Transformations
Grade 6 Math and Art
Integration
Unit Plan
By Dani Peters
1
Grade 6 Transformations: Stage 1 – Desired Results
Established Goals
Students will:
 perform
transformations
(translations,
rotations and
reflections) in a 2D
space.
 illustrate how
transformations
can be used in the
real world and in
art.
 create their own
stained glass
windows using
different types of
transformations.
 describe
transformations
using
mathematical
language.
TRANSFER GOAL
Students will perform and describe transformations and show an appreciation for how
transformations can be used in art.
MEANING
Enduring Understandings:
Essential Questions:
Students will understand that…
Students will keep considering…
U1 – Transformations are all around us.
Q 1 – What does a pattern look like that has
been made using transformations?
U2 – Transformations provide the framework
for artistic representation in many cultures.
U3 – Mathematical properties of rotations,
reflection and symmetry are found in many
designs in everyday life.
Q2 – What information must be given to
describe a transformation?
Q3 – Why are transformations used in art?
ACQUISITION OF KNOWLEDGE & SKILLS
Students will know…
Students will be skilled at…
-
Transformations are all around us.
-
-
There are different types of
transformations called reflections,
rotations and translations.
identifying and classifying
translations, reflections and
rotations in 2D images
-
making connections between
mathematics and art.
STAGE 2 – Evidence
Evaluative Criteria
Assessment Evidence
Performance is judged in terms of
Students will need to show their learning by:
Math journal
Transfer Task:
Stained glass window
Students will create their own stained glass window using paper and cellophane using
their knowledge of transformations and complimentary colours. They will then describe
the transformations evident in their window in mathematical terms. Students will then
do a peer review of the description of the transformations in the stained glass window.
When they have finished the peer review, students will be graded on a rubric for their
stained glass window, description of transformations and use of complimentary colors.
Reflection
Critique
2
Unit Summary:
This unit is centred on the grade 6 math curriculum and integrates pieces from the art curriculum
as well. Students will take a more meaningful look into transformations and see how they are evident in
the world around us. In order to include art history, students will start by looking at and encountering the
famous artist M. C. Escher to see how he used the manipulation of 3D objects to 2D objects to create
illusions within your mind. He also used tessellations and transformations and other mathematical
curiosities in his work to portray certain elements. This encounter will help students see that math is an
important element in art and in the real world. It will inspire students to make their own creations using
similar techniques to Escher. By critiquing others work they will learn to demonstrate a mutual respect
towards others. They can cognitively apply the knowledge and skills they have learnt to other parts of
their life.
Students will observe other peoples work as well as Escher’s and critique them. Students
experiment with paint combining primary colours to create secondary colours. They will use their
knowledge of complementary colours to create a stained glass window. Students can design their own
stained glass window using their knowledge of transformations. They will use their hands and practice
to increase accuracy. They will be using paint to apply different brush strokes. This applies to the
psychomotor domain. They will also be writing in a math journal. I believe it is important to involve
English and writing in math so that students can become mathematically literate.
Unit Rationale:
I believe learning is more powerful and meaningful when you can integrate different subjects
together. In the real world all subjects are incorporated together, but in school there is a huge
segregation between the different subjects when there does not have to be. This unit is suitable for the
grade level because art makes math more interesting for many students and will also show students how
mathematics has had a powerful impact on the arts. This unit allows students to be creative in a subject
where there is usually “one right answer.” Transformations are excellent examples of how mathematical
principles are used in art. This unit is a great way to incorporate hands on activities in the math
classroom. When students are interested in what they are learning, they are more motivated and
engaged. At this age, students will be very intrigued by Escher’s work, especially his illusion of the
staircase that keeps going up and up. Depending on the culture in the classroom, I may also use quilting
as an example of how transformations are used in art.
This unit engages students and challenges them to think outside the “math box.” As I stated
earlier, students are used to doing math in math class. Having art incorporated will increase student
engagement. Throughout the unit, I use different taxonomical level questions and engage students in
higher level thinking. Students have two different encounters with art that help to keep them engaged.
The lessons always start with something that will engage the students right off the bat.
