N. Digon Da i Fwyta
Introduction |
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An activity on exploring types of numbers. Children work out rules of increasing complexity to describe numbers that either fit a hidden rule or do not. They look at the rules they make as a class to check, combine and refine them. They then look at the process of finding the rule, from initial ideas and testing and refining. The children will need to have previously explored prime numbers. |
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: Finding the best description of the numbers that fit a hidden rule |
Children think of ideas that show how their rule works for both sets of numbers: ‘eaten’ and ‘not eaten’. The teacher responds with new examples that test the children’s rules. The discussion shifts to evaluating the rules listed on the board. These are compared to eliminate duplicates, to combine similar rules and to summarise everything established so far. Children finish with the most succinct and clear rule. |
Episode 2: Describing the process of arriving at the succinct rule and using it for a second example |
Children address the idea that you need to have more than one example to generalise, and the need to test hypotheses in order to confirm or eliminate them. They discuss the advantages and disadvantages of relying on memorised knowledge. They try to use their newly acquired strategies with other sets of numbers. They discuss and agree that itis not necessary to test it for divisibility by 4 if the number is not divisible by 2. Children progress to how to test for prime numbers. |
Reflection |
Children share strategies regarding how the prime numbers were identified. The need to test divisibility of a number by ever increasing primes is discussed and the existence of some ‘half-way mark’ considered. |
BEFORE YOU TEACH |
For the start of the lesson you may wish to develop the context more fully, into a puzzle or story. Encourage children to jot down their ideas at different times in the lesson, so that they can ask questions based on their hypotheses. Encourage basing later ideas on examination of earlier ones. |