EDUS 516 Unit Plan
By: Stan Kandebo and Crystal Mentz
I.
Subject Areas: Spanish Level I&II and Algebra I Grade level: 8
Unit Title: Moorish Influence On Spanish Culture and European Mathematics
II.
Estimated Time: The unit will take place over the course of one week. Three lessons will be
conducted in Spanish Level I&II (Virtual Field Trip, Spanish foods, Spanish dance), two in
Algebra Level I (Islamic Arithmetic-Number Concepts and Islamic Arithmetic- Geometry).
III.
Student Population: 25 students: 15 girls and 10 boys. No IEP’s
Stage 1 – Desired Results
IV. Standards
Lesson 1: VIRUAL FIELD TRIP TO BAR FERDINAND
PA State Standard
Mathematics (2.1) Numbers, Number Systems and Number Relationships
Mathematics (2.4) Mathematical Reasoning and Connections
Mathematics (2.8) Algebra and Functions
Mathematics (2.9) Geometry
Spanish (1) Communication: Communicate in Languages Other than English
Spanish (2) Connections: Connect with Other Disciplines and Acquire Information
Spanish (3) Comparisons: Develop Insight into the Nature of Language and Culture
Spanish (4) Communities: Participate in Multilingual Communities at Home and Around the World
Lesson 2: SPANISH FOOD – The Imperative
PA State Standard
Communication: Communicate in Languages Other than English
1.1 Students engage in conversations, provide and obtain information, express feelings and
emotions, and exchange opinions.
1.2 Students understand and interpret written and spoken language on a variety of topics
1.3 Students present information, concepts, and ideas to an audience of listeners or readers on a
variety of topics.
Connections: Connect with Other Disciplines and Acquire Information
2.1 Students reinforce further their knowledge of other disciplines through the foreign language.
2.2 Students acquire information and recognize distinctive viewpoints that are only available
through the foreign language and its cultures.
Comparisons: Develop Insight into the Nature of Language and Culture
3.1 Students demonstrate understanding of the nature of language through comparisons of
language studied and their own.
3.2 Students demonstrate understanding of the concept of culture through comparisons of the
cultures studied and their own.
Communities: Participate in Multilingual Communities at Home and Around the World
4.1 Students use the language both within and beyond the school setting.
4.2 Students show evidence of becoming life-long learners by using the language for personal
enjoyment and enrichment.
Lesson 3: SPANISH DANCE – Flamenco
PA State Standard
Communication: Communicate in Languages Other than English
1.1 Students engage in conversations, provide and obtain information, express feelings and
emotions, and exchange opinions.
1.2 Students understand and interpret written and spoken language on a variety of topics
1.3 Students present information, concepts, and ideas to an audience of listeners or readers on a
variety of topics.
Connections: Connect with Other Disciplines and Acquire Information
2.1 Students reinforce further their knowledge of other disciplines through the foreign language.
2.2 Students acquire information and recognize distinctive viewpoints that are only available
through the foreign language and its cultures.
Comparisons: Develop Insight into the Nature of Language and Culture
3.1 Students demonstrate understanding of the nature of language through comparisons of
language studied and their own.
3.2 Students demonstrate understanding of the concept of culture through comparisons of the
cultures studied and their own.
Communities: Participate in Multilingual Communities at Home and Around the World
4.1 Students use the language both within and beyond the school setting.
4.2 Students show evidence of becoming life-long learners by using the language for personal
enjoyment and enrichment.
Lesson 4: ISLAMIC MATHEMATICS – Number Concepts
PA State Standard
2.1 Numbers, Number Systems, and Number Relationships
2.1.8. A. Represent and use numbers in equivalent forms (e.g., integers, fractions, decimals,
percents, exponents, scientific notation, square roots).
2.1.8. E. Simplify and expand algebraic expressions using exponential forms.
2.1.8. F. Use the number line model to demonstrate integers and their applications.
2.1.8. G. Use the inverse relationships between addition, subtraction, multiplication, division,
exponentiation and root extraction to determine unknown quantities in equations.
2.2 Computation and Estimation
2.2.8. A. Complete calculations by applying the order of operations.
2.2.8. B. Add, subtract, multiply and divide different kinds and forms of rational numbers
including integers, decimal fractions, percents and proper and improper fractions.
