Preschool students should be able to understand how to represent single-digit numbers in Arabic. Students also should be able to perform the reverse: interpreting Arabic numbers in real language. In addition, students should be familiar with the idea of counting by the end of preschool, to the extent that they can reliably answer questions as to how many objects are in a certain set of objects. This skill includes the ability to recite the numbers in order.
Today's schools implicitly introduce algebra to students before rigorous algebra classes are available. In preschool, this includes simple activities that help children understand mathematical patterns that will later be characterize by equations. Specifically, preschool children must learn how to classify and sort objects of different types. Activities teaching such skills help the students learn that there is a certain order to the objects and that then can rearrange the objects in many ways. The learning of such patterns has a spillover into different areas, such as spelling and reading.
Preschoolers should learn the basic forms of measurement. While you need not emphasize how to measure or how to calculate measurements, you should teach the students to recognize basic concepts of measurement such as length, weight, area, volume and time. Students can learn these skills from hands-on measurement activities, which in turn will help students familiarize themselves with the basic units of measurement.
Diagrams play an especially important role in introductory mathematics curriculum. Students at the preschool level frequently have trouble with visualizing mathematical concepts or problems. Students should not only learn how to interpret basic diagrams but also construct them. As a goal, students should learn how to use diagrams as problem-solving tools, such as using diagrams of their neighborhoods to count the number of houses between their homes and others' homes.