For a long time, young children learned shapes by sight, without regard to attributes (characteristics). An octagon looked like a stop sign, by golly, and any 8-sided figure that didn't look like a stop sign must not be an octagon. Standards today, whether they are common core or our Texas TEKS, emphasize defining shapes based on attributes. ANY 8-sided polygon is an octagon. An octagon is defined as such because it is a polygon with 8 sides. Period.
Let's look at some of the common core standards:
K.G.2--Correctly name shapes regardless of their orientations or overall size.
K.G.4--Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/"corners") and other attributes (e.g., having sides of equal length).
1.G.1--Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.
2.G.1--Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.What are some things you notice? First, I notice orientation and size. Be sure kiddos see lots of examples of each of the shapes. The shapes below are all triangles, although the look quite different. Geoboards are a GREAT tool for exploring different shapes.
Here's a little assessment I made for my 2nd grade teachers. Click here to grab it. For more information on helping kiddos identify geometric attributes, check out this blog post.