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Shapes in the Octagon Wreath

Deborah Crocker & Betty Long

the form of visual activities involving identifying shapes. These students would be at the Visualiza tion level, Level 0, in the van Hiele model. Prior to experiences with shapes in later grades, students should investigate attributes and properties of shapes. These students would be at the Analysis level, Level 1, in the van Hiele model and advance to Level 2. This activity can be used, depending on the questions asked by the teacher, to extend the identification of shapes for early grades and to practice and improve the understanding of attrib utes and properties of shapes for later grades. It can also be used to begin the study of symmetry and the classification of triangles by the types of angles they contain. Some examples of questions teachers might ask will be included after the directions for the folding activity. The Virginia Mathematics Standards of Learning (2016) indicate the following in kindergarten, first, and third grades: • identify and describe plane figures (circle, triangle, square, and rectangle); • compare the size (smaller, larger) and shape of plane figures (circle, triangle, square, and rectangle); and • describe the location of one object rela tive to another (above, below, next to) and identify representations of plane figures (circle, triangle, square, and rec tangle) regardless of their positions and orientations in space. • identify, trace, describe, and sort plane figures (triangles, squares, rectangles, and circles) according to number of sides, vertices, and angles; and • identify and describe representations of • 1.11 The student will: • K.10 The student will:

The study of shapes is one of the most basic activi ties in elementary school mathematics. It provides a foundation for the study of geometry. Howse and Howse (2014 – 2015) state that, “ Students begin to understand geometry through direct interaction with their physical world ” (p. 305). The van Hiele Model of Geometric Understanding is a widely ac cepted framework for geometric understanding. In the model, van Hiele (1999) states that, “. . . the ‘ lowest ’ is the visual level, which begins with non verbal thinking. At the visual level of thinking, fig ures are judged by their appearance ” (p. 311). As students progress through the levels, attention to attributes of the shapes are learned and studied. Students study and learn a variety of shapes in dif ferent grades. The activity described below pro vides opportunities for students to engage in hands on exploration of shapes, their appearance, and their attributes. It is important for students to have experience with shapes prior to beginning this ac tivity. In early grades, this experience might take

Virginia Mathematics Teacher vol. 47, no. 1

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