Platonic Relationships

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SWBAT describe polyhedra in terms of their structure. Students will understand how the parts of a solid are related to points, segments, angles, and polygons.

Big Idea

Students analyze the structure of polyhedra and discover something unexpected that they have in common: f + v - e = 2.

Lesson Open

5 minutes

Using the slideshow, I display the warm-up prompt for the lesson as the bell rings.  The warmup asks students to define a pentagon in terms of its structure (MP6, MP7), reviewing the topic of the previous lesson.

The warm-up follows our Team Warm-up routine, with students writing their answers in their Learning Journals.


Displaying the Agenda and Learning Targets I tell the class that today we will be analyzing the structure of 3-dimensional objects: polyhedra.

Platonic Solids Investigation

30 minutes

As I explain in the video, the goal of this activity is for students to analyze the structure of a polygon. 

I display the instructions and distribute the handout for the activity.  I point out where students can get materials:  scissors, glue sticks or tape, and model templates for making a Tetrahedron, Hexahedron (cube), Octahedron, and Dodecahedron.  This activity follows a Team Jigsaw format, with members of each team filling different Roles.

After working as a team to complete the table in the hand-out summarizing the number of faces, edges, and vertices of each solid, students should record the same information in the table in Portfolio Problem 1.  They will need this information to complete the problem.

I offer the model template of the Icosahedron as a challenge students can complete for extra credit at home.  There are always takers.


Summarizing Polyhedra

15 minutes

I ask students to take out their Guided Notes on Structure.  We complete the sections on polyhedra: polyhedron, face, edge, vertex, the interior of a polyhedron, adjacent faces, edges, and vertices of a polyhedron, and diagonal.  By now, students should be seeing how certain terms like vertex or adjacent can have precise meanings that differ in different contexts.  More on how I use Guided Notes can be found in my strategies folder. 



Lesson Close and Homework

4 minutes

Displaying the lesson close prompt, I ask students to summarize what they learned from the lesson with their team-mates, then select the best answer to write on the board.  This activity follows our Team Size-Up routine.



I assign problems #24-25 from Homework Set 1.   These problems ask students to analyze the structure of polyhedra.  Problem #25 will challenge some students, as they must visualize the planes in which the faces of the solid lie.  In addition, I assign Portfolio Problem 1 for the unit.