Geometric Window Art Unit
Contents
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IV.
V.
Student Handouts
Rubric
Teacher Notes
Outline of Lessons
MYP Unit Planner
Name: ____________________________
Geometric Window Art
Due Date: ______________
Unit Question: Why and how do we create?
Content Question: In what ways has geometry influenced art?
AoI: Human Ingenuity
TEKS: 7.6B, 7.8C, 7.9A, 7.13A, 7.14A
The purpose of the project is to improve student understanding and to apply
concepts of geometry and measurement, such as area and perimeter. It will also
encourage student appreciation of geometric applications and principles that
influence art.
Instructions:
1. Create a rough draft of your design
2. Draw your design on a sheet of black cardstock paper or construction
paper using a ruler, compass, or other necessary tools
3. Cut out the shapes (using Exacto knife, box cutter or scissors) and this
sheet will become a stencil
4. Use the stencil to draw the design onto a 2nd sheet of black
cardstock/construction paper
5. Cut out the shapes again
6. Glue colored tissue paper over the previously cut shapes on one of the
black papers
7. Glue the other black paper to the other so that the tissue paper is between
the two black sheets
Design Requirements:
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Your design must be composed of at least four different geometric figures
and three different colors
You may use the same shape more than once, but you have to use at
least four different figures in your design
Student Handouts
1
Project Booklet Requirements:
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Cover page – title, name, date, class period
Identify and list all of the geometric shapes used in your design (2nd page
of the booklet)
At least four different geometric figures used in your design should be
sketched to actual size (each on a separate sheet of paper), then
complete the following for each figure:
• Give the definition of the shape
• List the necessary dimensions of the figure and find their
measurements
• Label the measurements on the figure
• List the appropriate formulas and/or procedures needed to find the
perimeter and area
• Find the perimeter
• Find the area – round your answers to two decimal places or leave in
fraction or mixed form
• Show ALL work and calculations in a neat and logical manner
Measure at least one shape in customary units (inches) and use mixed
numbers or fractions to calculate the perimeter and area, then measure
the other shapes in metric units (centimeters) and use decimals
Answer the reflection questions on a separate sheet of paper (last page of
the booklet)
Staple all the pages together to form a booklet
Reflection Questions (answer in complete sentences):
1.
2.
3.
4.
How did you go beyond the minimum requirements for this project?
How could you improve your project?
What part of the project did you find challenging?
How did the project improve your knowledge of geometry and the formula
chart?
5. In what ways has geometry influenced art? (research your answer)
6. List some suggestions of how the teacher could improve this project for
next year.
Suggested Geometric Figures:
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Triangle (classify the type)
Circle
Irregular polygons
Parallelogram
Rectangle
Kite
Half or quarter circle
Student Handouts
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Regular polygons (square,
pentagon, hexagon, etc)
Rhombus
Trapezoid
A combination of the shapes
in this list
2
Scoring Rubric (Based on MYP Mathematics Criterion A):
Achievement
Level Descriptor
Level
0
The student does not satisfy any of the requirements.
1-2
Uses 1 to 2 geometric shapes in their design. Minimum evidence
of a creative design. Attempts to select and apply basic rules to
find the area of three or less geometric shapes. Answers some of
the reflection questions.
3-4
Uses 3 geometric shapes in their design. Some evidence of a
creative design. Identifies several of the geometric shapes.
Measures in both customary and metric units. Sometimes selects
and applies basic rules to find the area and perimeter of three
geometric shapes. Answers the reflection questions.
5-6
Uses 4 geometric shapes in their design. Adequate evidence of a
creative design. Identifies most of the geometric shapes and gives
the definitions. Measures accurately in both customary and metric
units. Generally selects and applies basic rules correctly to find the
area and perimeter of four geometric shapes. Answers and
elaborates on the reflection questions.
7-8
Uses 4 or more geometric shapes in their design. Ample evidence
of a creative design. High level of craftsmanship. Accurately
identifies all geometric shapes and gives the definitions. Measures
precisely in both customary and metric units. Selects and applies
basic rules correctly to find the area and perimeter of four or more
geometric shapes. Clearly answers and elaborates on all of the
reflection questions. Suggests ways for improvement.
