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 * Meredith Tate **
 * EDUC 519- Math Methods and Content **
 * Drexel University- Fall Semester 2011 **
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 * Performance Task- 26 October 2011 **
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 * __Performance Task Focus __**: The mathematical characteristics that define geometric shapes and the significant relationships among geometric properties.

*How do features of geometric shapes (such as angles, lengths, volumes, areas, etc.) interact to define and categorize a shape? *How do we interpret and understand shapes in terms of dimension? *How do we identify similarities and differences among geometric shapes? *How can we use quantitative information about one property of a geometric shape to calculate other unknown properties?
 * __Essential Questions __: **

<span style="font-family: 'Arial','sans-serif'; font-size: 16px;">*It is possible to categorize geometric shapes by studying their properties and comparing these observations to the defining features of each shape. <span style="font-family: 'Arial','sans-serif'; font-size: 16px;">*Geometric shapes may exist as two or three dimensional objects and are categorized based on many features. It is important to pay close attention to small distinctions between similar objects. <span style="font-family: 'Arial','sans-serif'; font-size: 16px;">*Known quantities can be used to calculate new information and gain insight into mathematical relationships.
 * __<span style="font-family: 'Arial','sans-serif'; font-size: 16px;">Enduring Understandings __<span style="font-family: 'Arial','sans-serif'; font-size: 16px;">: **

<span style="font-family: 'Arial','sans-serif'; font-size: 16px;">(available: [])
 * __<span style="font-family: 'Arial','sans-serif'; font-size: 16px;">National Council of Teachers of Mathematics- Geometry Standard: __**

<span style="font-family: 'Arial','sans-serif'; font-size: 16px;">Grades 6–8 Expectations: In grades 6–8 all students should–
 * <span style="font-family: 'Arial','sans-serif'; font-size: 16px;">precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties;
 * <span style="font-family: 'Arial','sans-serif'; font-size: 16px;">understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects;
 * <span style="font-family: 'Arial','sans-serif'; font-size: 16px;">create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.