Groovy Geometry + Making Mandalas = Math MASTERPIECES !
In this lesson, students will learn the history of a MANDALA, a circular shape containing designs made of geometric shapes, shapes found in nature, parallel and perpendicular lines, and various designs.
In ancient cultures, looking closely at mandalas and/or creating them was used as a way to relax, settle one's mind, meditate, and feel calm...and this is STILL the case. No wonder some of the world's most beautiful cathedrals have huge stained glass windows picturing gigantic mandalas, as people come and sit quietly for prayer or meditation time before services. Today, it is no different - many people who enjoy artwork and/or doodling can warm up their brains, calm down their stress, and release tension by focusing for a while on the drawing of a simple mandala pattern.
The use of mandalas originated hundreds of years ago in India and surrounding middle eastern regions. These cultures felt that a mandala represented the cosmos or UNIVERSE ,but in common usage nowadays, the mandala has become a generic term for any circular [ mandala means "circle" in the Sanskrit language] design that utilizes geometric and assorted shapes, lines, and designs in an organized, symmetrical, and extremely intricate patterns. Later on, Tibetan monks began to blend in square shapes to contain the mandala pattern [as is shown in an attached video].
We will delve into creative artwork possibilities by reviewing geometric figures, line patterns, and commonly used shapes. Enjoy the relaxation and absorption into quiet creative time as you draw your own mandala!
Essential Question
Students will learn to draw TWO TYPES of mandalas...1) "freestyle", which begins at the center, and by drawing shapes free-handed, measuring only by estimating, it grows outward symmetrically, becoming larger and more elaborate and 2) a SYMMETRICAL mandala, which will be "framed" first by measuring CONCENTRIC CIRCLES, utilizing measurement tools, & then filling in these circles with geometric shapes, parallel & perpendicular lines, designs, and the concept of symmetry as they enjoy drawing and possibly coloring a mandala. Math is combined with artwork, and also with the history of a concept that originated in ancient India and the Middle East.
Grade(s):
- 6
Subject(s):
Recommended Technology:
1. Student Chromebook...for reading the lesson & watching attached videos
Other Instructional Materials or Notes:
The student will need :
-a flat surface, desk or table, on which to place a drawing pad when mandala art designing begins.
-a drawing pad with unlined paper- can range from 6-8" square and up
-a thin-tipped black marker, or medium tipped black marker
-colored markers, if desired
-MATH TOOLS - ruler, protractor, compass (if possible), pencil, eraser
TIME ALLOWANCE ( suggested)
-The student will need at least 10 -15 minutes to complete the FREE-HAND MANDALA
-The student will need at least 30 - 45 minutes or more to complete the "MATH-MEASURED MANTRA."
[The relaxing aspect of either mantra is allowing enough time to be absorbed into the activity with NO RUSHING...enjoy!!]
Lesson Progression
1. Read the LESSON OVERVIEW & ESSENTIAL QUESTION. "Mandala" is a Sanskrit word meaning "circle". [SANSKRIT is an ancient Middle Eastern language.] In ancient times, the sun and moon appeared in the sky as CIRCLES. Stars looked like circular "dots". The circle shape came to have meaning representing concepts such as THE UNIVERSE, and things that are NEVER ENDING/ ETERNAL. Therefore, a MANDALA held special significance for people in the Middle Eastern & Indian cultures.
Find these MIDDLE EASTERN countries on a world map: Egypt, Saudi Arabia, Iran, Iraq, Israel, Jordan, Kuwait, Lebanon, Syria, Turkey, Palestine.
NOW FIND: India, Tibet, France, Germany, England. The middle eastern countries seem very close together...but for the art of mandalas to spread to all the way to the EUROPEAN COUNTRIES of France, Germany, England, and others, took many centuries.
To draw mandalas was like having a quiet meditative time... letting the MIND RELAX without worry, akin to silent prayer, or even as we say now, "just chill out." People in those ancient times( just as we do now) appreciated those precious, QUIET moments of enjoyment from drawing a mandala, without worrying about the outcome. It is about living in the PRESENT MOMENT, as you enjoy drawing the lines and designs.
2. There are many shapes & terms used in drawing mandalas that are the same ones we have studied in math and geometry. Most times MANDALAS are SYMMETRICAL, drawn with CONGRUENT CIRCLES that have a CIRCUMFERENCE, RADIUS, & DIAMETER ...sometimes there are TRIANGLES, QUADRILATERALS, PARALLEL LINES, & PERPENDICULAR LINES used in the designs.
3. In most of the attached videos, you will see circular mandalas. However, the group of Tibetan Monks that are building a SAND MANDALA have the circular mandala locked within an arrangement of quadrilaterals and/ or triangles. As the artist, it is up to you to decide. However, the mandala needs SYMMETRY, in any event.
4. Hopefully, you have your materials collected. Watch the attached videos.
a.) "free-hand" style mandala, which begins at the center point, and grows outward symmetrically. [If you have a pad and marker, go ahead and try this one first! The video that guides you is #
b) "perfectly symmetrical" mandala, which begins with concentric circles drawn with a protractor and ruler (& compass is you have one), and then these circles become the GRID within which you draw your designs
c) TIBETAN MONKS building a sand mandala from ground-up colored stones, which incorporates more of the quadrilateral and triangular shapes.
d) "PUFFERFISH mantra", which is just a fascinating example of how a creature in nature can create a design SO SIMILAR to a mantra as a means of making a "hatching nursery" for its baby fish...pretty cool and amazing!