Parent Signature: _____________________________
Rubric
1
Geometric Window Art
Teacher Notes:
Necessary Materials:
 black cardstock or black
construction paper
 rulers
 compasses
 geometric stencils
 protractors
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
scissors, Exacto knives, or
box cutters
multi-colored packs of tissue
paper
Time Required:
 Three weeks of geometry and measurement lessons (see the lesson plan
outline)
 One week of in class work on the window art and booklet
This student project should be introduced at the beginning of a unit on geometry
and measurement, even though the students have not learned the prerequisite
skills needed to complete it. The teacher should give the students the handout
with the instructions and requirements on the day they introduce the project. To
motivate student interest in the project it helps to display a PowerPoint with
pictures of stained glass that contain geometric shapes. It also helps to discuss
the historical relevance of stained glass and the more modern ways it has been
included in architecture. I use pictures of rose windows from cathedrals in Europe
and Frank Lloyds Wrights’ stained glass creations. Have the students take the
requirement/rubric handout home to be signed by the parent. This will
communicate to the parent that they might need to provide materials for the
artwork if the teacher cannot provide them, and it also gives them an idea of what
their student is doing in the classroom. I suggest keeping the signed handout
when the student returns it, and give the student another copy of the handout
when it is time to actually begin making the art work and project booklet. This
way you have a record of the parent signature and the student is less likely to
lose it over a shorter period of time.
There are two main reasons to introduce the project at the beginning, prior to any
lessons. First, it gives the students something to look forward to and they are
more motivated to learn the material. Secondly, as you teach the measurement
lessons you can refer back to the project. For example, I would say, “Does
anybody plan on using a triangle in their design? So what measurements are
necessary to find the perimeter of a triangle? What measurements are required
to find the area? This will be something you need to know in order to complete
the project booklet.”
Teacher Notes
1
When you give the instructions for creating the design it helps to have a fully
completed exemplar and a partially completed exemplar that only has the shapes
cut out. That way you can show the product at different stages in the process.
Most of the visual learners will respond better to the instructions if you show them
examples.
When you describe the design requirements it helps to demonstrate a design that
meets the requirements and one that does not. Also, most students need to be
told why they cannot use shapes within other shapes. I would draw a picture of a
rectangle on the board and then draw a circle inside of it. Then I would ask,
“What happens to the circle when I cut out the rectangle?” Most students catch
on at that point. In addition, if a student wants two separate shapes, but connects
them in the design, then it will look like an irregular polygon or some composite
figure. Tell them to keep them separated, “not touching”, if they intend for there to
be more than one shape. I would also demonstrate this for them.
The students need guidance and feedback on their design before they put it on
the black paper. I would designate some time to give approval to their design
before you give them the black paper. This will help eliminate the need for a
student to do several trials of the artwork.
I strongly suggest having stencils of geometric shapes available for the students
when they are putting the design on the black paper. You might also require
them to bring rulers, protractors and compasses, or provide them yourself.
The students will need about two class periods to cut out their design from both
black papers. If you allow them to use Exacto knifes or box cutters then you will
need to closely monitor them as they use these potentially dangerous tools. I
also ask the science teacher for old science boards that the students can use as
a cutting surface so that the students do not damage the desk.
The teacher can either provide many different colors of tissue paper, or you can
ask different students to purchase and bring different colors of tissue paper.
Allow them two days of access to the tissue paper in case they mess up or need
more time.
The most important part of the student project is the booklet. Make sure you
clearly describe the requirements for the booklet and give them an opportunity to
ask questions about it. I would not do this until the students are ready to begin
working on the booklet, otherwise they might forget and not do it correctly. If you
have an exemplar this will really help the visual learners. Also, review the rubric
and allow them to ask questions about it.
