In Common Core math, place value is the most important idea that second grade students learn. They develop an understanding of this concept through exposure and through practice.
In far too many textbooks pre–Common Core, the study of place value was limited to naming places, which robbed many children of the opportunity to know place value well and to learn algorithms with meaning. In a Common Core classroom, second graders study place value in ways that allow them to learn it well, which provides a stronger foundation for later arithmetic and algebra learning.
The usual way of writing numbers is a place value number system. In other words, a limited set of symbols (called digits) builds numbers (0, 1, 2, 3, and so on up to 9) and you can write all numbers using these symbols. Most importantly, the values of these symbols change depending on where they appear in the number. In other words, their location (place) determines their worth (value).
As an example, consider these three numbers: 346, 463, and 634. These numbers all have the same digits but have very different values. The 6 in 346 represents six. Six ones. But the 6 in 463 represents sixty. Six tens. In the number 634, the 6 represents six hundred. In each case, it's six things — six units — but the unit you're counting changes depending on where the 6 is in the number.
As an adult, you're probably so accustomed to this system that this concept seems obvious. But place value is a tremendous achievement of the human mind. People used numbers for thousands of years before inventing place value systems, which means that the rules and behavior of place value number systems aren't obvious at all.
In fact, the development of the number zero was a huge achievement that needed to take place before place value number systems could exist. Without zero, how do you tell 6 from 60?
Comprehending the place value system involves more than knowing the names of the places. It also involves being able to use relationships among the places.
For example, you can decompose 346 as 300 + 40 + 6 or three hundreds, four tens, and six ones. But you can decompose it in several other ways using different combinations of hundreds, tens, and ones units. Some examples include
0 hundreds, 34 tens, and 6 ones
3 hundreds, 0 tens, and 46 ones
2 hundreds, 14 tens, and 6 ones
You can think of these in terms of money. There are many different ways to make $346 using $1, $10, and $100 bills.