1. Modular Origami From Christmas Crafting to Middle School Math Lessons… Soraya Dangor 4/18 Sequences ✓ Equations ✓ Communication ✓ Spacial Reasoning ✓ Angles ✓ Polygons ✓

2. Building Units

3.  Right isosceles triangular pyramid “Half-cube” or “partial triangular prism” 

4. # of units# of pyramids# of vertices 325 648 9611 12814

5. Units × 1.5 = Pyramids Pyramids ÷ 1.5 = Units Units + 2 = Vertices -Area -Interior Angles -Graphing -Other building units Sequences!

6. Definitions of Polyhedra

7. Regular Cube (made with sonobe units) -6 congruent square faces -8 vertices -8 edges Oxi Module Cube -6 faces? -each face consists of 4 ½ cubes and 6 congruent square holes -OR do we count all the surfaces? -8 Pyramids (are these part of the faces?) -Vertices? - edges? -Interior angles?

8. Exploration Project - Analyzing and describing units - Exploring what can be built - Exploring area and angles - Writing definitions - Recording patterns - Representing patterns algebraically - Creating a new shape X

9. NCTM 6-8 Algebra Standards represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules; relate and compare different forms of representation for a relationship; identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations. NCTM 6-8 Geometry Standards precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties; understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects; create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

10. Extensions -Koch Snowflake -Interdisciplinary possibilities -Creating new origami units -Middle School Math Unit Source: http://michal.kosmulski.org/origami /fractals.html