Compass or circle template, Drawing Pencils, soft lead pencils (like Ebony), Erasers, scissors, Colored Pencils, 12" (30 cm) square white Drawing Paper, Black Construction Paper White Glue (or Rubber Cement)

Alternate:

Sharpie Ultra-Fine Point Marker, Markers, 6" (15 cm) square white paper, pie shape template, rulers, pencils, paper clips, masking tape, 12" (30 cm) square white paper.

Math Vocabulary:

Resources:

Assorted examples of radial design in art: Rose windows, mandalas from various cultures, Hawaiian quilt designs. Mandalas Internet Resources (see Earth Mandalas in particular) Mandalas of Tibet
Insects - plants - pictures of flowers - nature images (If Chinese influence is chosen - have handouts of Chinese art - motifs found in Chinese art)
See Ray Rasmussan Mandalas from Art

Books:

Coloring Mandalas 1 - The forty-eight drawings presented here for coloring include designs inspired by forms of nature, Native American and Tibetan sand paintings, Hindu yantras, Turkish mosaics, the illuminations of Hildegarde of Bingen, and the art of M.C. Escher. See also Volume 2.

One Million Mandalas: For You to Create, Print, and Color - This book includes a CD with art that is usable in three ways: with a couple of clicks you will be able to select and print one of the basic mandala designs, construct your own mandala by different ring designs from a drop-down menu, or randomly generate a mandala. Because there are 100 centers, 100 middle rings, and 100 outer rings, the disk supplies one million possible permutations and combinations!

1. Show examples of Radial design in art - PowerPoint or slides of Rose windows and various mandalas
2. Demonstrate steps to make symmetrical design - and transferring to rest of circle
3. Demonstrate/review colored pencil techniques - blending of colors - varying pressure for different values. Review color planning

Note: Larry taught this lesson to 6th graders the first trimester (see first dragon fly design above).  After seeing Alix Peshette's mandalas done in Paint Shop Pro, he adapted the lesson for colored pencils for the final 7th grade project.  He is now testing two versions...one a little complicated and the other more complicated  with different groups of 7th graders.

1. Trace circle template onto 12" square paper (or 12" x18" / 30 x 46 cm). May use compass to make circle (11 to 11 1/2" (30 cm) circle). Neatly cut out circle.  
2. Fold the circle in half, then in quarters, then in eighths. Crease
3. Unfold and draw on only one of the "pie slices." 
4. Unfold and draw on only one of the "pie slices." This is the stage that can be adapted to fit an elementary through high school lesson.  The drawing can be simple or complex. Guide students to at least have the drawing touch the edge of the pie slice a few times. Dragonfly was drawn from life. The science teacher had students collect bugs. Once the projects were graded and students no longer wanted the collection - these were given to the art department. Insects could be a theme - or other items from nature drawn from life - flowers - plants - fish. Go over lines with soft lead pencil
5. Once the pie drawing is completed, the slice is folded inward and then the back of the paper is rubbed with a smooth hard tool to transfer the drawing to the adjacent pie slice. 
6. Outline on the adjacent pie shape - this 1/4 of the circle is folded in and transferred to the next quarter. 
7. Fold over to transfer to the other half of the circle.
8. Color according to your needs.  Select a color plan.  For the 7th grade project, students blend colors and values using colored pencils.
9. Mount on black paper when finished.

For the more complicated design:

1. Use a compass to draw a large circle approximately 11.75 inches (30 cm). (any desired size)
2. From the center, measure a 36 degree angle and then cut out a 36 degree pie slice. These are used to make templates out of poster board. See Pie slice template
3. Students trace the pie slice onto their paper and follow through with the process described in the above project.  The only difference is now they have 10 slices instead of 8. Color as above. Compare the eight slice dragonfly with the ten slice one next to it. Mount on black paper.

Bunki Kramer - Los Ceros Middle School did a twelve pie section. 

If I were doing the twelve section - I would have the students trace the mirror image - then trace that six times around the circle. I would have had the student mark each half into thirds (using a compass) then position the 1/6 pie wedge for tracing.