2.2.8. E. Determine the appropriateness of overestimating or underestimating in computation.
2.2.8. F. Identify the difference between exact value and approximation and determine which is
appropriate for a given situation.
2.3 Measurement and Estimation
2.3.8. A. Develop formulas and procedures for determining measurements (e.g., area, volume,
distance).
2.4 Mathematical reasoning and connections
2.4.8. D. Construct, use and explain algorithmic procedures for computing and estimating with
whole numbers, fractions, decimals and integers.
2.8 Algebra and Functions
2.8.8. A. Apply simple algebraic patterns to basic number theory and to spatial relations.
2.8.8. C. Create and interpret expressions, equations or inequalities that model problem situations.
2.8.8. D. Use concrete objects to model algebraic concepts.
Lesson 5: ISLAMIC MATHEMATICS – Geometry
PA Mathematics Standard (2.9) Geometry
2.9. Geometry
A. Construct geometric figures using dynamic geometry tools.
E. Solve problems involving inscribed and circumscribed polygons.
H. Construct a geometric figure and its image using various transformations.
J. Analyze figures in terms of the kinds of symmetries they have.
K. Analyze objects to determine whether they illustrate tessellations, symmetry, congruence,
similarity and scale.
V. Understandings:
1.) Identify the “big ideas” of the unit.
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The West’s contact with Islam goes far beyond the Medieval Crusades and current headlines. The
Islamic peoples of the world have, for centuries, had a direct and profound influence on western
European thought and life, with Spain providing the early link between the two cultures.
2.) Identify specific understandings about the “big ideas.”
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Islam came to Spain through the African Moors (adopted from
http://www.spain-barcelona.com)
-In 711 the Muslim northwestern Africans, known as the Moors, asserted their claim to Spain and
through war conquered most of the Iberian peninsula.
-The Moors remained in Spain until the small, independent Christian kingdoms of Spain united
under one ruler, fought the Moors to a standstill, then turned the tide against them. By 1276 the
only Moorish kingdom left in Spain was the southern state of Granada.
-In 1492, the same year Columbus discovered America, the Christian armies of King Ferdinand
and Queen Isabella finally overcame the Moors and put an end to their authority in Spain.
Moorish influence is visible, on a daily basis, in modern Spain. (adopted from
http://www.medieval-life.net/medieval_history_spain.htm)
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- The Moors' influence on Spain during the Middle Ages is still very evident. More than 4,000
words of Arabic origin are used in modern Spanish. Moorish architecture can be found
throughout Spain, with its slender columns, horseshoe arches, cupolas, and airy, colorful
buildings.
Spanish food has been heavily influenced by the presence of the Moors. (adopted from
http://www.foodtimeline.org/foodfaq6.html)
-The Moors obtained rice, sugarcane, and eggplants from India through the Persians who
already traded with India and China. They brought honeydew melons from Egypt,
watermelons from Africa and figs from Constantinople. They spread Near Eastern citrus
fruits, peaches and apricots, carob and quinces, almonds and pistachios as far as the
Atlantic coast. Later, dates arrived from Iraq and coffee from Yemen.
-Herbs and spices also played an important role in the cuisine of al-Andalus. Particularly
popular were basil, cumin, coriander, saffron, aniseed, mint, ginger and jasmine, as well
as almonds, pistachios, pine nuts, sesame, tamarind, and cinnamon.
-As a source of protein the Arabs favored mutton and lamb as well as fish, and they also
brought suitable methods of preparing these with them. They were inspired by the Persian
cooks and also Egyptian and Turkistan customs. They combined meat and fish dishes
with fruit, spices, and herbs, and invented dishes such as tuna with sour cherries, dried
cod with orange, mutton with apricots, or lamb with mint or cumin sauce. The Arabs also
introduced the rice pudding with honey that is still highly popular in Spain today, as well
as countless different types of almond pastries and other cookies, quince jam, and dates
stuffed with nuts and almonds.
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Spanish Dance reflects the musical trends and rhythms of the Moors. (adopted from
http://www.andalucia.com/flamenco/history.htm)
-Several hundred years of Moorish domination also left a strong and lasting impact on
southern Spanish musical forms. Such evidence can be seen today in the traditional
Spanish dance of Flamenco. El baile flamenco is known for its emotional intensity, proud
carriage, expressive use of the arms and rhythmic stamping of the feet. The frilly,
voluminous spotted dresses are derived from a style of dress worn for the annual Feria in
Seville.
