Patterns and relationships

Students at level two should understand that numbers are counts that can be split in ways that make the operations of addition, subtraction, multiplication and division easier. From Level One students understand that counting a set tells how many objects are in the set. Building on this thinking at Level Two is to realise that the count of a set can be partitioned and that the count of each subset tells how many objects are in that subset. Also required is understanding that partitions of a count can be recombined.

This means the students will explore sequential patterns. A sequential pattern is one in which further members of that pattern can be predicted from previous members. So ..., and 1, 3, 5, 7, ... are sequential patterns. At Level One students should be able to reproduce a given pattern using objects, drawings or symbols and continue the pattern on with justification.

This means students will understand the link between the cardinal and ordinal aspects of counting. The ordinal aspect refers to the fact that counting numbers have a conventional order. The last number in a count tells how many objects are in a set if all the objects are matched in one-to-one correspondence to the sequence of counting numbers. The next number in the counting sequence tells the result of adding an object while the number before in the sequence tells the count when an object is removed.