Negative numbers

When a negative or minus sign is attached to a number as a prefix, it indicates the polarity of that number with respect to zero. Natural numbers are considered as positive numbers.

Both positive and negative numbers have both magnitude and direction. Negative numbers can cause confusion between magnitude and order. For example, –4 is conventionally less than –1, despite –4 appearing to have a magnitude of more than –1.

Pause for thought

Think back to when you were learning negative numbers. Did it all seem straightforward?

Try to express why negative numbers seemed straightforward to you (if they did). Maybe it was because the negative numbers fitted in with the ideas you already had about natural numbers and extended those ideas in a satisfactory way? Try to remember how you came to understand how to perform mathematical operations on negative numbers – did you learn rules by rote first?

Think about some students in your classroom and the difficulties they have with natural numbers. Think about students you have taught and how they can get mixed up about when to apply the rule ‘two negatives make a positive’. How can your students be helped to understand negative numbers and not rely solely on remembering rules?

2 The need for negative numbers