P. Lindys

Introduction
An activity to investigate chains of numbers in rings of a caterpillar from head to tail. The chains follow the two rules: if even: halve, if odd: add 1. End when the chain reaches 1. The starting number dictates the length of chain. The length is also linked to the types of numbers and results are tabulated. Pupils explore types of numbers beyond odd and even and multiples of 4.
This activity has two episodes. Each episode consists of an introduction, paired or group work and whole class sharing. The session must finish with a whole class reflection phase, regardless of how far the class has got.
Episode 1: Using rules and finding patterns
Children use the rules for particular starting numbers, such as 6, 10, or 18. This leads to a simple generalisation that the larger the number, the more steps down to 1. The teacher then disproves this by offering other numbers such as 20 and 32 to produce shorter chains. In pairs, children work on four or more consecutive numbers. Some will find halving large numbers hard. Most recognise a pattern within each group of numbers but find the pattern complex. They produce number chains for display. The children’s work is collated into a results table. They look for: a repeat pattern in each group; the first group’s special case (numbers 1 to 4); limitation of rules involving odd and even; and ‘multiples of 4’. All chains end with 8,4,2,1 or 3,4,2,1.
Episode 2: Shorter and longer chains
Children focus on what kind of numbers are within the shorter chains, and within the longer chains. They may analyse chains by looking at odd or even patterns within the chain, or at the ending of the chain. By sharing ideas, the children approach the special nature of powers of 2 as repeated doubling or repeated halving. They may produce diagrams linking numbers to the common endings 8,4,2,1 or 3,4,2,1.
Reflection
Children discuss the patterns that they have discovered in this activity and how they arrived at these.
BEFORE YOU TEACH
Children need to recognise odd numbers, even numbers and multiples of 4. They also need to be able to halve even numbers (small and large). Remember that the objective is for children to gradually go deeper into the patterns and types of numbers rather than just revise the things they already know. Steer children through simpler features of how numbers are arranged on the page towards patterns of increasing depth. Be clear about the focus of work in each phase, while accepting different ideas.

License

Gwersi PCAME a Dewch i Feddwl Mathemateg (9 i 11 oed) Copyright © by Ann Longfield, David Johnson, Jean Hindshaw, Linda Harvey, Jeremy Hodgen, Michael Shayer, Mundher Adhami, Rosemary Hafeez, Matt Davidson, Sally Dubben, Lynda Maple, and Sarah Seleznyov. All Rights Reserved.

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