Geometry Standard for Grades 3–5

Grades 3 - 5: Geometryhttp://www.nctm.org/fullstandards/document/chapter5/geom.asp8 of 9 7/27/2010 4:20 PMFig. 5.16. Views of a three-dimensional object (Adapted fromBattista and Clements 1995, p. 61)ExploringRectangles andParallelogramsTechnology affords additional opportunities for students toexpand their spatial reasoning ability. Software such as Logoenables students to draw objects with specified attributes andto test and modify the results. Computer games such as Tetris(Pajitnov 1996) can help develop spatial orientation andeye-hand coordination. Dynamic geometry software provides anenvironment in which students can explore relationships andmake and test conjectures.Students should have the opportunity to apply geometric ideasand relationships to other areas of mathematics, to otherdisciplines, and to problems that arise from their everydayexperiences. There are many ways to make these connections.For example, measurement and geometry are closely linked, asillustrated in the problem in figure 5.11, where geometricproperties are used to relate the areas of two figures of differentshapes. Geometric models are also important in investigatingnumber relationships. Number lines, arrays, and manymanipulatives used for modeling number concepts aregeometric realizations of arithmetic relationships. In algebra,students in grades 3–5 often work with geometric problems toexplore patterns and functions (see, for example, the "tower ofcubes" problem in fig. 5.5).In addition to its utility in exploring and understanding otherareas of mathematics, geometry is closely associated with othersubjects, such as art, science, and social studies. For example,students' work on symmetry can enhance their creation andappreciation of art, and their work on coordinate geometry isrelated to the maps they create or use in their study of theworld. The study of geometry promotes a deeperunderstanding of many aspects of mathematics, improvesstudents' abstract reasoning, and highlights relationshipsbetween mathematics and the sciences.