Spatial Sense

Your students already have well-developed spatial sense, as you have seen in their sports and dancing, but in the realm of mathematics, that spatial sense may seem nonexistent. All the activities in this unit help to develop a degree of comfort in the 3-D math zone, but the exercises below aim particularly to increase learners’ ability to move between the two-dimensional and three-dimensional worlds of school mathematics.

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Space Blocks: Algebra (Grades 6-8) http://nlvm.usu.edu/en/nav/frames_asid_195_g_3_t_2.html

Working in three dimensions requires and develops spatial sense. In these activities, students use an applet to model shapes with cubes, constructing a figure, for example, that has eight cubes and the largest possible surface area. In other problems, they connect a colored cube to the one pattern that can be folded into that cube. MSP full record

Decorating Boxes: How Do You Print a Ribbon on a Box? http://www.figurethis.org/challenges/c55/challenge.htm

Here is the problem: four boxes are shown opened flat. Each box pattern shows a ribbon crossing several sides of the box. Students are asked to decide which of the box patterns can be folded into a box that has a ribbon running continuously around it. The essential problem is to visualize the three-dimensional object that can be made from a two-dimensional pattern. MSP full record

Using Cubes and Isometric Drawings http://illuminations.nctm.org/LessonDetail.aspx?ID=U166

Students first explore the online isometric drawing tool, which allows them to draw and manipulate figures built with “blocks” on isometric paper. In further lessons in the unit, they construct three-dimensional figures using a front-right-top view and, later, only a mat plan. The preliminary work needed to know the drawing tool is well worth the exercise in spatial sense and reasoning.

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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.