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

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Conceptual structures underpinning addition and subtraction

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add

+

more

Conceptual structures underpinning addition and subtraction

plus

less

subtract


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 + 2 = 5

Addition: augmentation of one quantity

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


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.


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


‘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’.


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


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