Developing a number sense begins with learning to state numbers 1 through 10 in order, and being able to count a group of objects with the understanding that the last number tells how many there are. Before entering kindergarten, children should be able to count backwards from five. Preschoolers work on identifying written numbers and distinguishing between "more" and "less." Ordinal numbers can be a difficult concept to master in preschool, but children should be exposed to the concepts of "first" through "fifth."
Children manipulate and identify basic shapes in preschool. Squares, rectangles, triangles, circles, stars and hearts are the most common shapes that kids are exposed to. Students work on sorting objects according to size and shape. Art projects can be integrated easily into geometry skills by having the children combine basic shapes to make designs.
Basic algebra skills begin with identifying and working with concrete patterns. Preschoolers learn to recognize a pattern and predict what will come next. They are encouraged to create their own simple patterns using blocks or toys. Sorting objects by color or other attributes is addressed in preschool algebra skills as well.
Preschool age children discover ways of measuring time, temperature, length, volume and weight. They also begin to study how to use measurement tools including a calendar, clock, ruler, scale and measuring cups. Kids learn how to compare objects using big/small, short/tall and long/short. Measurement skills also include using specific features, such as length or height, to put objects in order.
Students learn to use mathematical information to answer questions. Preschoolers are exposed to simple graphs that represent concrete information. They are taught how to create graphs using characteristics of objects such as shape and color. After making a basic graph, children identify categories as having the most or least of a specific object.