Crossing Borders/Breaking Boundaries
The Arts of India, 1556-1658
June 23 - July 1, 2008
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Unit of Study:            Mathematics linked to Art

Lesson Title:              The Use of Symmetry in the Mughal Empire

Discipline:                  Math / Art

Grade Level:              5th Grade

Author:                      Claudia Wiseman

County:                      Baltimore City, MD

Time Period:              Two 45-minute class periods



After being introduced to the ideal/meaning of symmetry the students will do a “hands on” activity using symmetry and their understanding of the art of the Mughal Empire to create their own symmetrically designed garden.


Students will be introduced to the Mughal Empire by observing the art of that empire. They will use the resources listed to observe the artwork of that era. They participate in several discussions reflecting on what the Mughal people valued and believed and how that is reflected in their artwork. They will be guided through several sessions of examining the artwork of the era for clues to what the Mughals valued, with the emphasis on flowers and nature. They will also see how the Mughals used symmetry in their gardens to reflect both a love of nature and a love of order showing that the Mughals were a very educated people eager to learn from other cultures.

Students should have an understanding of the term “symmetry” and “garden”.

Students should be able to locate the country of India on a map.


Grid paper, ruler, colored pencils/crayons/markers, pencil, list of required items to be inserted in finished product, examples of Mughal art obtained from various resources, world map, map of India, samples/pictures of Mughal gardens-symmetrical gardens


A History of India, by Buton Stein
What Your Second Grader Needs to Know, by E.D. Hirsch
Muraqqa' Imprial Mughal, Albums from The Chester Beatty Library, Website for virtual tour of Taj Mahal
Taj Mahal, Wikipedia

Standards/Learner Outcomes:

Fine Arts Standards:

Standard 1.0 Perceiving and Responding: Aesthetic Education-Students will demonstrate the ability to perceive, interpret, and respond to ideas, experiences, and the environment through visual art.

Standard 2.0 Historical, Cultural, and Social Context: Students will demonstrate an understanding of visual art as an essential aspect of history and human experience.

Standard 3.0 Creative Expression and Production: Students will demonstrate the ability to organize knowledge and ideas for expression in the production of art.

Standard 4.0 Aesthetics and Criticism: Students will demonstrate the ability to identify, analyze, and apply criteria for making visual aesthetic judgments.

Math Standards:

Standard 1.0 Knowledge of Algebra, Patterns, and Functions
Students will algebraically represent, model, analyze, or solve mathematical or real-world problems involving patterns or functional relationships.

Standard 3.0 Knowledge of Measurement
Students will identify attributes, units, or systems of measurements or apply a variety of techniques, formulas, tools or technology for determining measurements.

Standard 7.0 Process of Mathematics
Students demonstrate the processes of mathematics by making connections and applying reasoning to solve problems and to communicate their findings.


Fine Arts Objectives:

Identify and describe observed form
Use of elements of art and principles of design to organize personally meaningful compositions
Describe how artists use the elements of art and principles of design to organize visual compositions that convey thoughts and feelings
Determine ways in which works of art express ideas about one’s self, other people, places, and events
Create artworks that explore the uses of the elements of art and selected principles of design, such as pattern, repetition, contrast, balance, variety, and unity/harmony to express personal meaning
Identify and describe the elements of art and selected principles of design, such as pattern, repetition, contrast, balance, variety, and unity in artworks
Establish criteria for judging artworks by interpreting exemplary models
Identify and apply criteria to evaluate personally created artworks and the artworks of others

Content/Math Objectives:

Numeric and Graphic Representations of Relationships
Locate points in a coordinate grid.  
Using Measurement Tools
Measure in customary and metric units
Select and use appropriate tools and units
Applications in Measurement
Estimate and apply measurement formulas
Determine perimeter
Problem Solving
Apply a variety of concepts, processes, and skills to solve problems
Identify the question in the problem
Decide if enough information is present to solve the problem
Make a plan to solve a problem
Apply a strategy, i.e., draw a picture, guess and check, finding a pattern, writing an equation
Select a strategy, i.e., draw a picture, guess and check, finding a pattern, writing an equation
Identify alternative ways to solve a problem
Show that a problem might have multiple solutions or no solution
Extend the solution of a problem to a new problem situation



  • Symmetrical
  • Taj Mahal
  • Inlaid
  • Artisans
  • Line
  • Shape
  • Color
  • Texture
  • Repetition
  • Balance
  • Unity
  • Pattern
  • Mausoleum
  • Measurement
  • Graph
  • Perimeter
  • Line of symmetry
  • Symmetric
  • Match up
  • Intersecting lines
  • Trefoil
  • Purs
  • Paradise


Teacher will present a Power Point on the art of the Mughal Empire featuring gardens and the gardens of the Taj Mahal.

