Modular Origami

From Christmas Crafting to Middle School Math Lessons…

Soraya Dangor 4/18

Sequences ✓

Equations ✓

Communication ✓

Spacial Reasoning

✓Angles ✓

Polygons ✓

Building Units

Right isosceles triangular pyramid

“Half-cube” or “partial triangular prism”

# of units # of pyramids # of vertices

3 2 5

6 4 8

9 6 11

12 8 14

Units × 1.5 = Pyramids

Pyramids ÷ 1.5 = Units

Units + 2 = Vertices

-Area

-Interior Angles

-Graphing

-Other building units

Sequences!

Definitions of Polyhedra

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?

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

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.

Extensions

-Koch Snowflake

-Interdisciplinary possibilities

-Creating new origami units

-Middle School Math Unit

Source: http://michal.kosmulski.org/origami/fractals.html