Brendan Kelly Pub. Geometry and Spatial Sense

DESC.- BRENDAN KELLY PUBLISHING

Features:

• By Dr. Brenden Kelly
• This module addresses the expectations for grades 6 through 8 in the geometry strand of the NCTM's Principles and Standards for School Mathematics 2000. There are two units with five activities per unit. The content of the activities in each unit is described below.
• Unit 1: Activity 1 opens with a review of the concept of congruence. Students are challenged to divide a 3 · 3 grid into two congruent halves in as many ways as possible. To provide a transition from two-dimensional shapes to three-dimensional figures, students are guided to visualize a truncated cube and cuboctahedron and to enumerate their edges, faces, and vertices. Activity 1 culminates in the students construction of the truncated cube and the cuboctahedron from provided templates.
• In Activity 2, students construct frame structures of pyramids and prisms of various types and are guided to the discovery of Euler?s Theorem for these figures.
• Activity 3 provides templates for the construction of each of the five Platonic solids. By counting the edges, faces, and vertices of their models, students extend Euler?s theorem to these figures.
• Then in Activity 4, they construct their own classroom geodesic dome and test Euler?s Theorem for this structure.
• Unit 2: Activity 1 involves students in selecting a point B on Front Street and a point C on Main Street so that the perimeter of DABC, a subway connection network, is a minimum. Students do this by using a string on a geoboard, by employing trial-and-error on grid paper, or by using dynamic software such as Sketchpad.
• In Activity 2, students count squares on a grid and apply the Pythagorean theorem to calculate (rather than estimate) the perimeter of DABC for various choices of grid points B and C.
• Then in Activity 3, students discover how to find the optimum locations for B and C by reflecting in two different lines.

* Finally, Activity 4 involves students in the application of the
sum of the angles in a triangle theorem to determine the measures
of the angles in DABC. All their findings are consolidated in a
report to the City Planner indicating where subway stations B and
C should be located.