Subtraction:
key ideas and important concept knowledge
Key ideas
The overarching key ideas of estimation, benchmarks, visualisation, equality and equivalence, language and strategies need to be considered when developing units of work in subtraction. The specific key ideas in subtraction are: separation, comparison, part–part–whole, partitioning and properties of subtraction. The properties of subtraction include: identity property and inverse property.
Separation
Separation is subtracting or 'taking away' a quantity from a given collection.
Comparison
The relative size of two quantities can be compared and expressed as a difference.
Part-part-whole
A relationship exists between the parts and the whole. This relationship assists in finding the unknown quantity.
Partitioning
A quantity can be separated into parts while maintaining a sense of the whole.
Properties of subtraction
Identity property
Subtracting zero from the minuend (initial quantity) has no effect on the difference.
Inverse property
Subtraction and addition are related operations that undo each other, therefore addition can be used to solve a subtraction problem.
The inverse property is applied to form fact families.
Important concept knowledge
Meaning of the numbers
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
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.
Part-part-whole
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.
