An example of an activity that students do in the course, relates to this topic. The activity suggests a base five system, but students are encouraged to be creative as they work in small groups. Each group must submit a written description of their system, including an evaluation of its strengths and weaknesses. In addition, each group must present its system to the rest of the class and answer any questions posed. As students deal with numeration systems other than the base ten place-value system with which they are familiar, they gain an appreciation for the difficulty and questions children experience.
Attention then turns to focusing on the whole number, the integer and the rational number systems.
Models of the operations in each system are discussed and studied. Set theory is used to introduce the set models of whole number operations, and then the whole number models are used to build some of the integer models. Students again see that in the structure of mathematics, new ideas build on previous ideas. In addition to the models of the operations, students investigate properties of the number systems and elementary number theory. Manipulatives add to the understanding of, for example, the commutative property of integer addition.