Encourage tinkering with ideas, relationships, connections. Set up situations where students have to find information not readily available in school texts. Provide opportunity for students to design open-ended explorations of the concept. Provide multiple options so students can plan a unique "proof" of learning.

Students test algebraic properties and creatively demonstrate three of them.

Objective: To create representations of the algebraic properties using various modalities.

Activity: 1. Student teams will find or invent a number system and an operation in which at least one of the properties studied does not hold. They will use a matrix to chart the operations of their system within the set. They will demonstrate whether or not the algebraic properties they have learned hold true in their new system. They may create a new property for their system, name it, and demonstrate it in some way. 2. Working in cooperative groups, students will create a song, poem, rap, sculpture, painting, dance, or role play to demonstrate three of the properties. All properties must be divided up by the class so that each is demonstrated in at least one form.

Assessment: Ability of students to work together on group project. Quality of projects.