ABSTRACT
This chapter returns to the construction of numbers, building from the construction of whole numbers, discussed in Chapter 1. New actions generate new units, which, in turn, generate new numbers. For example, the mental action of partitioning a whole unit, 1, into seven equal parts produces the unit fraction, 1/7, which can be iterated to produce other fractions, even fractions that go beyond the whole, such as 11/7. The chapter also investigates other representations of number, including decimal (base-10) and binary (base-2) representations. Generalizing numbers and ways of operating on numbers can support operating on unknown units, the basis for algebra.
