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University of Nottingham
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Generalizing patterns: the difference of two squares
This resource requires problem solving using skills in forming and factorising expressions.
Students begin by working out numerical examples where a number can be written as the difference of two square numbers. They need to choose systematic ways to collect and organise data, and examine it for patterns.
The work then moves to both algebraic and area representations of the concept. Students explain why certain results are possible/impossible and move towards a proof. Examples of misconceptions are provided for discussion.
This is a problem solving lesson from the Mathematics Assessment Resource Service, a collaboration between UC Berkeley and the Shell Centre team at the University of Nottingham. Further information on the collection is given here.
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