1 The meaning of numbers

Numbers were probably invented for the purpose of counting animals or other possessions. Numbering systems were originally thought to only have words for ‘one’, ‘two’ and ‘many’, as that was all that was needed. Further developments allowed herds to be counted, and as trade between people increased, the number system we use today was developed – including zero and negative numbers. Number names are almost always structured using a logical procedure so that they can express numbers that are to all intents and purposes, infinite.

Numbers are used to represent:

• quantity, for answering questions like ‘How many?’ or ‘How far?’
• relationships between numbers, for answering questions like ‘How many more?’ or ‘How many less?’
• transformations in terms of quantities, for answering questions like ‘Imagine if Zuree owed Mary three rupees. She gave Mary one rupee. How much does she owe now?’, or ‘Manu won three marbles in the first match and lost five marbles in the second. How many marbles did he lose altogether?’

Pause for thought Reflect on how and where your students may have encountered negative numbers. They may, for example, have come across the idea that the temperature in an ice cream freezer is below zero. Where else might they have encountered these ideas?