U. Traciau Un Ffordd
Introduction |
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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. |