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What is it?
Fractions are a minefield of misconceptions. Despite the fact that students technically encounter equivalent fractions for the first time in Year 2, many still enter Year 11 with some serious holes in their understanding of fractions. Hence, any activity that can help students develop a deeper understanding, perhaps by presenting fractions in a different way, is going to be a Godsend for me. Step forward Diminishing Fraction Areas. This is a wonderful collection of fraction diagrams, accompanied by a series of questions. These include things like “what fraction of the whole shape is the red square?”, right the way up to “what is two thirds of a half?”. The supporting diagrams help illuminate potentially abstract concepts and should provoke plenty of discussion amongst your students.

How can it be used?
In my opinion, there is no point taking on an activity like this until students’ basic understanding of equivalent fractions and fractions of a shape is reasonably secure. You cannot teach the basics of fractions through this activity, but you can use it to help students make connections and deepen their understanding. Personally, I would have the students working in paris on one sheet at a time. The collection of questions is well structured in that it increases in difficulty as you go through it, so starting everyone off on the first square challenge seems sensible. Students will undoubtedly need support, and periodically stopping the class to discuss strategies and assumptions may be a good way to go. But even if students run into difficulties, I would advise you persist with this wonderful resource, because the concepts involved are crucial, not only for students’ understanding of fractions, but they also transcend into topics such as area, geometrical properties of shapes, ratio and more.

Thanks so much for sharing
Craig Barton

Download: Diminishing Fraction Diagrams
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