Addition:
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 addition. The specific key ideas in addition are: combining, partitioning, part–part–whole and the properties of addition. The properties of addition include: identity property, commutative property, associative property and inverse property.
Combining
Combining is the operation that represents the joining of two sets or quantities.
Partitioning
A quantity can be separated into parts while maintaining a sense of the whole.
Part-part-whole
A relationship exists between the parts and the whole. This relationship assists in finding the unknown quantity.
Properties of addition
Addition has several properties, which are outlined below.
Identity property
Adding zero to a number will not affect the quantity. Zero is called the ‘identity element’ because it leaves the number unchanged.
Commutative property
The order in which two numbers are added does not affect the sum.
Associative property
The order in which three or more addends are added does not affect the sum. Numbers can be arranged in different ways to make them easier to add.
Inverse property
Addition and subtraction are related operations that undo each other, therefore subtraction can be used to solve an addition problem.
The inverse property is applied to form fact families.
Important concept knowledge
Meaning of the numbers
Addition equations have at least two addends (numbers being added) and a sum (total).
Addition strategies
Addition strategies are methods to solve mathematical problems. With addition, 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 forward from a given number (jump
strategy)
• jumping strategies can be represented on an empty number line
• rounding and adjustment strategies
• transformation strategies, involving the shifting of a quantity from one addend to another
• compensation strategies, involving the adjusting of one of the addends to make an equation easier to solve.
Written strategies are often algorithms, meaning step-by-step methods to find an answer. The most common algorithm for addition applies 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 addition.
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 addend) problems have an initial quantity and a result quantity, but ask for the change quantity.
Start-unknown (missing addend) problems ask for the
beginning quantity.