I think the final product for this unit is exciting and interesting for students. They are able to
create and design their own stained glass while keeping certain criteria in mind. They need to include
complimentary colours and 2 types of each transformation. This challenges students to create which is
the highest order of thinking. They are given guidelines and then create their own piece to fit the
guidelines.
3
Lesson Summaries:
Lesson 1: This lesson will serve as a review of the 3 different types of transformations by diving
into the story of Escher. Students will look at how Escher used transformations and
other mathematical information to create art of all sorts. I will introduce the topic, by
giving a short biography of Escher’s life, followed by looking at and critiquing many
of his famous creations such as “Drawing hands” or “Relativity.” We will take a
deeper look at “Sky and Water” and look at what principles are needed to create a
piece that uses transformations. Student will then take the time to try a piece like that
on their own. To close, students will hang their final products on the wall and do a
gallery walk around the classroom.
Lesson 2: For the second lesson, students will look into primary colors, secondary colors and
complementary colours. First students will begin by mixing the primary colours to
make the secondary colours. They will use three different types of paint brushes and
try using different strokes on the paint brush. They will then use the colours they have
made to make a colour wheel. The colours opposite each other are complementary
colours. To close, students will look at examples of stained glass windows and identify
different transformations in the windows. Tell them about the final product so that
they have a goal in mind for the next day.
Lesson 3: During this lesson, students will complete a project that includes both math and art.
First, we will encounter stained glass windows from Matisse’s chapel. Since they
spent the end of last class looking at examples of stained glass windows and the
transformations in then, they will be able to design their own stained glass window
using cellophane and black paper that includes two examples of each type of
transformation. The stained glass window must be divided into 4 sections and each
section will contain complementary colours. When they have finished, they are to
write a paragraph describing the transformations evident in their window using proper
mathematical language.
4
LESSON #1
Subject: Math and Art 6
Lesson Duration: 90 minutes
Unit: Shape and Space (Transformations)
OUTCOMES FROM ALBERTA PROGRAM OF STUDIES
General Learning Outcomes:
Students will:

Describe and analyze position and motion of objects and shapes.
Specific Learning Outcomes:
Students will:

Perform a combination of translations, rotations and/or reflections on a single 2-D shape, with and without
technology, and draw and describe the image.
LEARNING OBJECTIVES
Students will:
1. Describe how transformations are used in various art forms.
2. Describe how transformations are used in Escher’s art.
3. Create an exemplar of Escher’s work based on their knowledge of transformations.
ASSESSMENTS
Observations:
Key Questions:
1. How did Escher use his knowledge of
 Students should be engaged with the lesson
transformations to create art?
at all time. Watch for students who seem
2. What other techniques did Escher use while
disconnected and ask them 3rd level
creating these pieces?
questions to keep them engaged.
3.
How do you make a piece similar to Eschers
 All students should participate in discussion.
“Sky and Water”?
 Students should be actively working on their
4. What are important factors to consider while
final product in the appropriate time slot.
critiquing the works of others?
 Students should be engaged in constructive
critiques at the end of the lesson.
Written Performance Assessments:
 N/A
LEARNING RESOURCES CONSULTED
Resource #1 : http://www.mcescher.com/about/biography/
MATERIALS AND EQUIPMENT
 grid paper
 variety of pencil crayons
 Powerpoint with pictures and instructions
 SMART Board or projector
 tape or sticky tack
 pencils and erasers
 graph paper
PROCEDURE
INTRODUCTION: (10 minutes)
 Prior to this part in the unit, students will have been taught each type of transformation and will have
had at least one class working and practicing with each type of transformation.
Hook/Attention Grabber: Hook the class by having Escher’s picture of relativity on the board. Ask: What is
unique about this drawing? How old do you think it is? What characteristics of art is the artist taking
advantage of to create this kind of illusion? What medium was used in this drawing? What stands out from it?
Transition to Body: This drawing was made by M. C. Escher who is one of the world’s most famous graphic
artists. Today we will be taking a look at his life and how he used mathematics in his art.
5
BODY: (40 minutes)
1. Give students a short run down on Escher’s life: Maurits Cornelis Escher (1898-1972) is one of the world's
most famous graphic artists. His art is enjoyed by millions of people all over the world, as can be seen on the
many web sites on the internet.
