Since the publication of the original Curriculum and Evaluation Standards for School Mathematics (NCTM 1989), we have come to embrace the importance of the “big ideas” of mathematics—the complex web of ideas that goes beyond content and includes reasoning, problem solving, and communication using multi-ple representations. Big ideas in classrooms give students opportunities to see mathematics as an integrated whole and to make thoughtful connections among related concepts and applications to other domains. This article illustrates how mathematical insights can arise naturally from a rich learning task when the teacher facilitates a stimulating and responsive dialogue.

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