Geometry and Spatial Sense, Grades 4 to 6 - EduGains

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When planning activities that involve working with rectangular views, it is important to
keep in mind the second van Hiele level – analysis. The focus is on the properties of shapes
and figures, and the ability to generalize from observations. For example, students might
recognize that the number of sides of a prism base is the same as the number of rectangular
faces of the prism. Students are likely to realize this generalization after taking part in a
variety of carefully planned activities.
Isometric diagrams use an isometric grid. An isometric grid shows three axes instead of the
two found in a rectangular grid. One axis runs vertically; the other two axes run “down” at
30° angles to the left and right.
Isometric diagrams encourage students to visualize pieces or sections of solids that cannot
be seen. When working from an isometric view and building a solid from interlocking
cubes, students may be required to make assumptions about cubes they may or may not
be able to view directly. For example, in the diagram below, students would have to justify
placing a cube in the space indicated by the arrow.
Geometry and Spatial Sense, Grades 4 to 6
This cube has been drawn using isometric grid paper. Note the
directions of the three axes – one is vertical; two run down
diagonally left and right.
Note that the perimeter of the two-dimensional drawing is a
perfect hexagon, and all the thick lines are of equal length.
Is this the top of a cube,
or the side of a cube?