Conceptual structures underpinning addition and subtraction

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Conceptual structures underpinning addition and subtraction

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Conceptual structures underpinning addition and subtraction

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add

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Conceptual structures underpinning addition and subtraction

plus

less

subtract

3 + 2 = 5

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

This model of addition involves adding to an existing quantity thereby augmenting it.

3

2

3 + 2 = 5

5

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.

Partitioning involves splitting one quantity into two or more sub-quantities. This is the inverse of the combining model for addition.

5 – 2 = 3

‘take away’

2 cubes

3 are left

5 – 2 = 3

5 cubes

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’.

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