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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Conceptual structures underpinning addition and subtraction

add

+

more

Conceptual structures underpinning addition and subtraction

plus

less

subtract


Addition combining two or more quantities

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.


Addition augmentation of one quantity

3 + 2 = 5

Addition: augmentation of one quantity

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


Addition comparative addition

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

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


Subtraction reduction

‘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

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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