Understanding what numbers are and what they represent is the base on which the rest of mathematics studies rests. First, children learn counting or natural numbers. These numbers are used in basic mathematics functions such as counting and basic addition and subtraction. The initial lessons on numbers are geared for younger students, but they may be used with older ones in need of remedial work.
Sets are taught to older primary students to establish prealgebraic skills. These early skills are taught to introduce concepts like variables and notation. Set theory also teaches students about grouping numbers and variables, so that they can recognize what belongs in a set and what doesn't. Venn diagrams are a good visual aid to demonstrate this concept. A Venn diagram has two rings that overlap, and within the overlap are the items that belong to both groups. Items that only belong to one set appear in either the left or right circle.
Young children lack the ability to gauge volume accurately. You can pour the same volume into a squat, round container, and then into a tall, skinny one, and the child will think that the tall, skinny one has "more." After about age 7, they begin to grasp that the amount hasn't changed. This is called conservation of volume, and it is necessary for children to grasp this concept before learning how to measure volume.
Understanding money is a critical skill for children. Practicing making change helps children understand grouping and improves addition and subtraction skills. It can also be a primer for division multiplication concepts -- five groups of five makes 25, if you stack pennies in fives and group them together. This shows students that even within a unit of money, individual units as well as the whole unit of five are represented.