U. Traciau Un Ffordd

Introduction
An activity on use of numbers to describe networks. Children explain why they can start from some
nodes but not others. They continuously trace networks without going over a line twice. They explore
rules governing networks, which they check by generating new ones. The activity involves branched reasoning using ‘either-or’ and ‘if-then’ (informally).
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: Exploring networks and classifying nodes
Children trace carefully sequenced three-node, one-way networks. They agree on common visual ways of
labelling and numbering stations. Children find which nodes can be 'starters' and which cannot, and why.
In the discussion of these examples, children should agree that all the three-station networks are
traceable, and that in the examples explored, the starting stations in the networks have the property of
odd-ness. They begin to explore the meaning of odd and even numbers in terms of lines coming in and out
of stations.
The children work on the remaining examples on the notesheet. In the class sharing they also look at a
new example, one where all three stations are starters. They then recognise this as an alternative
condition for a station. Children refine the two alternative rules (that either all the stations are terminals
with even number of lines from each, or if only two terminals can be starters, they must have an odd
number of lines from them). They approach some of the reasons for these rules, e.g., the fact that the total
number of node-lines is twice the number of drawn lines, and how three numbers make up an even number.
Episode 2: Rules for adding a station
Children consider what happens when a fourth station is added to either type of network – the all even or
the two odds. They formulate a conditional ‘if’ rule, possibly including recognition that some two-station
networks are not traceable. They approach a generalisation on the traceability of any size network.
Reflection
Children look at the way they linked shape and space with number, and how they worked systematically
and generalised; constructed a complex rule from combining simpler or partial rules, and how they looked for a mathematical reason for their decisions.
Reflection
Children look at the way they linked shape and space with number, and how they worked systematically
and generalised; constructed a complex rule from combining simpler or partial rules, and how they looked for a mathematical reason for their decisions.
BEFORE YOU TEACH
Some children will find networks, and the use of numbers to describe them, daunting. So pace your
start carefully. Focus on the numbers and reasons. Follow the careful sequence of examples. Ensure that only the relevant drawings are on the board.

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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