When you grade the booklet make sure to give feedback to the student. Show
them where they went wrong if they made any mistakes. Many students will
make measurement and calculation mistakes. Some will use the wrong formula.
Teacher Notes
2
They need to understand why they got something incorrect to be able to avoid
the mistake from happening again. Allow plenty of time to grade these projects,
possibly up to a week depending on your pace.
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Teacher Notes
3
Outline of Lessons for Geometric Window Art
This outline consists of twelve lessons that are necessary to cover prior to the
completion of the project. The Geometric Window Art Project is meant to serve
as a summative assessment for the measurement concepts perimeter and area.
Many of these lessons contain prerequisite skills that are essential for the
students to be able to do in order to classify and measure their shapes.
I. Spatial Thinking
a. Points, Lines, and Planes
i. define, name and identify points, lines, planes, segments,
rays, parallel lines, and perpendicular lines
b. Angles
i. define and indentify adjacent, vertical, congruent,
supplementary, complementary, acute, right, obtuse and
straight angles
ii. draw and find the measure of angles
iii. find the measure of angles based on angle relationships
c. Classifying Polygons
i. classify triangles and quadrilaterals by their sides and angles
ii. define and indentify regular polygons
iii. name polygons based on their number of sides
d. Congruence
i. define congruence
ii. identify corresponding parts
iii. find the measure of angles and sides based on congruence
e. Circles
i. explore and discuss the value of pi
ii. define what a circle is and define the parts of a circle: radius,
diameter, circumference, and chord
II. Perimeter and Area
a. Measuring in Customary Units
i. measure lengths of segments using inches and feet
ii. write customary units as fractions, mixed numbers and
decimals
b. Perimeter
i. define perimeter
ii. walk the perimeter of an irregular shape for kinesthetic
learners
iii. measure and find the perimeter of regular and irregular
polygons
iv. develop formulas for the perimeter of rectangles and regular
polygons
Outline of Lessons
1
c. Circumference
i. define circumference
ii. develop the circumference formula
iii. find the circumference of circles given the radius or diameter
d. Area: Parallelograms
i. define area and square units
ii. indentify the height and base of rectangles and
parallelograms
iii. develop the area of a parallelogram formula
iv. measure and find the area of rectangles and parallelograms
e. Area: Triangles and Trapezoids
i. discover the relationship between parallelograms and
triangles
ii. develop the area of a triangle formula
iii. identify the base and height of a triangle
iv. measure and find the area of triangles using the formula
f. Area: Circles
i. discover the formula for area of a circle by relating it to a
parallelogram
ii. review the order of operations as it pertains to exponents
iii. measure and find the area of circles using the formula
g. Area: Regular and Irregular Polygons
i. deconstruct a figure with five or more sides into shapes
found on the formula chart, such as triangles and rectangles
ii. measure and find the area of a regular hexagon by adding
the areas of the composite shapes
iii. measure and find the area of an irregular pentagon by
adding the areas of the composite shapes
Outline of Lessons
2
MYP unit planner
Unit title
Geometric Window Art
Teacher(s)
Pamela Cordova
Subject and grade level
Mathematics, Year 2
Time frame and
duration
Four weeks
Stage 1: Integrate significant concept, area of interaction and
unit question
Area of interaction focus
Significant concept(s)
Which area of interaction will be our
focus?
Why have we chosen this?
What are the big ideas? What do we
want our students to retain for years
into the future?
Human Ingenuity
Knowledge and appreciation of
geometric applications and principles.
Students will discover geometry in art,
as well as create their own art.
MYP unit question
Why and how do we create?
Assessment
What task(s) will allow students the opportunity to respond to the unit question?
What will constitute acceptable evidence of understanding? How will students show what they
have understood?
Task - creation of geometric window art that is inspired by stained glass. Students will also
create a “project booklet” that will allow them to answer the unit and content questions by
doing research. In addition, the task requires them to identify geometric shapes used in their
art design and use measurement skills to find the dimensions, perimeter or circumference,
and areas of those shapes.
