Conceptual structures underpinning addition and subtraction

1. add + more Conceptual structures underpinning addition and subtraction plus less subtract

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

4. 3 2 3 + 2 = 5 5 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.

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. ‘take away’ 2 cubes 3 are left 5 – 2 = 3 5 cubes 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’.

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. There are 3 more red cubes than green. The difference is 3 cubes. 3 cubes