Missing Sequence Numbers - A Maths Investigation: Year 6+

This mathematics investigation was designed primarily for use by children of Year 6 - for exploring and understanding integer sequences. The material could alternatively be used for consolidation or assessment purposes.

Most of the sequences are arithmetic (i.e. linear) but there are also more challenging ones such as squares, cubes, geometric progressions and good old Fibonacci’s sequence.

There are sixteen sequences, and four levels of solution:

1. Simply fill in the missing values in the sequence (least challenging).
2. Find and express a rule which describes the sequence (more challenging).
3. Find an algebraic expression to define a sequence value from the previous one.
4. Find an algebraic expression to define a value from its position n in the sequence.

Steps 3 and 4 provides the greatest challenge. Sometimes it is easier to determine one kind of expression than the other and so the challenge is increased considerably when both expressions are required for each sequence (i.e. steps 3 and 4).

Although the material is designed to be challenging but accessible (with guidance) to children working within the government’s expectation for children at the end of Key Stage 2, it is possible that teachers of children in KS3 and potentially KS4 may find the resources useful.

In addition, children of earlier KS2 years may be able to access and complete many of the sequences, even if a grasp of the more complex rules might currently elude them.