- In traditional flamenco, young people are not considered to have the emotional maturity
to adequately convey the "duende" (soul) of the genre. Therefore unlike other dance
forms, where dancers turn professional early to take advantage of youth and strength,
many flamenco dancers do not hit their peak in their thirties and will continue to perform
into their fifties and beyond.
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Muslim learning helped civilize Europe (adopted from
http://www.muslimheritage.com/topics/default.cfm?ArticleID=952)
-With Europe engulfed in the dark ages, the Moslem Moors had a far more advanced culture than
was known by most of the people of feudal Europe. Under the Moorish occupation, Spain became
more civilized that most European countries.
-Thanks to the Moors, the ideas and learning that flourished in the Islamic world of the middleeast made their way west into mainstream European culture. Mathematics, science, medicine, art,
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architecture and design grew and blossomed, and people from every corner of Europe journeyed
to Moorish Spain to study and learn.
Not all Muslim knowledge was self-generated (adopted from http://www.islamicspain.tv/Artsand-Science/The-Culture-of-Al-Andalus/Mathematics.htm)
-Some of the new knowledge in math and science came from India, a region with which the
Muslim middle-easterners had direct contact. Other ideas were directly linked to the classical
Greeks.
-Much of Western Europe’s knowledge of ancient Greece can be traced directly to the Muslims;
middle-eastern libraries were able to preserve the texts that European barbarians destroyed when
they sacked Rome.
Muslim learning revolutionized the European concept of math. (adopted from
http://www.engr.sjsu.edu/pabacker/history/islam.htm)
-Islamic learning did not influence the way Europeans viewed and utilized mathematics, it
revolutionized it.
-Through the Moors of Spain, Arabic numbers, the same number system we use today,
supplanted the cumbersome system of Roman numerals invented by the Romans. The Codex
Vigilanus, written in Spain in 976, is the oldest European manuscript containing Arabic numbers.
-The Moors also were responsible for introducing Europeans to such basic concepts as the base
ten system; the zero, which actually appears to have been an idea the Muslims imported from
India; and decimal fractions. Around 952 Abu'l-Hasan-al-Uqlidisi wrote the Book of the parts of
Indian Arithmetic which contains an explanation and application of decimal fractions.
-Not content with transmitting the basic architecture of math to Europe, the Muslims also
invented and exported a mathematical tool called algebra. Persian mathematician and astronomer
Muhammad Ibn Musa al-Khwarizmi (780-850 CE) is known as “the father of algebra,” from the
title of his work, Hisab Al-Jabr wal Muqabalah, The Book of Calculations, Restoration and
Reduction.
-Al-Khwarizmi’s algebra introduced such concepts as moving terms from one side of an equation
to the other to find the value of an unknown. He also described how to find the square root of a
number, and was the first to demonstrate the concept of exponents for unknown variables. He
demonstrated the use of equations, algebraic multiplication and division, and measuring area.
- In 1202 Leonardo of Pisa (also known as Fibonacci) published his Liber Abaci, a book of
arithmetic and algebraic information. Al-Khwârizmî's book was a major influence on Fibonacci.
-The influence of the Moors is felt every time we use numbers in our daily lives. It is there when
we make purchases and pay for them, when we look at a clock that expresses time in a numeric
format, and when we drive at a specific numeric speed. Even the type of clothing we wear on any
given day can be traced to Moorish influences because dress, to some extent, is a response to the
numerically-expressed predicted temperature.
Geometry has been strongly influenced by the Muslims (adopted from
http://www.metmuseum.org/explore/publications/islamic_geometric.asp)
-Given Islam’s early tendency to view renderings of living things as blasphemous, the Muslims,
including the Moors, adopted complex shapes and patterns as the basis for enhancing everyday
objects. Such complex patterns simply could not be developed and replicated with a fundamental
knowledge of geometry.
-Many geometrically-based patterns and adornments are executed with the simplest of tools such
as a straightedge, compass and basic system of measurement.
-Throughout Spain, carpets, scarves, tapestries and paintings are decorated with complex and
colorful geometric patterns and shapes. The walls, floors and ceilings of public and private
Spanish buildings likewise reflect this preference for geometric patterns. In many cases, even
shapes and sizes of individual buildings themselves were, and are, designed with strict geometric
proportions in mind.
