As well as developing an increasingly sophisticated concept of ten, students display their thinking about addition and subtraction through three procedures:
- a mental replay of the written algorithm
- a counting-based approach to building on (or decreasing) from one number in tens and ones (the jump approach)
- a collection-based approach, allowing separation and recombining of tens and ones (the split method).
These different approaches mean that the tens and ones level has two elements: one describing the jump method and the other the split method. Both ways enable students to add and subtract two-digit numbers in the absence of any concrete materials.