Ellipses vary in shape from circular to nearly parabolic. An ellipse's eccentricity indicates the location of its foci, but its aspect ratio is a direct measure of its shape. This article takes a careful look at the shape of an ellipse and offers practical suggestions and specific activities to deepen students' understanding of the geometry of an ellipse. Using the Common Core (2010) practices and NCTM (2000, 2009) Standards, the activities link an ellipse's shape to algebra, data, and measurement and make connections between mathematics and astronomy. (Contains 8 figures and 1 table.)