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Addition and subtraction
Addition is the joining of two sets to form a new set.
When we write 4 + 3 = 7 we are representing that the result of joining a set of four to a set of three is a set of seven objects.
Addition is a binary operation in that we can only join two sets at once. When we work with the set of counting numbers {1, 2, 3…} the answer is greater than either of the sets being joined.
This is not always true when we add integers which include zero and negative numbers.
Subtraction is the separation of a subset from a set, sometimes described as taking away a part from the whole.
When we write 7 – 3 = 4 we are representing the result of taking a subset of three from a set of seven objects, leaving a subset of four objects.
Addition and subtraction are also applied when comparing sets.
We can represent the difference between a set of three and a set of seven using either addition, 3 + ? = 7, or subtraction, 7 – 3 = ?
Bridging decades
Our place value system is established on base ten. The decades (multiples of 10) are important reference points for early addition and subtraction.
Standard place value
Standard place value is the structure of grouping into tens, hundreds, thousands etc. Using these groupings makes counting and calculation efficient in comparison to working with individual units (ones).
Friendly numbers
'Friendly numbers' are numbers that are easy to calculate with. Turning unfriendly numbers into friendly ones is a way to make difficult calculations easy.
Subtraction as difference
Many students believe that subtraction means 'take away'. Comparing the size of two sets by finding differences is a common context for subtraction.
Making choices
To be flexible and fluent calculators, students need to make sensible choices about strategies. They need to look closely at the demands of problems and choose ways to combine and partition the numbers to make the calculation as easy as possible.