Separation is subtracting or 'taking away' a quantity from a given collection.

The relative size of two quantities can be compared and expressed as a difference.

A relationship exists between the parts and the whole. This relationship assists in finding the unknown quantity.

Subtraction equations that represent separation situations have a minuend (the whole collection) and a subtrahend (the part being removed) and a difference (the result).

Subtraction strategies are methods to solve mathematical problems. The strategies may be mental, written, digital or a mix of the three.

Mental strategies are calculations worked in one's mind and may involve using one of the following methods:

• partitioning and recombining numbers, usually using place-value structure (split strategy)

• jumping backwards from a given number (jump strategy)

• rounding and adjustment strategies (compensation)

• equal differences.

Written strategies are often algorithms, meaning they are step-by-step methods to find an answer. The two most common algorithms for subtraction are decomposition (of the minuend) and equal addition (to both the minuend and subtrahend).

These two methods apply place-value structure and should only be introduced once students have explored a range of other strategies and have developed a sound conceptual understanding of subtraction.

The unknown in result, change and start

Result unknown, change unknown and start unknown refer to different locations of the unknown in arithmetic problems.

Result-unknown problems have the answer as the result of the action.

Change-unknown (missing subtrahend) problems have an initial quantity and a result quantity, but ask for the change quantity.

Start-unknown (missing minuend) problems ask for the beginning quantity.