D. Rhannwch Afal
Introduction |
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An activity to explore children’s understanding of the basic part-whole relations – through spoken language and demonstration on objects – and how this is represented in fraction notation. |
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: Meaning of unitary fractions and their notations |
Children rehearse the meaning of a half, then a quarter and an eighth, through demonstrations on objects, focusing on the equality of parts. They work in pairs to decide how to halve and quarter a book, a glass of water and a coin. This is followed by work on the convention of writing fractions and describing the ‘top’ and ‘bottom’ numbers and the partition line. Children should be able to compare fractions and add unitary fractions (that is, fractions where the numerator is 1). |
Episode 2: More fractions and their sums |
Children find ‘one third’ practically and as a mental activity. While children of this age are able to do this, it does require careful handling on paper and in terms of language used, especially when combined with ‘two thirds’ and comparison of size with earlier, simpler fractions. Children compare two fractions and justify their reasoning. They decide whether their sum is equal to or more or less than 1. Their lines of reasoning are then shared, with the implicit ideas of equivalent fractions made explicit, where feasible. |
Reflection |
Children look back at their work. They describe their understanding of a fraction as a mental image, in response to language use and the convention of written notation. They share ideas on how to compare and combine written fractions. |
BEFORE YOU TEACH |
Remember that the intention is to address existing misconceptions and clarify the connections. Children can find fractions confusing. The idea of equal parts is important since, in continuous quantities, it is nearly impossible to achieve. Equal parts, however, is absolutely exact as a mathematical idea. Encourage any insights at any level. For example, ideas about 1⁄4 may include ‘one over 4’, ‘one divided by 4’, ‘a fourth’, ‘a quarter’, ‘one slash four’, ‘one out of the 4 equal parts’, ‘the 1 is still inside the 4’, or others. |