Pattern and structure
Pattern is a regularity or consistency. Students who detect patterns see both similarity and difference in situations.
Structure is the way the pattern is organised.
For example, a student might notice that a situation involves equal sharing among three people: equal sharing is a pattern. Further, a student may recognise that the result of the sharing can be anticipated by asking "How many threes are in…?" This is structure, in this case the connection between sharing (partitive) and measuring (quotitive) division.
In mental calculation there are structured connections. Addition, subtraction, multiplication and division relate to each other and have particular properties. Here are some examples.
The commutative property can be generalised by noticing patterns in addends and factors
(e.g. 3 \(\times\) 8 = 8 \(\times\) 3).
- Multiplication and division are inverse operations, in that one undoes the other. Students apply this property when they check their division calculations by multiplication.