Evaluation:

1. Did student exhibit radial balance in completing a design inspired by nature - Did they draw from life to create a center of interest in their design?
2. Did students exhibit craftsmanship in coloring their design with colored pencils
3. Did students show color blending and varied values in their design?

Alternate process using markers by Judy Decker:

Personal Symbolism - Example from Lin Altman Cedar Creek Elementary - fifth grade I have done radial design with a number of different themes with 6th graders.  One time it was personal symbols (initials could be included - Charles Demuth and Marsden Hartley served as motivation). Another year it was flowers drawn from life. Another year, we did gargoyles and beasties. Each year, I used the same methods of transferring and medium. We used fine point and Ultra fine point Sharpies and various kinds of markers.

Motivation for each lesson was Rose windows of the Middle Ages. Georgia O'Keeffe was used in addition when we did flowers and Gothic architecture and gargoyles were studied with the beasties design. Materials listed above.

Procedures:

1. Fold 6" square of white paper diagonally. Draw end of "pie" wedge using desired line (students had a variety of options and could create their own line). 
2. Draw design on folded triangle wedge - make design touch the edges (Have a central shape be a focal point). Break up the negative spaces with line/shapes. (6" (15 cm) square tracing paper could be used - and design simply transfer to the other side by tracing) With Georgia O'Keeffe influence - negative space was broken up with stems and leaves. Gargoyles, space was broken up with architectural elements.
3. When satisfied - transfer design to other side of paper using carbon paper (place carbon side up on on table - and lay folded paper on carbon - trace over lines)
4. Open and go over lines with Sharpie marker - Fine point or ultra fine point.
5. Measure six inches in on a 12" (30 cm) square paper - mark in two places. Draw a light pencil line down center. Measure from the other side in 6" (15 cm) in two places and draw a light perpendicular line across. 
6. Paper clip design under 12" (30 cm) square paper lining up outside edges and lining up with the pencil lines. We marked a small C in the center (temporarily so students would rotate the design around keeping the same point in the center).
7. Tape up to window with small pieces of masking tape and trace over lines.
8. Rotate one quarter turn - match up lines and edges -paper clip - tape and trace lines into the next quarter of the circle. Continue rotating around and tracing at window until all four quarters are traced. We did it this way so there would not be fold lines in the finished work.
9. Outline with fine point Sharpie -- or ultra fine point.
10. Color with a variety of markers (Overwriters were fun to use for the Beasties). Color the same shape the same color in all sections for perfect radial balance. Some small shapes may be left white. Optional: Alternate colors in shapes as shown in example above.
11. Cut out and mount to colored construction paper - select a color that will bring out the colors of the design. Mount with tiny dots of glue.

From Lin Altman: We used compasses and protractors to create the 8 pie shapes. The students were then given a pie shape piece of paper of the same size as one of the sections. They drew their designs which had to be filled with symbols about them. Then they traced the design on the other side of the paper by holding them up to a window. Finally, they traced them onto the mandala circle alternating around the center.

Submitted by Mike Sacco Radial design "Earth Mandalas" - colored pencils

This is how Mike did this lesson: Through trial and error I found a system that works for students and myself. I have large circle tracers that are 10 slice sectioned off. Students trace this onto their drawing paper and then while it's still on the their paper, they mark off the lines that divide the circle. Using a ruler they connect the lines on their circle. They label the sections a, b, a, b, etc, all around the outside of the circle. They then have a piece of tracing paper that is the same size as a slice which also has their design on it. One side of this tracing paper we label a, the other b. Finally, they position the tracing paper on the circle with the corresponding letter and transfer. Flip and then transfer again, etc. This is the only way that I know of to guarantee very accurate placement.

Elementary Adaptation:

I did this project for "Math Week" with fourth graders. We used Charles Demuth's Figure 5 in Gold for inspiration - along with Rose windows. Marsden Hartley's works using symbols also served as inspiration.