He is most famous for his so-called impossible constructions, such as Ascending and Descending, Relativity,
his Transformation Prints, such as Metamorphosis I, Metamorphosis II and Metamorphosis III, Sky & Water
I or Reptiles. But he also made some wonderful, more realistic work during the time he lived and traveled in
Italy..
M.C. Escher, during his lifetime, made 448 lithographs, woodcuts and wood engravings and over 2000
drawings and sketches. Like some of his famous predecessors, - Michelangelo, Leonardo da Vinci, Dürer and
Holbein-, M.C. Escher was left-handed.
Apart from being a graphic artist, M.C. Escher illustrated books, designed tapestries, postage stamps and
murals. He was born in Leeuwarden, the Netherlands, as the fourth and youngest son of a civil engineer.
After 5 years the family moved to Arnhem where Escher spent most of his youth. After failing his high
school exams, Maurits ultimately was enrolled in the School for Architecture and Decorative Arts in
Haarlem.
After only one week, he informed his father that he would rather study graphic art instead of architecture, as
he had shown his drawings and linoleum cuts to his graphic teacher Samuel Jessurun de Mesquita, who
encouraged him to continue with graphic arts.
After finishing school, he traveled extensively through Italy, where he met his wife Jetta Umiker, whom he
married in 1924. They settled in Rome, where they stayed until 1935. During these 11 years, Escher would
travel each year throughout Italy, drawing and sketching for the various prints he would make when he
returned home.
Many of these sketches he would later use for various other lithographs and/or woodcuts and wood
engravings, for example the background in the lithograph Waterfall stems from his Italian period, or the trees
reflecting in the woodcut Puddle, which are the same trees Escher used in his woodcut "Pineta of Calvi",
which he made in 1932.
He played with architecture, perspective and impossible spaces. His art continues to amaze and wonder
millions of people all over the world. In his work we recognize his keen observation of the world around us
and the expressions of his own fantasies. M.C. Escher shows us that reality is wondrous, comprehensible and
fascinating.
2. Look at Escher’s drawing of “Sky and Water.” How has the artist achieved such an effect? How does this
relate to mathematics? Is this drawing an example of any kind of transformation? What else do you notice
about the picture?
6
3.
3. Pass out a sheet of white paper to the students. Instruct the students to draw a polygon (i.e.: triangle, square,
rhombus, etc.) on the piece of paper and cut it out. Then ask the students to cut out a shape from one side of
the polygon. Have the students slide that shape over to the other side of the polygon. Then ask them to flip
the shape and see how it changes the original polygon.
4. Creating an Escher-Style Tessellation- Pass out another sheet of white paper to the class. With the help of a
Mira and tessellation grid, have the students repeat the curved shape they created in the exercise. They can
use the appropriate tessellation grid to make sure they are creating a straight pattern. Have the students
create rows of these objects. There will be negative space between these rows. By definition a tessellation
cannot have negative space or overlapping objects. Have the students create a new object to fill in these
negative spaces. Once the students have created their Escher-style tessellations they can colour it.
CLOSURE: (10 minutes)
When students are finished, they will use sticky tack or tape to hang their Escher style drawing up
around the classroom. Students will then do a gallery walk and practice critiquing and commenting
on the works of their classmates. Each student will get 3 sticky notes. They have to leave 3 critiques
for 3 different people. When they have wrote it, they stick it beside the person who owns the
drawings. When everyone is finished, students pick up their own work and can take the comments
that are beside their drawing.
Sponge Activity: Students can either add more shapes to their Escher style drawing or try another shape
with a separate piece of paper.
Consolidation: Next class we will be looking at complimentary colours. You will be using complimentary
colours and transformations for your final project for this unit.
7
LESSON #2
Subject: Math and Art 6
Lesson Duration: 90 minutes
Unit: Shape and Space (Transformations)
OUTCOMES FROM ALBERTA PROGRAM OF STUDIES
General Learning Outcomes:
Students will:

Describe and analyze position and motion of objects and shapes.
Specific Learning Outcomes:
Students will:

Perform a combination of translations, rotations and/or reflections on a single 2-D shape, with and without
technology, and draw and describe the image.
LEARNING OBJECTIVES
Students will:
1. experiment with different brush strokes
2. experiment with different types of paint brushes
3. create a colour wheel
4. determine the complimentary colours.