Teacher will present a brief overview of the Mughal Empire and its influence in the development of India.

Teacher will help students locate India on a map and globe.

Scope and Sequence:

Teacher Directed:

Teacher leads discussion on the Garden of the Taj Mahal

The Persian style garden

The lush green garden expands from the main gateway to the plinth, over which stands the tomb. The garden in essence is based on symmetry and geometrical measurements.
The Persian style garden has a close link with paradise, since Quran describes paradise as a beautiful garden.

Water garden

Through the centre of the garden runs the two marble canals with fountains and lined with cypress trees (symbolizing death).
This divides the garden into four equal squares (Islam considers four to be a holy number); evoking the image of Islamic paradise that has rivers of water, milk, wine and honey flow. The stone paved pathways further subdivide each flower bed into 4, making total of 16 flower beds.
The mausoleum, unlike most mughal mausoleums, stands majestically at the north end just above the river and not at the central location. At the centre of the garden, in the mid of the tomb and the gateway, is a raised marble lotus shaped tank with a cusped and trefoil border.
The tank has been arranged to provide a clear view of Taj in its water from any point in the garden. The view looks amazing with the reflection of Taj amidst the green cyprus trees.

Water devices and irrigation mechanism

Water in the canals was drawn from the river using purs, a system of drawing water manually from river using bucket and ropes. For irrigation the water from the overflowing canals was used.
The north-south canals had its water inlet through fountains and east-west canal had its water inlet through an interconnection with north-south canal.

Review of symmetry: A figure has symmetry if it can be folded along a line so that both parts match exactly.

Guided Practice:

Activity One

Review the meaning of a line of symmetry.
Have students cut out a scalene triangle, a kite, a rhombus, and a regular pentagon.
Remind students that a line of symmetry may go in any direction. There also may be no lines of symmetry
Ask students to find all the lines of symmetry for each shape by folding.
How many lines of symmetry does the scalene triangle have? The kite? The rhombus?

Activity Two

Symmetry is an important feature of art. Make a drawing with as many lines of symmetry as you can. Trade with your partner. Then write a description of all the symmetry in your partner’s drawing.

Independent Practice:

For homework the students will complete their symmetrical garden drawing by creating a garden that is 8X10 inches in size divided into two to four separate sections that are symmetrical in nature. Students will use graph paper to complete the project.  Each will have a selection of plants, decorations, and buildings appropriate to the setting of a garden to choose from. Students will use the mathematic principles of geometry and measurement aligned with those of art to create their garden. Their design will give examples of repetition using the elements of design such as color, shape, line, and texture. Each section will have an additional section reflecting perfect symmetry with it. Students will name their garden and use their design to represent the principles of the name they give it. Examples: Peace Garden, Quiet Garden, Water Garden, Tranquility Garden, etc.


The teacher will observe the students during class discussions and while constructing their own garden.
Students will exchange their gardens with a partner to measure the placement of items in the garden and evaluate their partner’s garden to see if it is symmetrical.  
Using the rubric below, they will grade their partner's paper/garden.


4-point answer
The answer is correct; shows complete understanding of symmetry.
Each section is an exact copy/representation of the other section/s.
Students will show 4 examples or repetition such as color, shape, line, texture to illustrate design principles

3-point answer
The answer is partially correct; shows some understanding of symmetry. Most of the areas are mirror images of the other. Students will show two of the design principles, color, shape, line, texture.

2-point answer
The answer is partially correct; shows some understanding of symmetry. A few of the areas are mirror images of the others. Students gave no examples of design principles such as color, shape, line, texture.


Students will reflect on the key concepts of

Art must be appreciated.
Art is a reflection of its creator.
Art reflects the complex nature of a given culture.
The students will develop an understanding of art through a historical perspective.
Students will integrate the arts into increasing their mathematic skills.
Students will understand that some figures have a line or lines of symmetry which divide the figure into congruent parts.
Students will identify and make symmetrical figures and draw a line or lines of symmetry.

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Sponsored by
the Center for Renaissance & Baroque Studies
and the Maryland State Department of Education