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In this unit, students create a shape sorter and consider all possible moves that will return a shape to its original position. They investigate the results when two of these moves are performed consecutively, to learn about the commutative and associative properties.
Math Content
- Symmetry
- Rotations, Reflections
- Identity
- Inverse
- Commutative Property
- Associative Property
Individual Lessons
Lesson 1 - Commutative Rectangle 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. Lesson 2 - The Plus Sign and Triangle Using a scheme similar to the one in the Rectangle lesson of this unit, students will further explore the concepts of identity, inverse, commutativity, and associativity. Students investigate and analyze moves performed with a plus sign, and an online activity is available to help students with this investigation.
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