ASSESSMENTS
Observations:
Key Questions:
1. What are the different types of paint brushes
 Students should be engaged with the lesson
we will be using?
at all time. Watch for students who seem
rd
2. Which paint brush would be best for filling
disconnected and ask them 3 level
in a background?
questions to keep them engaged.
3. Which paint brush would be best for
 All students should participate in discussion.
drawing a straight line?
 Students should be actively working on their
4. How are primary colours used to make
colour wheel in the appropriate time slot.
secondary colours?
 Students should be engaged in constructive
5.
Where do complimentary colours appear on
critiques at the end of the lesson.
the colour wheel in relation to one another?
Written Performance Assessments:
 N/A
LEARNING RESOURCES CONSULTED
Resource #1 : https://www.youtube.com/watch?v=iVCz0fJAJzQ
Resource #2: http://www.tigercolor.com/color-lab/color-theory/color-harmonies.htm




MATERIALS AND EQUIPMENT
matching game cards
 SMART BOARD (with sound)
tempera paint for students
 Paper
3 different types of brushes for each group
 colour wheel paper
math journal
PROCEDURE
INTRODUCTION: (10 minutes)
Hook/Attention Grabber:
https://www.youtube.com/watch?v=iVCz0fJAJzQ
Watch video on different types of paintbrush strokes and brushes which pertains to the psychomotor domain.
Today we will be experimenting with using paint brushes as well as mixing colours.
Transition to Body: Assign certain people in each group to get painting supplies, and another student in each
group to grab paper. Each group needs to have red, yellow and blue paint.
8
BODY: (40 minutes)
1) First, students will use a piece of paper to practice working with their paintbrushes. They should use each
type of paint brush that was listed in the video at least once and get a feel for how they differentiate. Students
should feel free to talk with one another about their painting at this point in the lesson. While students are
working, I will be walking around and giving people tips on the use of their brushes.
2) Next, I will get the classes attention and tell them to mix the three primary colours to make the 3 secondary
colours. They should already know how to do this from previous grades so it will mainly serve as a review.
While students are doing this, I will hand out a black wheel for them to make their colour wheel on.
3) As a review : Who can identify a warm color or a cool color on the color wheel? What happens when
I layer warm and cool colors or place them adjacent? Explain to students that a colour wheel is different
colours organized by blending of different colours such as a rainbow in the shape of a circle. Each colour
should naturally flow to the next colour. Students are to use the 3 primary colours and 3 secondary colours to
make their colour wheel. Ask: Is this colour wheel restricted to six colours? Students should understand that
colours come in a variety of shades and the colour wheel is
“infinite.”
4) Ask students to make a guess of what complimentary colours are opposite each other on the colour wheel.
This works for any colour wheel and it doesn’t matter how many colours are on the wheel.
CLOSURE: (10 minutes)
Matching: This activity will get students up and moving as the lesson closes. Each student will be
given a piece of paper. Some have the names of colours, some have a name of a transformation, and
some have a picture. This is a matching game. The student with the picture needs to find the
corresponding transformation shape and complimentary colour combination. Once students find a
group of three that match, students will then find another group of three with different classmates in
it. When students are finished they will sit down for the last two minutes of class
Sponge Activity: The matching game can be repeated several times until there are no more
combinations. If this still isn’t long enough, students can write in their math journal and answer the
question “How do you think transformations are related to art?”
Consolidation: Tomorrow we will wrap up the unit by starting our final project. For our final project, we will
look at stained glass windows. We will be making our own windows and incorporating transformations and
complimentary colours in them. Please feel free to stick around and ask me any questions. Make sure to bring
scissors to class tomorrow.
9
10
LESSON #3
Subject: Math and Art 6
Lesson Duration: 90 minutes
Unit: Shape and Space (Transformations)
OUTCOMES FROM ALBERTA PROGRAM OF STUDIES
General Learning Outcomes:
Students will:

Describe and analyze position and motion of objects and shapes.
Specific Learning Outcomes:
Students will:

Perform a combination of translations, rotations and/or reflections on a single 2-D shape, with and without
technology, and draw and describe the image.
