Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

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Teacher's Lab
Shape and Space in Geometry
IntroductionAbout ShapeAbout Space
  Across the Grades

This activity is all about 3-dimensional visualization—and the 2-dimensional representations of 3-dimensional objects. Students are asked to figure out the structure based on its silhouettes as seen from front and side.

These silhouettes are similar to the traditional front and side views drafters have used. But here, you cannot see any features in the view except for the outline. This has two effects on the problem: It is simpler to explain and more likely to have multiple solutions.

across the grades

Because of the multiple solutions and the small numbers, this activity is accessible to quite young children—perhaps as young as grade 2. You can make the activity more interesting for older children by asking them to find as many solutions as they can. You can challenge still older students by asking for a complete set of the solutions and the one that uses the fewest (or the most) blocks.

To extend the activity, you can have students draw the resulting structure on isometric dot paper to make a "3-D" rendering.


In the overview to the Geometry and Spatial Sense standard (grades preK–12), the NCTM describes things similar to the activity. See Figure 3.5 in the current version of the Principles and Standards document.

For grades 6–8, the Council gets specific about this content.

It is important for middle-grades students to develop an understanding of the relationship between three-dimensional shapes and their two-dimensional representations, so that students will be able to both interpret two-dimensional representations and draw them. Instructional activities that ask students to interpret or draw different views of buildings, such as the base floor plan and front and back views, using dot paper, can be useful in developing this understanding.


In the Teaching Math 5–8 video series, Pam Hardaway's classroom is doing a similar activity with physical materials. This is part of an extensive unit from the Connected Math project, called The Ruins of Montarek.

Back to Plot Plans and Silhouettes Activity


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