# Off-the-shelf Masterclass: Rabbits and sequences

Off-the-shelf Primary Mathematics Masterclass all about sequences, including a very special sequence of rabbits.

Explore ways of spotting patterns and finding rules for different numerical sequences. Have a go at modelling a rabbit population to find out about the famous Fibonacci numbers and explore a few places where they crop up unexpectedly.

• Credit: Jo Garbutt via Flickr creative commons

In mathematics, a sequence is a string of objects, like numbers, that follow a particular pattern. They are useful for studying patterns, shapes, and other mathematical structures. Sequences found in nature are extraordinary and students will be fascinated to discover their mathematical properties and the rules that define them.

In this challenging workshop, students will explore sequences and use their pattern-spotting skills to predict the next terms in the sequence, discussing the reasons for their answers. They will look at the different ways to give mathematical rules for sequences, discovering and using the mathematical notation.

The students will use this to help solve a historical problem modelling the growth rate of rabbit populations, which leads them to the famous Fibonacci Numbers. They will find other places these numbers appear in the world around them, and if there is time, will start to try and discover patterns in the prime numbers - one of maths's greatest unsolved problems.

Note that this is a relatively challenging workshop for KS2 students, so better suited for a Masterclass than general classroom resource.

Length: 2 hours (see the session leader notes for ideas on how to extend the Masterclass).

## Resources needed

• Calculators
• 1p and 2p coins - around 10 1ps and 5 2ps per student; coins can be obtained from the bank in bags of £1 - two bags of 1ps and two bags of 2ps will be enough for 20 students
• Squared paper
• Whiteboard or flipchart at the front of the room, with appropriate pens
• Copy each of ‘find the next number in the sequence’ worksheet 01
• Copy each of Rabbit rules 1 worksheet 02 and Rabbit Rules 2 worksheet 03 (produced 2 per page)
• Optional: Copy each of prime number sieve worksheet 04
• Computer and data projector
• Further details of quantities etc. can be found in Session Leader Notes

## Support

The Session Leader Notes offer full notes on the activities and a detailed list of resources, including quantities needed and what you need to prepare in advance. For additional guidance, a session script gives a full run-through of the Masterclass.

The Session Helper Sheet can be distributed amongst helpers. The additional information sheet gives more details on the history and background of each section of the Masterclass and are provided for added interest. This sheet also gives the full list of sequence rules for the questions posed in the class, including those posed in the session leader notes as extension questions if the students have time.

You can collect any student questions and email them to the Ri Masterclass team at masterclasses@ri.ac.uk - we will endeavour to answer them before the next Masterclass in your series.

Masterclass series support

For more information on running a Masterclass series and the support, templates and other resources available to you, please get in touch via masterclasses@ri.ac.uk.