-Muslim scholars helped lay the groundwork for European work in geometry by making available
to Christendom the long-lost works of Euclid and other classical Greek scholars.
VI. Essential Questions:
What questions will foster inquiry, understanding and transfer of learning?
1. What mathematical concepts were transferred from Moorish Spain to the rest of Europe?
2. Is it easier to use Roman numerals to add, subtract, multiply and divide numbers or Arabic numbers?
Why?
3. It is 1300 AD. You are the son of a wealthy western European nobleman. Do you travel to Moorish
Spain to receive an education, or do you seek your education in Christian Western Europe? Explain your
answer.
4. What modern Spanish recipes reflect the influence of the Moors?
5. What elements of Flamenco can be attributed to the Moors?
VII. Attitudes and Values:
What positive attitudes and values will students develop?
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Appreciation of the history of Spain.
Appreciation of Spanish culture and traditions.
Appreciation of the history of Islamic peoples.
Appreciation of the contributions Muslim’s have made to mathematics (and science).
Admiration for Spanish Dance.
Appreciation for Spanish Cuisine.
Religious and ethnic tolerance.
VIII. Skills:
1.) What skills related to acquiring, organizing and using information will students develop?
 Identify issues, problems, and solutions
 Distinguish between fact and opinion
 Demonstrate sequential thinking
 Identify main idea, detail, sequence of events, and cause and effect
 Construct geometric shapes and patterns
 Draw conclusions and make generalizations
 Use PowerPoint technology
 Differentiate grammatical structures.
 Use meta-linguistic strategies for comprehension.
2.) What technological skills will students develop?
 Ability to construct geometric shapes and patterns using a compass and straight edge
 PowerPoint
 Internet research
 Multimedia use
3. What interpersonal skills will students develop?
 Decision-making
 Problem-solving
 Intercultural communication
 Cooperation and collaboration
Stage 2 – Assessment Evidence
IX. Performance Tasks
Other evidence
Through what authentic performance tasks will
students demonstrate the desired understanding,
attitudes, and/or skills?
 Working on paper with a straight edge and
compass, students will explore geometric
concepts by constructing various geometric
shapes.
 Working with pencil and paper, students
will compare and contrast the Roman
numeral system with the Arabic numeral
system by performing the operations of
addition, subtraction, multiplication and
division to solve simple equations.
 Students will create a PowerPoint
presentation describing the sequential steps
of a Spanish recipe. They will focus on the
grammatical structure: The Imperative
voice.
 Students will perform the basic steps and
hand movements of Flamenco with a
partner.
Through what other evidence (e.g., quizzes, tests,
observations, homework, journals, etc.) will
students demonstrate achievement of desired
results.
 Mathematical achievements will be
assessed primarily through observation.
 Students will be formally assessed
according to a rubric for the PowerPoint
Presentation.
 Students will be formally assessed
according to a rubric for their dance
presentation.
 In Spanish class, students will be
informally assessed throughout the class
period for participation.
How will students reflect upon and self-assess their
learning?
 In the area of number concepts, students
will receive immediate feedback regarding
their learning based upon the accuracy of
the solutions they generate for several
mathematical equations.
 In the area of geometry, students will
receive immediate feedback regarding their
learning based upon the accuracy of the
geometric shapes and patterns they
generate.
 Classmates and dance partners will provide
immediate feedback regarding mastery of
Flamenco steps and movements
 Classmates will provide immediate
feedback on the quality of the Tapas
PowerPoint presentation.
Stage 3 – Learning Plan
X. Learning Activities
Lesson #1:
Title: The Virtual Field Trip
Time estimation: One 45 min. period
Objective(s):
1. Students will be able identify how the Moors influenced Spanish culture.
2. Students will be able to identify how the Moors influenced European mathematics.
Description: Students (combined Spanish and Algebra classes) will view the Virtual Field Trip to Bar
Ferdinand ( http://www.youtube.com/watch?v=gu0pD9dWnQ0). A group discussion, moderated by Mr.
Kandebo and Ms. Marull, will explore how the Moorish presence on the Iberian Peninsula left its mark on
modern-day Spain and Western mathematic scholarship. Students will have the opportunity to sample
Spanish cuisine that demonstrates Moorish influences.