1. Discuss Rose windows - radial design - and work of Charles Demuth -Figure 5 in Gold. Point out geometric shapes - repetition of numbers - and breaking up of negative space.
2. Demonstrate steps and how to draw numbers with double line so they can be colored in.
3. Students fold 6" square white paper diagonally. Mark off end of "pie" wedge. Draw a number of personal choice - one that has some special meaning - large in triangle - have numbers touch sides. Draw some smaller numbers. Add some geometric shapes - and break up the space with straight or wavy lines. (I used my son's birthday in my sample - 11 and 17). When satisfied - go over lines with Ebony pencil.
4. Transfer design to other side by folding to the inside and rubbing over back side with handle of scissors. Go over lines with Ebony pencil
5. Fold 12" square white drawing paper in half - crease. Fold in half the other direction and crease (make sure students get the folds as perfect as possible).
6. Transfer design to first quarter by rubbing on back - go over line with Ebony pencil.
7. Fold to transfer design to the next quarter - go over lines with Ebony pencil.
8. Fold to transfer design to other half . Outline entire design with Sharpie marker. Erase any stray pencil smudges with art gum erasers.
9. Color with markers - use over lapping strokes in one direction - limit colors (use a color plan). Color same shape with same color all the way around for perfect radial balance.

Note: Students could also use the window transfer method described above.

Submitted by Michael Gerrish  UNIT: Radial Design Lesson Marker Radial Name Design Grade: upper elementary - middle school This lesson is done the same way as above.  Students design name on one pie wedge (outline pie wedge on folded 6" square) - create a mirror image on the other side. Then trace all around the circle. Color with colored pencils, crayons, or markers. Students could use compass and protractor to mark off 12" (30 cm) circle.

Motivation:

Rose windows and drawings of Leonardo da Vinci.

Demonstrate steps - reflection - transferring design - colored pencil techniques

Note: Seventh graders did this project at the end of the year while they were waiting for ceramics to get bone dry and fired. No digital images are available.

Objectives:

Same as above - close observation of nature -drawing from life - math skills.

Materials:

6" (15 cm) square tracing paper, pencils, white crayons, Compass, 12" (30 cm) square black paper rulers, paper clips, Crayola Metallic Colored Pencils, assorted pearl and metallic Gel Pens. 16" (41 cm) construction paper for frames (colors to coordinate with metallic pencils), Scissors. Insects from science department, life plants, live fish. Shells and other natural objects.

Procedures:

1. Fold 6" square tracing paper diagonally. Mark off end of pie wedge (radius of 6"). Draw insect (top view - centered) - fish - and or plants on one side of triangle. Make design run off edges. When satisfied - turn tracing paper over and trace lines on other side.
2. Color heavily with white crayon on back side of tracing paper.
3. Mark center of 12" (30 cm) square black paper - measure in from side 6" in two places and draw a straight line with ruler. Measure down from top 6" (15 cm) in two places and draw a straight line perpendicular to the first line.
4. Make circle using compass (12" (30 cm)circle templates could be supplied)
5. Paper clip tracing paper to one quarter matching up outside edges and lines in center. Trace over lines of design. 
6. Rotate one quarter turn (keeping same shapes toward center) and paper clip to the next quarter - trace over lines. Continue moving around until the entire circle has been transferred.
7. Color with metallic pencils. Vary pressure. Color more heavily at lines and vary pressure towards center of shapes. Create different values with the pencil. Some shapes may be left black for contrast.
8. Accent with gel markers in small shapes
9. Use compass to draw circle on 16" (41 cm) construction paper (or trace template). Cut out and mount radial design to frame with masking tape.
10. Critique work.

Evaluation:

1. Did students show close observation of nature in drawing their composition for the radial design?
2. Did students successfully compose a radial design by transferring their image around the circle?
3. Did students show color planning in choice of colors for composition?
4. Did students show various values by changing pressure of pencil. Did they show gradations?
5. Did students exhibit craftsmanship in cutting their frame and mounting their design?

Additional Notes on Drawing from Observation:

From Mike Sacco: I am going to accept their drawings (at their skill level) but I have tried to include simpler objects such as sand dollars, some simple seashells and silk flowers for those who don't have the confidence in their drawing abilities. I will have them do a contour drawing of two objects in their sketchbook to become familiar with the objects first before designing their pie slice.

