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Investigating the Commutative and Associative Properties Using Geometric Shapes Students typically learn about the concepts of identity, inverse, commutativity, and associativity by exploring the four basic operations (+, –, ×, and ÷) with integers. In this lesson, students investigate these concepts using a geometric model. Moves are performed with a rectangle, and the results of an operation that combines two moves are analyzed. Students determine if the operation is commutative or associative; if an identity element exists; or if there are inverses for any of the moves.
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