By the end of pre-kindergarten programs, students should have developed an understanding of what numbers are and what numbers do. They need to know that numbers are both words and symbols as well as that they represent quantities. This objective can be met by exposing them to numeric symbols and teaching the children to count objects such as their fingers.
Before students enter kindergarten, they should be able to count by ones to at least 10, if not higher. Teachers and parents also want to ensure that pre-kindergarten kids can count concrete objects up to at least five. For example, if you tell them to give you three blocks, they can count three blocks and bring them to you.
Pre-kindergartens also need to work on developing spatial concepts such as basic shape -- circle, square or triangle -- and measurement. They can identify and sort objects based on shape such as putting balls in one pile and blocks in another. Kids demonstrate they understand measurement or size when they can fit the correct-sized lid on the proper container. They also use and understand words such as above, below, beside and inside.
Pre-kindergarten programs also strive to help children develop an understanding of patterns. Young children come to recognize patterns by lining objects up according to size, such as smallest plush toy to largest plush toy. They also find patterns in color such as separating blue blocks from yellow blocks.
While young children aren’t expected to know how to add and subtract numbers on paper, they should have an awareness of these concepts. For example, if you show a pre-kindergartner three blocks then take away one block, he should be able to tell you that there are now two blocks. Or, if you add one ball to a group of three balls, he knows that there are now four blocks.