V. Bag Ffa Codi
Introduction |
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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. |