten number system all these ones are organized in a particular way -- in tens and multiples of ten. Our written numerals and most of our spoken numbers reflect this organization. As young students are developing their understanding of the sequence of ones, they also begin to make sense of how our written and spoken numbers are structured. A first grader who is determined to count to 100 sometimes says "47, 48, 49, what's the next one?," and as soon as "50" is supplied, the student takes off again, "51, 52, 53, 54 . . ." until the next multiple of ten is reached. This student has recognized that each decade has a familiar pattern. A second grader exploring different ways to count a large group of objects comes to understand that each number in the counting-by-tens sequence 10, 20, 30... represents a quantity that is 10 more; another student exploring a variety of number patterns notices that each time 10 is added to a two-digit number, the tens digit increases by 1 and the ones digit remains the same. Through experiences such as these, students begin to recognize "place value" -- that where a digit appears in a number determines its value. The "2" in 24 represents 20, the "2" in 247 represents 200.
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. Source: http://investigations.terc.edu/library/curric-math/qa-1ed/place_value.cfm
Base Ten Number System
Our number system is based on 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), thus giving it the name "Base-ten." Most often though, we need to work with numbers greater than these digits. This is accomplished through using place value. We use place value to help us make daily decisions, such as using money.
A visual representation of a mathematical concept is known to be an essential tool for helping children to develop a solid understanding of basic ideas. Base Ten Blocks are a very useful tool for teaching place value. The units represent 1, the longs represent the regrouping of 10 units for one 10, the flats represent the regrouping of 10 longs for 100, and the cubes represent the regrouping of 10 flats for 1000.
Be sure to teach the links between numbers, symbols and models. Some children have faulty number conceptual understanding and fail to make the relationship between a model and the actual numbers.
Source: http://www.primary-education-oasis.com/teaching-place-value.html
Elementary Place Value
Place value is defined as a positional system of notation in which the position of a number with respect to a point determines its value (4). It took humans, specifically the Babylonians, nearly 28,000 years to come up with the idea of place value. Before place value, symbols were repeated in order to represent a number (5). Think about Roman Numerals. There is no easy way to add them, which is what people experienced before place value was established. Many children have difficulty when learning and applying place value concepts (1). Unfortunately, research has not determined the most effective way to teach place value, so textbooks remain the same.
https://eee.uci.edu/wiki/index.php/Elementary_Place_Value
How Do Children Build An Understanding of Place Value?
To understand place value is to understand the structure and sequence of our base ten number system. As students count, interpret the values of written and spoken numbers, decide which number is larger or smaller, and explore relationships among numbers, they are developing a picture of our number system.At first this picture is a single sequence of counting numbers: 1, 2, 3, 4, 5 ... Young children become familiar with this sequence, and through many experiences with quantities, they gradually come to see that each number in the sequence represents an amount that is one more than the previous counting number. Even before students can count very high themselves, they begin to appreciate that the numbers can go on forever, with each number representing "one more."
In our base ten number system all these ones are organized in a particular way -- in tens and multiples of ten. Our written numerals and most of our spoken numbers reflect this organization. As young students are developing their understanding of the sequence of ones, they also begin to make sense of how our written and spoken numbers are structured. A first grader who is determined to count to 100 sometimes says "47, 48, 49, what's the next one?," and as soon as "50" is supplied, the student takes off again, "51, 52, 53, 54 . . ." until the next multiple of ten is reached. This student has recognized that each decade has a familiar pattern. A second grader exploring different ways to count a large group of objects comes to understand that each number in the counting-by-tens sequence 10, 20, 30... represents a quantity that is 10 more; another student exploring a variety of number patterns notices that each time 10 is added to a two-digit number, the tens digit increases by 1 and the ones digit remains the same. Through experiences such as these, students begin to recognize "place value" -- that where a digit appears in a number determines its value. The "2" in 24 represents 20, the "2" in 247 represents 200.
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.
Source: http://investigations.terc.edu/library/curric-math/qa-1ed/place_value.cfm