5. On a sheet of notebook paper, define these terms: [They'll come in handy for following the assignment ahead:]
*circumference, *diameter,* radius, *concentric circles,*symmetry, *quadrilaterals, *triangles, *parallel lines, *perpendicular lines, *the word "mandala" =? [what does it mean in Sanskrit?]
6. DRAWING: Begin by creating a "shape sheet" of all the shapes you can imagine. See the attached example. Hopefully, you can use this as a REFERENCE if you feel like you need a new idea.
7. You're ready to draw mandalas!
ASSIGNMENT:
-Draw 2 "freestyle" mandalas that begin at the middle and move outward, both at least 5" in diameter. These will be draw WITHOUT pencil markings (freehanding with black felt-tip pens). Strive for variety in shapes and markings!
-Draw 2 "perfectly symmetrical" mandalas, a 5" diameter mandala, and a larger one, your choice of diameter.
DRAWING TIPS:
-Do not rush. In the videos, the action is sped up. Slowly and quietly is the key to a good FEELING while drawing.
-On your "perfectly symmetrical" mandalas, challenge yourself to use some squares, triangles, trapezoids, and other geometric shapes that you can combine and decorate with parallel lines, perpendicular lines, and other geometric oddities! Remember how the Monks included the squares intersecting with the mandala circle? That may be too complex...but maybe not!
How to draw a Mandala/Basic Shapes/Mandala Art
This is a tutorial on drawing a mandala using a compass to create a "starting grid" of concentric circles, and then starting at the center and FILLING IN DESIGNS of your choice and imagination.
View ResourceTibetan Buddhist Sand Mandala
This video shows a group of monks from Tibet who use mandala building as a spiritual tool to demonstrate the "impermanence" of things in the material world. After grinding colored stones, the monks use straws & small sticks to tap and pour the sand into intricate designs. Notice how they have incorporated other geometric shapes WITH the mandala circle.
View ResourceA Pufferfish's Masterpiece
Just for fun and inspiration! Lovely and complex design circles on the sea floor near Japan were a mystery, until divers observed the white-spotted Pufferfish creating these designs. It seems like fish even enjoy creating "mandalas", especially as a nursery to hold the eggs of new little pufferfish.
View ResourceWikipedia "stained glass"
Stained glass windows in European cathedrals demonstrate how an art form used to travel across CONTINENTS, even though it took decades, & perhaps centuries! Originated in Asia, the mandala design made its way across a continent to be an inspiration for worship in cathedrals across Europe and North America. SCROLL DOWN THE PAGE to see an array of incredible examples of mandalas.
View ResourceCreating Mandalas Step by Step
This is the more structured design, which is started by
1. Drawing concentric circles, one inside the other.
2. If you don't have a compass, make a DOT in the middle of your paper, and then trace a small round object around the dot; then a LARGER round object , & then a SUPER LARGE object for the outside circle.
3. Follow by filling in with as many designs as possible.
Episode 2: How to draw perfectly symmetrical mandalas for beginners
This is a great site, as the artist really describes the math that goes into figuring out the beginning math that sets up this mandala into 8 equal sections in which to add shapes, designs, and colors. She uses a compass to draw the concentric circles, but if you don't have one, try to trace circular objects of differing sizes.
View ResourceDrawing a Mandala, by Elsa Rhae
Elsa Rhae shows how to begin and keep a Mandala symmetrical, even if it's drawn by hand.
View ResourceAlhambra Nights Art Exhibit [Mandalas & Environmental Design] /3:20
Anila Quayom Agha is an Islamic artist. She was inspired by a visit to the ALHAMBRA, a huge, ancient Moorish palace in Spain. After her visit, she wanted to connect traditional Islamic art with architecture....AND ALSO blend in modern-day technology in connect with audiences in the U.S. As we meet her, she arrives on the scene to the BLINK winter festival in Cincinnati, Ohio, and begins her set-up. Taking an empty room, she constructs a meditatively restful and fascinating environment. Her tools? Lighting, shadows, music, cushions, and the metal mandalas she has designed and constructed to cast designs upon every wall and floor surface in the area. Watch, enjoy, relax and BE INSPIRED!
View ResourceMandala Art for Beginners on Black Paper with White Paper
Whether you use white ink on black paper, or black in on white paper, this mandala drawing emanates from the center and is a good example of the basics. The artist DOES START with a compass to draw concentric circles. ]
View ResourceStandards
Assessments
1. The student must complete 2 - 5" diameter FREE-STYLE mandalas drawn w/ black felt pen, beginning from the center point, drawing out.
2. The student must also complete 1 - 8" or larger mandala, which will be in the PERFECTLY SYMMETRICAL STYLE, using a protractor, ruler, several sizes circular shapes [or compass if available] to make CONCENTRIC CIRCLES within the circle's CIRCUMFERENCE. All designs within the mantra must be drawn with black felt pen.....pencil marks for the circle grids should be erased after felt pen shapes are DRY.
3. The student should have completed the definition sheet of MATH TERMS [#5 in lesson description] and also the "shape sheet" for reference/future drawings.