LEARNING OBJECTIVES
Students will:
1. describe transformations visible in a stained glass window
2. determine complimentary colour pairs
3. describe how transformations are used in art
ASSESSMENTS
Observations:
Key Questions:
1. How are transformations used in art?
 Students should be engaged with the lesson
2. What is the importance of symmetry in art
at all time. Watch for students who seem
and why is it appealing to the eye?
disconnected and ask them 3rd level
3. What are the different types of
questions to keep them engaged.
transformations?
 All students should participate in discussion.
 Students should be actively working on their
stained glass window
 Students will take the time to peer review
someone else’s work.
Written Performance Assessments:
 math journal
 description of transformations in stained glass window
MATERIALS AND EQUIPMENT
 black paper
 rulers
 6 different colours of cellophane
 math journals
 scissors
 SMART Board
 glue
PROCEDURE
INTRODUCTION: (10 minutes)
Hook/Attention Grabber: Students will write in their math journal. They should pull out their individual
journals and take 6 minutes to answer the following question: “How do you think transformations are
related to art?”
Transition to Body: Show pictures of stained glass on the SMART BOARD. Before we start our final project lets
look at an example. In Vence, Matisse chapel displays many stained glass windows. Many include
11
transformations.
How has this artist
used his knowledge of transformations to make this window? What colours are used in the window and how do
they relate to each other? What is appealing about transformations in art.
BODY: (40 minutes)
1) Take a look at what is stained glass? Have some people volunteer their answers and then read: The
term stained glass can refer to coloured glass as a material or to works created from it. Throughout its
thousand-year history, the term has been applied almost exclusively to the windows of churches, mosques
and other significant buildings. Although traditionally made in flat panels and used as windows, the creations
of modern stained glass artists also include three-dimensional structures and sculpture.
Modern vernacular usage has often extended the term "stained glass" to include domestic leadlight and objets
d'art created from came glasswork exemplified in the famous lamps of Louis Comfort Tiffany.
As a material stained glass is glass that has been coloured by adding metallic salts during its manufacture. The
coloured glass is crafted into stained glass windows in which small pieces of glass are arranged to form patterns or
pictures, held together (traditionally) by strips of lead and supported by a rigid frame. Painted details and yellow stain
are often used to enhance the design. The term stained glass is also applied to windows in which the colours have
been painted onto the glass and then fused to the glass in a kiln.
Stained glass, as an art and a craft, requires the artistic skill to conceive an appropriate and workable design, and the
engineering skills to assemble the piece. A window must fit snugly into the space for which it is made, must resist
wind and rain, and also, especially in the larger windows, must support its own weight. Many large windows have
withstood the test of time and remained substantially intact since the late Middle Ages. In Western Europe they
constitute the major form of pictorial art to have survived. In this context, the purpose of a stained glass window is
not to allow those within a building to see the world outside or even primarily to admit light but rather to control it.
For this reason stained glass windows have been described as 'illuminated wall decorations'. What do you think
stained glass has to do with math or transformations?
2) Go through the rubric with the students. Make sure students understand how to
succeed in this assignment. The paper needs to have four corners each portraying a
different set of complimentary colours. Show students an example and give them the
directions for making it. First, sketch the pattern you want on the black paper. Once you
have a pattern that includes transformations Cut out the inside pieces. You then use
cellophane and glue to fill in the holes. It is a bit tedious to get the cellophane lined up
with the paper so make sure students take their time.
3) The supplies for each student will be set out for them. They should first take the black
12
piece of paper and sketch a drawing of the pattern for their window. Make sure that
students remember the frame must be divided into four sections. As students are
working, walk around and help students. Ask questions about complimentary colours
and transformations: Do you have the colours in the right spot? Why are these two
colours complimentary? Can you show me an example of a reflection? How is it a
reflection?
CLOSURE: (10 minutes)
When students are finished, they will complete the last part of their project. They need to describe to
examples of each type of transformation in their window. Make sure students are aware of how to
describe this. Do a quick review using someone’s completed product. Students are to hand in their
stained glass, and their description of the transformations. When students are done, they will do a a
peer review of a friends project.
Sponge Activity: Student can add and make changes to their math journal for the question: How do you
think transformations are related to art? After this lesson, students should have a more detailed answer
to the question.
13