Geometry Through Art
Norman Shapiro
How to Request Materials
________________________________________________
Table of Contents
________________________________________________
Norman Shapiro would like to share his copy-ready materials with teachers as well as students, parents. If
you would like more information, send e-mail to [email protected].
If youʼre a teacher, please state the grade and topic area you are most interested in. Send your postal address
if you are unable download graphics, and Shapiro will mail you a packet of ready-to-use materials. There will
be a fee for the costs of postage and printing.
“The Basic GTA Kit”
-containing 26 selections of copier master worksheets
1. 6 Squares / Oblique Squares Grid + Center / ʻWhat Is Geometry?ʼ ʻSecrets of the Squareʼ (Grades K - 4)
2. 3 Percentage Circles / ʻAnatomy of the Circleʼ (Grades 4 - 12 & Teachers)
3. ( (Grades 4 - 6)
4. 3 Circles With Inscribed Octagon Grids ʻAnatomy of the Circleʼ (Grades 4 - 10)
5. 1 Circle With Hexagon Grid / Importance of Visualizing (Grades 4 - 10)
6. 2 Circles With Hexagon Grids / Polygons and Polyhedrons / Point and Line Symmetries (Grades 4 -10)
7. 2 360 Degree Circle Grids / ʻWhy Pi is More Than 3ʼ (Grades (6 - 10)
8. Plastic Disc & Straight Edge Activities Chart (Grades 6 - 10)
9. Dial-A-Design % Circle / Patterns, Color Mapping and Congruence (Grades 3 - 6)
10. Ninety Nine Square Square / ʻSecrets of the Squareʼ ʻLooking For Patternsʼ (Grades 2 - 4)
11. Large Square/Dots Grid / Tesselations / ʻSlides, Turns and Flipsʼ (Grades 2 - 5)
12. 25 Squares Square Grid / Looking For Patterns / Tesselations / ʻSlides, Turns & Flips (Grades 5 - 10)
13. The Triangle Grid / Triangle Numbers / Looking For Patterns / Tesselations (Grades 4 - 10)
14. Similar Shapes, Small and Big/ ʻSecrets of The Squareʼ (Grades 4 - 6)
15. A Chart for Tallying Big Numbers (Grades 5 - 7)
16. Ideas for Inscribing Designs in a (%) Circle (Grades 5 - 8)
17. Fibonacci Numbers & Golden Rectangle (Grades 6 - 10)
18. Sierpinski Triangle /3gon grid (Grades 8 - 10)
19. Tangrams with Oblique Unit Squares / Area & Perimeter, Visualizing (Grades (4 -7).
20. An All Purpose Triangle Grid (Grades 3 - 10)
21. Cube Octahedron ʻDymaxionʼ with Triangle Gridʼ (Grades 6 - 8)
22. Cutting and Pasting a Truncated Cube Grades (3 - 4)
23. 22 Nwtworks / Pyramid and Cube (on triangle grids) ( Grades 4 - 5)
24. Octahedron (on Triangle Grid) A Network (Grades 4 - 5)
25. Inscribed Polygon Designs / Angles as Units of Measure (Grades 6 - 10)
26. NS Teaching / color mapping a grid pattern (tesselation (Grades 6 - 10)
.
The GTA Kit represents materials culled by Norman Shapiro for more than 20 years of working as an artistin-residence in classrooms. These are designed for teachers of elementary grades, math, art, special education
and the gifted. All are downloadable and printable on standard 8 1/2” X 11” paper. The activities include working with color, drawing, cutting & pasting. Most activities culminate with displayable one-of-a-kind works of
student art. The processes entail exploring and learning heuristically about math and geometry.
Norman Shapiro welcomes inquiries and requests for assistance.
State:
the age and grade level of your students,
and the topics you intend to investigate
describe any special difficulties you wish to address.
Contact Norman Shapiro at <[email protected]>
[Privacy Policy] [Terms of Use]
_____________________________________
Home || The Math Library || Quick Reference || Search || Help
_____________________________________
© 1994-2005 The Math Forum
http://mathforum.org/
The Math Forum is a research and educational enterprise of Drexel University.
Norman Shapiro
P.O. Box 205
Long Beach, NY 11561
Web page design by Sarah Seastone
4 November 1995
A 6 squares when cut out along the straight edges, and assembled will
form a cube ornament that can be suspended with string.
1. Cut all the squares out and fold the 4 corners to the dot at the center of
each of the 6 squares.
2. The 4 triangle flap, (flaps that are seen on the outside of the cube) when
pasted will set up a box with 4 sides.
3. Paste 5th quare on the top, then the last on the bottom.
4. A hole punch or paper cliip on the tip of any of the flaps can
attache string or yarn to it. Make one more and and color it this time
before assembling. Use the squares to create letters of your name
or a geometric design built out of squares.
Inscribed Hexagon Grids
by Norman Shapiro
During the late 1980s I discovered
ways of making grids in the circle. As of
this writing, there are essentially three
families of grids I've used for teaching children about the geometric attributes of the
circle:
-the Octagon Grid (based on inscribed squares.)
-the Decagon Grid (based on inscribed regular pentagons)
and the Hexagon Grid (based on an
inscribed regular hexagon.
As will be observed in the illustrations on these pages, (the circle itself a
closed and finite system defined by a center, a radius, and the closed arc of its circumference) are its prime elements. What
could be simpler? What could be more conducive to illustrate to learners young and
old the nature of complexity and chaos?
From three simple elements arises
the concept of a ratio called pi, of symmetries, (of a line or point,) of polygons ranging from the triangles, decagons to many
sides reaching into the thousands, millions,
and the infinite itself. We come to understand the circle as an envelope of polygons!
Using simple tools ( a straight edge
and any circle making tool), the student
explores the closed curve as did the ancient geometers.
How does one 'find' an inscribed
hexagon? It is innate to the circle! The
attributes of center, radius and circumference is an environment in which a straight
edge can be employed to 'find' a hexagon!
Observe!
A Circle with its radius.
Then, 2 Circles
2 Circles, then 3
Then,
6 intersects,
6 chords &
a hexagon