Submitted by Sue Stevens Rose Windows - Pen and ink design Grade level: middle school and up Present radial design/radial design to students. Show examples of Rose windows Students all begin with a piece of 8.5 x 11" (21.5 x 28 cm) photocopy/computer paper Students were instructed to draw one line, 8 inches long (close to the edge of the page) (8 inches will produce a 16 inch finished circle). Using a protractor, students then measured 30 degrees (exactly - very important that it is exact!) 5.  Students were then to draw a second line 8 inches long to complete the 30 degree wedge.

6.  Once the wedge was drawn, students planned out their design in pencil. Students had a few criteria:  there needed to be at least 3 continuous elements (things that would line up and continue all the way around), 2 stand-alone items (things that would not line up), a variety of line types (thin, thick, etc), and a balance between positive and negative (black and white) 7.  Students were instructed on how to line things up ie: measure 3 inches up on one side of the wedge, then 3 inches up on the other side of the wedge.  A line drawn between those two points will line up and go all the way around the circle when the wedges are put together. 8.  Students then completed their wedge using black fine pen and a black sharpie marker. Completed wedge was turned in. Sue took all the wedges to the photocopier and reproduced them 12 times each. (note: to save paper, several could be put on one page - then cut a part later on the paper cutter). 9. Students then carefully cut out all the wedges, and glued them onto a 18 x 24 inch (46 x 61 cm) sheet of white paper.10. Finished rose window/mandala could be cut out and mounted to contrasting paper or poster board.

Alternate Ideas - Hubcap Designs

Another project the might interest you would be hub cap designs in metallic pencils - on black paper. Cut out circle and mount on "tire" mat. Try a cardboard relief hub cap - glue cardboard to pizza pie plate. Cover with heavy duty aluminum foil and antique with India ink. Mount this to a black cardboard "tire"

Some resources:

Hubcap patterns fall into two distinct patterns. "Static" hubcap designs are symmetric about a point and have linear axes of symmetry. "Dynamic" hubcap designs have point symmetry but not line symmetry. (Their designs appear to lean to one side!)

And some math words to "borrow" in writing your own plan:
http://www.michigan.gov/scope

Show the kids the images on HubCap Creatures. See the corresponding article.

Cool hub caps images

http://hubcaphouse.com/cgi-local/shop.pl/page=specialties.htm
http://www.lordofthelooks.com/event_1/members/f.henkel/hub_cap.jpg
http://67fordtruck.com/hubcaps.jpg
Web Urbanist
Auto Blog
Jalopnik
Bliss Tree
Empty Kingdom

Alternate Idea:

Rose Windows on Recycled CD's
School Arts article by Stephanie Spruce Leonard

Might be neat to tie this in with a lesson on Architecture. Students make a cardboard relief façade to display their rose window. Use scrap mat board and/or foam core board.  If using corrugated cardboard for façade, try covering with heavy duty foil - then texture with a dull pencil.

Lesson Extension: Radial Design in the Environment - Manhole Covers

Manhole Sewer Art
http://www.manhole.ca/

To most of us a manhole is just something we drive over, a circular doorway into an underground world we'd rather not visit.  But to some city planners and urban artists, manholes are seen as iron  canvases on which to place seals, city logos, and original artwork.

This site is a gallery of 'Sewer Art', containing images of diverse manholes from every continent on the planet.  Check out the various photos, read a brief history of modern sewage systems, and more

Lesson idea: Cardboard Relief Sculpture Manhole Cover

Students create a cardboard relief manhole design (You could use pizza rounds and scrap cardboard) - cover with heavy aluminum foil - then antique with India ink. Glue piece of black poster board or construction paper on back side of manhole cover to cover where foil has been folded to back side. Manhole relief art could raise up to reveal a surreal drawing of what is beyond the cover. Hinge the cover to drawing with strip of poster board. If anyone does this lesson - send an image of student art to The Incredible Art Department.