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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.
longs for 1000,100, and the flats for 10000.1000.
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

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many other mathmaticalmathematical concepts that
It is also important to teach children the concept of place value because...
There is much to learn in this topic about regrouping and understanding why we round numbers that can be incorporated for a full understanding.

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This site offers different math strategies for teaching place value to Elementary school students. Students are introduced to place value as early as Kindergarten or first grade and it is reinforced in the later primary grades. In higher grade levels, place value becomes more complex as decimals are introduced and fractions are added to the curriculum. Teachers use a wide range of methods and strategies to help students understand the concept of place value, yet it still seems to be a concept that students struggle with. Since learning place value is a building block for more complex mathematical concepts and it is introduced to students at such a young age, we believe that it is important that all students understand place and value in numbers so that they do not fall behind in math early on in their learning career.
It is imperative that teachers know systematic ways of teaching the concept and build understanding because it is a foundation for so many other mathmatical concepts that children will struggle with if they do not master it early on.
It is also important to teach children the concept of place value because...

Common Core Standards:
Ten Computation
Core
Core Standards ⋅ understand that:
1. In comparing two-digit numbers, the number with more tens units is larger; if the number of tens units is the same in each, the number of ones units decides.
2. In adding or subtracting 2-digit numbers, one adds or subtract like units (tens units and tens units, or ones units and ones units).
and do:
a. Count to 100 or beyond, switching appropriately to the new decade after a 9 has been said in the ones place.
b. Compare and order numbers to 100 based on meanings of the tens and ones places.

Common Core Standards:
Base Ten Computation
Core Standards ⋅ Students understand that:
1. In comparing two-digit numbers, the number with more tens units is larger; if the number of tens units is the same in each, the number of ones units decides.
2. In adding or subtracting 2-digit numbers, one adds or subtract like units (tens units and tens units, or ones units and ones units).
Core Standards ⋅ Students can and do:
a. Count to 100 or beyond, switching appropriately to the new decade after a 9 has been said in the ones place.
b. Compare and order numbers to 100 based on meanings of the tens and ones places.
c. Easily write numerals to 20; write numerals to 100.
d. Use break-apart and make-a-ten strategies to add and subtract with teen totals as in 7 + 6 = 10 + 3 and 17 – 9 = 17 – 7 – 2.
e. Find 10 more or 10 less than a number without having to count.
f. Add one-digit numbers to two-digit numbers, and add multiples of 10 to one-digit and two-digit numbers.
g. Represent addition of two-digit numbers using 10-rods and unit cubes,18 including rearranging rods and cubes to show regrouping when needed.
h. Add two-digit numbers to two-digit numbers using strategies based on place value, Properties of Arithmetic, or the inverse relationship between addition and subtraction.

2010 Arizona State Standards:
First Grade:

2. Have students glue ten beans on each popsicle stick; a filled stick is one ten-group.
3. Students can then bundle them together with rubber bands and introduce the words, twenty, thirty, forty, etc.
4. Counta nyCount any leftover beans
Note: Counting in groups will help students understand more complex concepts such as multiplication.
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