A Number Sequences Resource

Stage: 4 Challenge Level: Challenge Level:1

Interactive investigations which result in number sequences

Changing Places

In this problem , students might be :
  • Appreciating the need to tabulate results
  • Formulating ideas and testing them out
  • Conjecturing about formulae that suggest themselves

Magic Potting Sheds

This activity offers students the opportunity to explore a new environment and challenges them to use some deductive reasoning.

More Magic Potting Sheds

This activity offers students the opportunity to go beyond the environment introduced in Magic Potting Sheds as the multiplying factor and the number of sheds can be increased to create a more challenging context.
As with Magic Potting Sheds before, it requires students to work systematically and challenges them to arrive at further generalisations.


This is a well known puzzle but even if you have met it before you may find more mathematics in it this time round. You can solve it on the computer below or use a line of coloured counters or act it out getting some friends to play the roles of frogs and toads.

Seven squares

This set of problems that encourage generation of sequences and finding the general term. The first problem includes some interactivities which highlight two important ideas
  • that there is more than one way to describe a pattern or relationship and that any "visualisiation" will generate an equivalent general term
  • when creating tables of outcomes and using them to helpdefinethe general term, it is important to look back at the original situation to make mathematical sense of the result.

Interactive help with summing simple number series

Sequences and series

In this problem you can investigate triangle numbers and their relationship to rectangle numbers.

More sequences and series

In this probelm investigate how the sum of consecutive odd numbers can be represented as square arrays.

Ideas based on the Fibonacci sequence

Gnomon I

This problem is about gnomons (not gnomes!) which are very remarkable mathematical L shapes. At the end of this question, it suggests that you look at the shapes of the gnomons for the alternate Fibonacci numbers and see what you notice.

Whirling Fibonacci Squares

An article with an accompanying spreadsheet that makes the connection between the Fibonacci Sequence and the Golden Ratio.

Proof sorter

These two interactivites enable you to test your understanding of the proofs for summing arithmetic and geometric series
Sum of an AP
Sum of a GP