NCTM Geometry and Measurement Standards

In its discussion of the Geometry Standard, Principles and Standards for School Mathematics takes care to include three-dimensional shapes as appropriate for study from preK on:

"Through the study of geometry, students will learn about geometric shapes and structures and how to analyze their characteristics and relationships. Spatial visualization—building and manipulating mental representations of two-dimensional and three-dimensional objects and perceiving an object from a different perspective-is an important aspect of geometric thinking" (NCTM, p. 41).

In particular, middle grades students should investigate a variety of geometric shapes, becoming comfortable with the characteristics of three-dimensional solids. They are encouraged to develop their visualization skills through hands-on experiences, such as building concrete models and exploring with software that can show a geometric solid from every angle. It is expected, as well, that students at the middle school level "recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life" (p. 232).

The Measurement Standard also applies to the study of three-dimensional shapes since volume and surface area are necessarily tied to these figures. For some solids—prisms, pyramids, and cylinders—middle school students should be guided to develop the formulas for these measurements (p. 244).

The resources offered here address each of these standards to some degree. They can help your students examine the geometric shapes of the 3-D world, develop their understanding of measurement and their powers of visualization, and come to see the artistry of mathematics in polyhedra.

Reference

National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA: Author.

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Copyright September 2006 — The Ohio State University. This material is based upon work supported by the National Science Foundation under Grant No. 0424671. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

This work is licensed under a Creative Commons License.