Teacher Preparation:
Prepare virtual field trip video. Order food from Bar Ferdinand.
Background Information:
Berggren, Lennart (2003). Episodes in the mathematics of medieval Islam. New York, NY: Springer.
Trutter, Marion (Ed.). (2010). Culinaria. New York, NY: H.F. Ullmann.
http://www.foodtimeline.org/foodfaq6.html
Teaching & Learning Materials:
Schmitt, Conrad (2006). Como te va? Nivel Verde. New York, NY: Glencoe McGraw-Hill.
Rubric, 1 copy per student
Lesson #2:
Title: Spanish Food – The Imperative
Time estimation: One 60 min. period
Objective(s):
1. Students will be able to write and illustrate the use of the 3rd person imperative form in
Spanish recipes.
Description: Students will create a PowerPoint presentation demonstrating the necessary steps to create
a Spanish recipe. Each slide will include a picture of the action as well as the instructions written in
Spanish using the imperative form. Students will finish the project at home and will present the next day.
Teacher Preparation:
Prepare rubric for scoring. Prepare a sample presentation as a model.
Background Information:
http://www.foodtimeline.org/foodfaq6.html
http://www.andalucia.com/flamenco/history.htm
http://www.engr.sjsu.edu/pabacker/history/islam.htm
Teaching & Learning Materials:
Virtual Field Trip video: http://www.youtube.com/watch?v=gu0pD9dWnQ0
Food from Bar Ferdinand
Lesson #3:
Title: Spanish Dance – Flamenco
Time estimation: One 60 min. period
Objective(s): Students will be able to identify and perform the basic hand and leg movements
of Flamenco.
Description: Students will watch several videos highlighting Sevilla and flamenco dance. An
instructional video of basic flamenco will guide the students through the basic steps and hand movements.
After learning the basic steps the students will pair up and practice a creative routine to be presented to
the class.
Teacher Preparation:
Prepare rubric for scoring. Acquire and load appropriate videos.
Background Information:
http://www.andalucia.com/flamenco/history.htm
Teaching & Learning Materials:
Schmitt, Conrad (2006). Como te va? Nivel Verde. New York, NY: Glencoe McGraw-Hill.
Rubric, 1 copy per student
Video - 01_Savilla.wmv
Take10 en Español
Video - 02_La_profesora_del_baile_flamenco.wmv
Take10 en Español
Video - 05_Ejercicios.wmv
Take10 en Español
Lesson # 4: Title: Islamic Mathematics-Number Concepts
Time estimation: One 45 min. period
Objective(s):
1. Explain who the Moors were.
2. Analyze the Roman system of numerals and identify its shortcomings.
3. Demonstrate the superiority and flexibility of the Arabic number system .
4. Explain how Muslim scholarship influenced European thought regarding
mathematics.
Description: Lecture students regarding the Moors and Spain and view, for a second time, the
Virtual Field Trip to Bar Ferdinand (http://www.youtube.com/watch?v=gu0pD9dWnQ0). Discuss the
engineering achievements of the Romans and provide a refresher on Roman numerals. Write four
arithmetic problems on the board in Roman numerals (one each for addition, subtraction, multiplication
and division) and ask the students to solve these, using Roman numerals, at their desks. Discuss the
results and during the ensuing discussion lead the students to identify the shortcomings of the Roman
system of numbers. Explain how Muslim mathematicians developed ideas and methods to eliminate
these problems. Lead students to the conclusion that the Arabic number system is superior to the Roman
system.
Teacher Preparation:
Prepare copies of the handout, “Moorish Influence on European Mathematics,” for distribution.
Background Information:
Berggren, Lennart (2003). Episodes in the mathematics of medieval Islam. New York, NY: Springer.
http://www.engr.sjsu.edu/pabacker/history/islam.htm
Teaching & Learning Materials:
http://www.youtube.com/watch?v=gu0pD9dWnQ0
http://www.muslimheritage.com/topics/default.cfm?ArticleID=472
http://www.muslimheritage.com/topics/default.cfm?ArticleID=952
Lesson # 5: Title: Islamic Mathematics-Geometry
Time estimation: One 45 min. period
Objective(s):
1. Explain why the Islamic cultures use patterns and geometric shapes for adornment.
2. Provide concrete examples of these designs.
3. Demonstrate that knowledge of geometry is needed to develop designs and patterns
derived from basic geometric shapes
4. Analyze the skills needed to create designs and patterns developed from basic
geometric shapes.
