**The augmentation structure of addition **

The term augmentation is used to refer to a situation where a quantity is increased by some amount and the operation of addition is required in order to find the augmented amount or increased value. For example, the price of a bicycle costing €149 is increased by €25: what is the new price? This is the addition structure which lies behind the idea of counting on along a number line and which we might use with young children for experiencing simple additions such as 7 + 5: ‘start at 7 and count on 5’.

The most important and relevant context for this structure is again that of money, particularly the idea of increases in price or cost, wage or salary. Another context that has relevance to pupils is that of temperature, where addition would model an increase in temperature from a starting temperature. A significant context for younger children is their age. ‘You are six years old now, how old will you be in four years time?’ This is a good way for children to experience ‘start at 6 and count on 4’.

The key language that signals the operation of addition is that of ‘increasing’ or ‘counting on’.