Work with mathematical concepts occurs in a variety of ways. Many of the activity areas in the classroom naturally integrate various math skills. Work with blocks, for example, allows children to express their perceptions of the outside world in an organized manner. The blocks are "units" of construction; each type is related to another by size. Children explore their ideas, they count, add and measure how many different blocks are part of their buildings.

We want to provide opportunities that facilitate the understanding that there are many ways to solve a problem. Through work with manipulative, we are creating a foundation for later abstract learning. The children are concrete in their thinking and need to physically manipulate objects in order to help support their thinking.

Work with sand introduces the concept of volume. Play at the water table invites experimentation with more than/less than, as well as, the concepts of volume and relationships (tall, thin container vs. short, wide container). Cooking introduces measurement and some beginning work on fractions. The daily curriculum reinforces the use of math skills, introduces new ones and helps children solve their conceptual problems. A math choice not only reinforces new skills and concepts introduced but also provides children with an initial independent experience, which they are responsible for completing within a certain time frame.

Children enter school with a considerable amount of mathematical knowledge. In Kindergarten we intend to build on the knowledge they've acquired through their interactions and experiences by providing them with games and activities which illustrate and reinforce specific concepts and skills. For example, most children can identify any patterns around them-- night follows day, seasons of the year, colors in a favorite striped shirt. They can explain that this series repeats itself over and over and can predict what comes next. During a series of choice time activities children participate in a game or activity designed to reinforce their understanding of simple patterns and gradually work towards not only recognizing but also recreating and predicting more complicated patterns. Colored cubes, buttons, beads, and a variety of other objects are used in patterning activities. Since mathematics is based on patterns that occur in a repeating and predictable order, recognizing and predicting patterns become important in first grade as children begin their work with place value and addition and subtraction.

Counting and Estimation
A large jar filled with a variety of objects provides us with many opportunities to count and estimate. Children need to consider different variables as they make an estimate and then check their guess by counting the objects.

Understanding the concept of number and the consistency of number is an important building block as children begin their work with numerals and numbers. Throughout the year they are involved with making sets of objects by sorting and classifying them according to specific characteristics and attributes. Later in the year we play with number sets and various ways to make a set of 8 (7+1, 4+4, etc.). The ideas of joining two sets to create one bigger set and then a smaller set away from a larger one move children into simple addition and subtraction.

Throughout the Kindergarten year, work with mathematical concepts involves the use of manipulative materials. Preceding the mathematical abstraction of a particular concept is the hands-on manipulation of materials and playing of games. Math should be and is a lot more than just learning the finite skills of computation (though these are extremely important). Learning how to organize one's work, figuring out what the problem is and then solving the problem through manipulating concrete materials, provided invaluable opportunities for children to understand the concept involved and to actually see why the computation is necessary.

Below is a list of skills and concepts covered this year. Please keep in mind that this is meant to be a guideline and that as children are ready they may progress beyond these skills:

• 1:1 correspondence/counting objects
• Number recognition
• Numeral writing
• Sorting/classification/recognizing attributes/sets
• Elementary geometry (shapes, trapezoid, triangle, hexagon, square, diamond etc.)
• Equivalency
• More than/less than
• Area
• Survey/graphing/interpreting results
• Measurement with non-standard implements (ribbon, cubes, etc.)
• Grouping (adding and subtracting–division and multiplication)
• Introduction of place value