V. Bag Ffa Codi

Introduction
An activity on exploring and symbolising the number of steps needed to visit an arrangement of dots.
Children look at systematic ways of ensuring that they visit all the dots, and the least number of steps
needed to do so. They then find a justification for the two-step relation involved in the case of a square
arrangement of dots.
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: Systematic coverage of a set of dots
Systematic coverage of a set of dots
Working with a 3 x 3 dot square, children find the number of steps needed to visit all the dots. They
recognise that retracing a step increases the length of the path. Finally, they recognise that the systematic
spiral or zigzag routes give the shortest path. They address the fact that there can be fewer steps than
dots, or more.
Episode 2: The relationships in a square arrangement of dots
The relationships in a square arrangement of dots
Now children work with 4 x 4 and 5 x 5 squares. They find the minimum paths for each and then they look
for a rule that connects the number of dots and the number of steps in the shortest path. They look for the
relationship between the number of dots on the side of the square and the total number of steps. They are
asked to check their rule by seeing if it works for other squares. Some are asked to see if they can prove
their rule.
A possible extension is finding the number of steps needed for any rectangular arrangement of dots.
Reflection: Being systematic and symbolising
Children compare their work on systematic visiting of dots and share their generalisations. They go on to
discuss common situations where the steps and stops are related, such as fence posts and fence lengths,
bus stops and bus trips.
Reflection
BEFORE YOU TEACH
This activity is intended to help children of different abilities to gain something from the various
stages of the tasks. In the whole class sharing phase, it is important to record publicly all the steps
children have taken in tackling the task and to acknowledge them as valuable.

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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