1. Conceptual structures underpinning addition and subtraction

2. Addition: combining two or more quantities In this structure, two or more quantities are combined to form a larger quantity. This is the easiest way of viewing addition. 3 + 2 = 5

3. Addition: augmentation of one quantity This model of addition involves adding to an existing quantity thereby augmenting it. 3 + 2 = 5

4. Addition: comparative addition This involves a comparison of equivalent situations at least one of which involves addition. A 3-rod and a 2-rod added together are equivalent to a 5-rod. 32 5 3 + 2 = 5

5. Subtraction: partitioning Partitioning involves splitting one quantity into two or more sub-quantities. This is the inverse of the combining model for addition. 5 – 2 = 3

6. Subtraction: reduction This type of subtraction involves reducing the value of one quantity. It is the inverse of the augmentation model for addition. It is often known as ‘take away’. 5 – 2 = 3 ‘take away’ 2 cubes 3 are left 5 cubes

7. Subtraction: comparative difference This form of subtraction involves comparison of 2 quantities and assigning a numerical value to the difference between them. This is the inverse of comparative addition. 3 cubes There are 3 more red cubes than green. The difference is 3 cubes.