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7.   Pythagorean Relationship:
Exploring abstract concepts using interactive models

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	SREB Readiness Indicator Understand and use the Pythagorean relationship to solve problems > Additional indicators
	Skills Understand the Pythagorean relationship as unique to right triangles Recognize the relationship in a range of scenarios Memorize the Pythagorean relationship
	Figure 1: Using a set of Tangrams to model the relationship (Click to enlarge)

Overview

Students investigate the Pythagorean relationship by exploring a series of nine interactive proofs that are available on the IEC-Math Manipula website. Each proof allows students to manipulate shapes to demonstrate that a2 + b2 = c2. Following a proof with tangrams (Figure 1), students extend their understanding of the relationship as they decipher and prepare presentations of the nine dynamic proofs.

The Value of This Technology

Technology has enabled mathematicians to create a wide range of models to illustrate complex concepts; virtual manipulatives make these models accessible to middle grades students and are invaluable in helping students develop their understanding of abstract concepts such as the Pythagorean relationship. In the past, middle grades students were often introduced to this relationship through static pictures of triangles or more limited manipulatives like tangrams. After examining a limited number of models, they moved quickly to memorizing the theorem in order to apply it to problem solving. This technology allows students to interact with a multitude of models, better connecting intuitive and formal understandings.

Look in the Classroom

Ms. Weber knows that the more models her students can explore in their investigation of the Pythagorean relationship, the more successful they will be in applying it to a range of problem-solving situations.
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