These ideas have been developed over time to help explain particular qualities such as size, weight, height, as well as relationships and comparison. Most adults can solve simple mathematical tasks by doing them in their head. Young children find such abstractions impossible to master because they first need to touch, see, feel, compare, and experiment through the senses.

The Mathematics materials provide a logical progression from concrete to conceptual. The child learns how to identify concrete quantity, then the symbols and then the two are combined. The decimal system, linear and skip counting, fractions and the mathematical operations of addition, subtraction, multiplication, division are taught using specific equipment. The benefit of this approach is quickly seen, when children of five fundamentally understand concepts not typically introduced until much later.