During the creation of the projects students consult with the teacher about their product and
this serves as a formative assessment for students to show understanding and receive
feedback. Also, by reaching a level of 5 or higher on their assessment rubric the student
demonstrates acceptable evidence of understanding. Please see attached rubric. Students
will illustrate what they know and understand through their product, which is the geometric
window art and project booklet.
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Which specific MYP objectives will be addressed during this unit?
A - Knowledge and Understanding
By the end of this unit, pupils should:

know and demonstrate understanding of geometry

use appropriate mathematical concepts and skills to solve problems in real-life contexts

select and apply general rules correctly
Which MYP assessment criteria will be used?
Criterion A: Knowledge and Understanding
(please see rubric)
Stage 2: Backward planning: from the assessment to the
learning activities through inquiry
Content
What knowledge and/or skills (from the course overview) are going to be used to enable the
student to respond to the unit question?
What (if any) state, provincial, district, or local standards/skills are to be addressed? How can
they be unpacked to develop the significant concept(s) for stage 1?
Knowledge and/or skills: geometrical elements and their classification, constructions,
perimeter/circumference and area
TEKS addressed: 7.6B (use properties to classify shapes), 7.8C (use geometric concepts
and properties to solve problems in fields such as art and architecture), 7.9A (solve
application problems involving length, area, and volume, 7.13A (identify and apply
mathematics with other disciplines), 7.14A (communicate mathematical ideas)
TAKS addressed: Objective 3 (Geometry and Spatial Reasoning), Objective 4
(Measurement), and Objective 6 (Underlying Processes and Mathematical Tools)
The project entails using measurement skills and concepts, which is typically my students’
weakest area for TAKS, and at the same time consists of art concepts that will help develop
student appreciation of geometric applications.
Week 1:
Introduce the project to students by showing them a PowerPoint about stained glass and
architecture. I highlight the rose window and the geometric design. Students receive a project
rubric and brainstorm a creative design for their art.
Weeks 1, 2 and 3:
Unpacking - Lessons on geometry concepts such as spatial thinking, classifying polygons,
perimeter, circumference and area.
Week 4:
Revisit the project requirements for both the art design and booklet. Students get their art design
approved and begin making their window art. Students are given the project materials after they
show and discuss their design with the teacher. The students reflect on their product and work on
the “project booklet” of their design. Pupils classify and find measurements for their shapes.
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Approaches to learning
How will this unit contribute to the overall development of subject-specific and general
approaches to learning skills?
Transfer - exploring how mathematics can be used to create artistic designs and effects
helps build connections across subjects
Organization – students must use time-management and self-management skills to complete
their art and project booklet
Reflection – students self evaluate their product and booklet and make suggestions for
improvement
Thinking – students have to plan their art design, apply knowledge and concepts of
geometry, and create novel solutions to find the area of shapes that they do not have
formulas for.
Learning experiences
How will students know what is expected
of them? Will they see examples, rubrics,
templates?
How will students acquire the knowledge
and practice the skills required? How will
they practice applying these?
Do the students have enough prior
knowledge? How will we know?
Students will be given general
requirements for their project on a
handout and they will also receive the
information on a PowerPoint. They will
receive rubrics that give detailed
information of what is expected of them to
succeed. Students will also be shown
finished products of the students’
geometric art from the previous year that
reflect a range of achievement levels.
Students will acquire the knowledge
through classroom lessons and from
student research. They will practice the
skills on homework and receive feedback
for improvements.
The students need to have basic
measuring skills, such as how to use the
ruler, compass and protractor. The
students will do exercises during the
lessons to establish if they do have these
basic skills. If they are lacking the skills it
will be addressed during the lessons.
Teaching strategies
How will we use formative assessment to give
students feedback during the unit?
What different teaching methodologies will we
employ?
How are we differentiating teaching and learning
for all? How have we made provision for those
learning in a language other than their mother
tongue? How have we considered those with
special educational needs?
Formative assessments, such as homework,
student observations and discussions, and
teacher approval of design plans, provided both
teacher and students with insights into the
development of understanding, knowledge and
skills.
