D. Rhannwch Afal

Introduction
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.

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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