T. Haneru a Thrydydd

Introduction
An activity to extend children’s use of fractions towards ratios and proportions. They start from fractions of fractions handled as a grid and are then given a paint-mixing problem that they can model on the page. The children use mathematics to compare depths of the colour green in two mixtures of blue and yellow.
This activity has three 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: Halving halves
The context is familiar: there is water in a jar, half of which is poured into a similar jar. So, each now
contains half of the original. Class discussion should focus on the different descriptions and connections
between these.
Episode 2: Thirding a half and halving a third on a grid
Given nine 36-cell grids, children shade squares to show two successive operations of halving, and two
successive operations of thirding. The aim of this episode is to encourage children to use both words and
fraction symbols to express what is happening in each operation on the notesheet and to discuss the
results using their own everyday mathematical language.
Episode 3: Symbolising fractions to solve a proportions problem
We know that blue mixed with yellow makes green, and the more blue, the deeper the green. But if you
mix them once, and then halve the mixture and pour half back, how do the greens compare in depth?
Children use methods learned in episodes 1 and 2 to compare the depth of colour in paint mixtures
containing different proportions of colours. The aim is to share the different strategies, symbolised in
different ways, and to discuss the difficulties that arise. The children have to construct fractions of
fractions. They use images and diagrams, and use reason and common sense to clarify for themselves
ideas of ratio and proportion. Children consider the links between multiple images.
Reflection
Children demonstrate the methods and symbolisation that they have used to approach the tasks and
discuss the advantages and disadvantages of each of them.
BEFORE YOU TEACH
Episode three is very challenging but is also very rewarding and effective. How much time you decide
to give episode three depends on how many of the children are tackling it in some way. It is also
worthwhile to leave the question ‘hanging’ in the air.

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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