They appear at every level because they form the core of what it means to do mathematics .
Some students think that because it is logical, the events of the story are possible.
Others will be certain that what the narrator describes cannot have occurred. Whether anyone changes their mind or not, the ensuing debate is a problem-solving session highly dependent on reasoning and communication. Students deepen their understanding of numbers over a period of many years. Our number system is founded on the notion of counting. The familiar whole number operations of addition, subtraction, multiplication and division are all based on counting.