5. Demonstrate how to construct basic geometric shapes using a compass and
straightedge.
Description: Introduce the concept of using geometric patterns and shapes as decoration and how
they are widely used in Spain. Explain the use of such “decorations” in the context of Islam and explain
how the Moors brought their decorative preferences to Spain. Present visual examples of such
decorations. Demonstrate how to create the “seven circle” design, and allow students to construct it.
Demonstrate how to identify two shapes in the design and allow students to do so. Lead a discussion on
what other shapes may be found in the design. Turn the discussion toward identifying the level of
geometry knowledge necessary to develop designs based on these shapes, as well as the level of work that
is necessary to develop a repeating design pattern.
Teacher Preparation:
Prepare copies of the “seven circles” activity for distribution.
Background Information:
Berggren, Lennart (2003). Episodes in the mathematics of medieval Islam. New York, NY: Springer.
http://www.metmuseum.org/explore/publications/islamic_geometric.asp
http://www.engr.sjsu.edu/pabacker/history/islam.htm
Teaching & Learning Materials:
http://www.ncetm.org.uk/resources/18030
http://www.engr.sjsu.edu/pabacker/history/islam.htm
http://www.muslimheritage.com/topics/default.cfm?ArticleID=952
http://www.scribd.com/doc/44990643/Islamic- Geometrical-Patterns-for-the-Teaching-of- Tics-ofSymmetry
http://www.medieval-life.net/medieval_history_spain.htm
XI. References:
Books, Magazines, and Secondary Sources:
Backer, Patricia, ed. (2005). Islam, Spain and the history of technology. Retrieved from
http://www.engr.sjsu.edu/pabacker/history/islam.htm
Berggren, Lennart (2003). Episodes in the mathematics of medieval Islam. New York, NY: Springer.
Burnett, Charles. (nd). Leonard of Pisa (Fibonacci) and Arabic Arithmetic. Retrieved from
http://www.muslimheritage.com/topics/default.cfm?ArticleID=472
Djebbar, Ahmend. (2008). Mathematics in the Medieval Maghrib: General Survey on Mathematical
Activities in North Africa. Retrieved from
http://www.muslimheritage.com/topics/default.cfm?ArticleID=952
Flamenco History in Andalucia. Retrieved from
http://www.andalucia.com/flamenco/history.htm
How the Moors Influenced Spanish Cuisine. Retrieved from
http://www.foodtimeline.org/foodfaq6.html
Islamic Art and Geometric Design Activities for Learning. Retrieved from
http://www.metmuseum.org/explore/publications/islamic_geometric.asp
Islamic geometrical patterns for the teaching of mathematics of
symmetry [Special issue of Symmetry: Culture and Science]. Symmetry in Ethnomathematics.
Retrieved from http://www.scribd.com/doc/44990643/Islamic- Geometrical-Patters-for-the-Teachingof- Tics-of-Symmetry
Kandebo,S. & Mentz,C. (2011). Virtual field trip to bar ferdinand. USA. Retrieved from
http://www.youtube.com/watch?v=gu0pD9dWnQ0
Material Culture of Al-Andalus /Mathematics. Retrieved from
http://www.islamicspain.tv/Arts-and-Science/The-Culture-of-Al-Andalus/Mathematics.htm
Medieva1 History of Spain. Retrieved from
http://www.medieval-life.net/medieval_history_spain.htm
Schmitt, Conrad (2006). Como te va? Nivel Verde. New York, NY: Glencoe McGraw-Hill.
Trutter, Marion (Ed.). (2010). Culinaria. New York, NY: H.F. Ullmann.
Lesson Ideas:
The art of mathematics, Islamic patterns. Primary Magazine, (13). Retrieved from
http://www.ncetm.org.uk/resources/18030
Islamic Art and Geometric Design Activities for Learning. Retrieved from
http://www.metmuseum.org/explore/publications/islamic_geometric.asp
XII. Reflections:
There are no reflections to record in this area as the lessons were not taught and the classroom activities
were not performed.