Geometry Through Art

I. The Square
A. Coloring Squares [graph paper || sketch]
1. Visualizing letters of the alphabet
2. Visualizing shapes and images
3. Exploring square and rectangle numbers
4. Exploring repeat designs by counting
B. Coloring, cutting, & folding activities [grid-on-the-bias worksheet || sketch]
1. Exploring square numbers
2. Patterns: concentric, rotational, and symmetrical
3. Visualizing: Perimeter area and volume
4. Pythagorean Theorem

IIa. The Circle [percentage circle worksheet || sketch]

A. Dial a design (cut and rotate a dial)
1. Exploring patterns
2. Visualizing congruence and concentricity - patterns with colors
B. Designing with a straight edge
1. Parallel and rotating chords
2. Inscribing stars and polygons
3. Inscribing polygon grids
C. Coloring Activities for visualizing
1. Concentricity
2. Rotation
3. Line and point symmetry
4. Analyzing designs to learn about parallel lines, angles, and degrees

IIb. The Circle [compass and straight edge constructions]

A. The hex and the 'anatomy' of the circle
B. Polygons and stars
C. Rotations, symmetries, and tessellations
D. Cutting, folding, and pasting: polyhedral constructions
1. The Cone (slitting the radius)
2. The Tetrahedron (slitting 1/2 diameter of an inscribed square)
3. The Pyramid (slitting the inscribed pentagon)
4. Assembling a Deltahedron (2 at a vertex)
5. Platonic polyhedrons and more (3, 4, 5, 6 at a vertex)

III. The Triangle [equilateral triangle grid || sketch; triangle grid w/ vertical lines || sketch]

A. Drawing and coloring activities
1. Visualizing shapes and images
2. Triangle numbers
3. Perimeter and area
4. Exploring Pascal's Triangle
5. Tessellation with grid-made polygons
6. Analyzing designs to learn more about transformation, rotation, and symmetry
B. Cutting, folding, and assembling activities
1. Making and assembling polyhedron networks
a. Tetrahedron
b. Pyramid
c. Octahedron
d. Cube Octahedron
e. Truncated Cube
2. Flexahedrons
3. Exploring patterns, symmetries, and tessellations on polyhedra and flexagons

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NOTES

In the heuristic (learning by finding out) method, students are encouraged to DO geometry with simple basic tools. Some concepts are axiomatic by virtue of simple definition, some because students have knowledge about them. At this stage of learning, it is important that this collection of givens or axioms be compiled.

It is not important, however, to define terms so they coincide word for word with textbook or dictionary definitions. It is far more useful for students to find out for themselves that such efforts as defining terms and enumerating properties are an ongoing and spiraling process. Investigation and analysis produce new assessments that warrant further exploratory investigations and lead to modifying definitions.

When (but not until) students are mature enough to have the ability and desire to study the learning process itself, the teacher may profitably raise the issue of learning how to learn.

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