Questioning strategies, direct instruction and
project-based learning are some of the different
teaching methodologies employed during this
unit.
The formative assessments described above
allowed for exploration of different learning styles
and for individual differentiated instruction during
class or tutoring. Special education colleagues,
ESL teachers, and counsellors are available for
assistance in differentiated instruction
Resources
What resources are available to us?
How will our classroom environment, local environment and/or the community be used to
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facilitate students’ experiences during the unit?
Media specialist or librarian
PowerPoint on stained glass windows
Websites
www.constructingtheuniverse.com/Chartres%20Window.html
www.therosewindow.com
www.delmars.com/wright/index.html
www.find-stainedglasspatterns.com/frank-lloyd-wright-stainedglasspatterns.html
Materials for the window art: construction paper, tissue paper, scissors or box cutters,
compass, protractor, ruler, geometric stencils and glue
Textbook: Prentice Hall Texas Pre-Algebra
The classroom environment allowed for student access to materials and individual
workspace. The classroom layout also permitted for the teacher to have easy access to all
students.
Ongoing reflections and evaluation
In keeping an ongoing record, consider the following questions. There are
further stimulus questions at the end of the “Planning for teaching and learning”
section of MYP: From principles into practice.
Students and teachers
What did we find compelling? Were our disciplinary knowledge/skills challenged in any way?
What inquiries arose during the learning? What, if any, extension activities arose?
How did we reflect—both on the unit and on our own learning?
Which attributes of the learner profile were encouraged through this unit? What opportunities
were there for student-initiated action?
Possible connections
How successful was the collaboration with other teachers within my subject group and from
other subject groups?
What interdisciplinary understandings were or could be forged through collaboration with
other subjects?
Assessment
Were students able to demonstrate their learning?
How did the assessment tasks allow students to demonstrate the learning objectives
identified for this unit? How did I make sure students were invited to achieve at all levels of
the criteria descriptors?
Are we prepared for the next stage?
Data collection
How did we decide on the data to collect? Was it useful?
The students found the concept and design of the “Rose Window” compelling, because not
only is it beautiful, but it also incorporates an abundant amount of geometry. I found their
creative art designs intriguing. The challenging part of the project for most of the students was
doing the measurements and using the appropriate formulas to find the area of the geometric
shapes they chose to include in their design. Quite a few of them also had trouble cutting out
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their shapes precisely. The challenging part for me was grading the projects as objectively as
possible.
Many students chose to use polygons, such as pentagons, that they did not have formulas for
because they were not taught how to find the area of them in the lessons and they were not
on their grade-level TAKS formula chart. Therefore, they inquired how to overcome this
dilemma. With some teacher guidance most students discovered they could break up these
polygons into shapes like rectangles, triangles and trapezoid, which they already knew the
formula for.
The students reflected on their learning by answering some questions that required them to
determine if they were successful and how much knowledge they gained. I reflected on the
unit by determining what parts of the unit should be used again, modified, or taken out. The
main component that was modified was the reflection questions for the students. I tried to
gear the new questions to necessitate more details, because some of the students were
answering them vaguely.
Reflection and inquiry were the two attributes of the learner profile that this unit encouraged.
Students discovered geometric style and concepts in art, and then created their own art.
Through collaboration of art and geometry students gain an appreciation and different
perspective of both subject areas.
The majority of students demonstrated mastery of the concepts and skills taught in this unit
through their final product. A few students did not turn in a completed project; therefore to
assess learning I gave the students an exam.
To allow students to achieve all of the criteria descriptors I made sure my students
understood the rubric and the project requirements. In the process of developing their art
design and reflection booklet I constantly monitored and gave feedback to students according
to the levels of the rubric. If the students wanted to achieve all of the criteria descriptors they
were informed of the necessity to go beyond the minimum requirements of the project.
I saw in most of the students a considerable growth in their measurement skills. This will help
them in future courses, especially high school geometry. I was also happy that the students
were better prepared for the state mathematics test.
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