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The Power of Expression
MATHEMATICS AND
ART
Developed by:
Paula Ridley
Concept:
Power
Topics:
Mathematics, Geometry, Algebra, Art
Grade Level/Subject:
Fifth Grade Gifted Students/Mathematics
The
connection between mathematics and art goes back thousands of
years. Mathematics has been used in the design of Gothic
cathedrals, Rose windows, oriental rugs, mosaics and tilings.
Geometric forms were fundamental to the cubists and many abstract
expressionists, and award-winning sculptors have used topology as
the basis for their pieces. Dutch artist M.C. Escher incorporated
math in his art through the use of Möbius bands,
tessellations, deformations, reflections, Platonic solids,
spirals, symmetry, and the hyperbolic plane. Mathematicians and artists continue to create startling works in all media
that enable us to visualize mathematics through art via origami,
computer-generated landscapes, tessellations, fractals, and more.
In
this curriculum, students will be given opportunities to work
collaboratively and independently. They will engage in anchor
activities, creative problem solving, divergent thinking,
think-pair-share, perspective and visualization activities to
enable them to communicate “The Power of Expression.”
Concept:
Power
Topics:
- Visual Art and Production
- Cultural Context and Art History
- Manipulatives and measuring instruments
Grade
Level/Subject:
Fifth Grade Gifted Mathematics
Objectives/Outcomes
- Students
will estimate and measure length using authentic measuring
devices.
- Students
will identify and describe situations representing the use of
perimeter, and use measuring devices to find perimeter in both
standard and nonstandard units of measure.
- Students
will investigate, identify, draw representations and describe
the relationship between and among points, lines, line
segments and rays using a straightedge or ruler, and
distinguish whether lines are parallel, intersecting, or
perpendicular.
- Students
will identify an angle, name the sides and vertices, and
describe it relative to a right angle.
- Students
will measure and draw angles using a protractor and classify
as right, acute, obtuse or straight.
- Students
will distinguish, draw and label triangles by exploring
interior angles.
- Students
will verify the Pythagorean Theorem by measuring and applying
it to find the missing length of a side of a right triangle.
- Students
will name the location of points on grids with ordered pairs,
and collect, organize, and display data in line and bar
graphs.
- Students
will learn to extend a given pattern using concrete materials
and tables.
- Students
will solve problems involving pattern identification and
completion of patterns.
- Students
will create and solve multi-step practical problems involving
computation and estimation using paper and pencil, mental
calculation, and calculators.
- Students
will illustrate and determine the perimeter and area of
polygons.
- Students
will find the volume of rectangular prisms.
- Students
will identify, describe, create and solve problems by finding
the diameter, radius, chord, and circumference of a circle
realizing it is not a true polygon, but a closed figure.
- Students
will identify the ordered pair for a point and locate in
appropriate quadrant.
- Students
will write verbal expressions and apply order of operations to
evaluate and solve problems.
- Students
will synthesize information from a variety of sources and use
available technology for research and editing final copy.
- Students
will use writing as a tool for learning in all subjects.
- Students
will use art media, subject matter, and symbols for expression
and communication.
- Students
will demonstrate understanding of and apply the elements of
art and the principles of design and the ways they are used in
the visual arts.
- Students
will solve visual arts problems with originality, flexibility,
fluency, and imagination.
- Students
will study various artists whose mathematical principles
influenced their artwork.
- Students
will develop understanding of the relationship of the visual
arts to history, culture, and other fields of knowledge.
- Students
will use materials, methods, information, and technology in a
safe and ethical manner.
- Students
will interpret, reflect upon, and evaluate the
characteristics, purposes and merits of their work and the
work of others.
- Students
will identify, analyze, and apply criteria for making visual
aesthetic judgments of their work and the work of others.
- Students
will develop aesthetic awareness and a personal philosophy
regarding the nature of, meanings in, and values in the visual
arts.
- Students
will develop awareness of copyright and royalty requirements
when exhibiting, producing, or otherwise using the works of
others.
Key
Generalizations:
- Power
enables us or others to overcome.
- Power
is the ability to influence.
- Power
evolves from knowledge.
- Power
may be used or abused.
- Power
may take many forms.
Essential
Questions:
- How
are geometry and mathematical expressions used to solve
meaningful problems and make connections to the world outside
the classroom?
- What
is the relationship between geometry, higher-level mathematical
concepts and visual communication an d production?
- How
can patterns guide and influence us to make discoveries about
our world and ourselves?
- What
media and processes are needed to create visual expressions?
STANDARDS OF LEARNING
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MATHEMATICS STANDARDS OF LEARNING
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Grade 5
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Computation and Estimation
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5.3
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The
student will create and solve problems involving addition,
subtraction, multiplication, and division of whole numbers,
using paper and pencil, estimation, mental computation, and
calculators
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Measurement
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5.8
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The
student will describe and determine the perimeter of a polygon
and the area of a square, rectangle, and triangle, given the
appropriate measures.
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5.9
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The
student will identify and describe the diameter, radius,
chord, and circumference of a circle.
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5.10
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The
student will differentiate between area and perimeter and
identify whether the application of the concept of perimeter,
area or volume is appropriate for a given situation.
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5.13
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The
student will measure and draw right, acute, and obtuse angles
and triangles, using appropriate tools.
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Geometry
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5.14
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The
student will classify angles and triangles as right, acute, or
obtuse
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5.15
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The
student, using two-dimensional (plane) figures (square,
rectangle, triangle, parallelogram, rhombus, kite, and
trapezoid) will
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Recognize, identify, describe, and analyze their
properties in order to develop definitions of these figures;
·
Identify and explore congruent, non-congruent,
and similar figures;
·
Investigate and describe the results of combining
and subdividing shapes;
·
Identify and describe a line of symmetry; and
·
Recognize the images of figures resulting from
geometric transformations such as translation (slide),
reflection (flip), or rotation (turn).
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Patterns, Functions, and Algebra
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5.20
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The
student will analyze the structure of numerical and geometric
patterns (how they change or grow) and express the
relationship, using words, tables, graphs or mathematical
sentence. Concrete materials and calculators will be used.
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5.21
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The
student will
- Investigate
and describe he concept of variable;
- Use
a variable expression to represent a given verbal
quantitative expression involving one operation; and
- Write
an open sentence to represent a given mathematical
relationship, using a variable.
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Grade 6
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Measurement
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The
student will determine if a problem situation involving
polygons of four or fewer sides represents the application of
perimeter or area and apply the appropriate formula.
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6.12
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The
student will
·
Solve problems involving the circumference and/or
area of a circle when given the diameter or radius; and
·
Derive
approximations for pi from measurements for circumference and
diameter, using concrete materials or computer model.
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6.13
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The
student will
·
Estimate angle measures using 45°, 90°, and 180° as referents and use the appropriate tools to measure
the given angles; and
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Measure and draw right, acute, and obtuse angles
and triangles.
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Geometry
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6.14
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The
student will identify, classify, and describe the
characteristics of plane figures, describing their
similarities, difference, and defining properties.
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6.15
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The
student will determine congruence of segments, angles, and
polygons by direct comparison, given their attributes.
Examples of noncongruent and congruent figures will be
included.
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6.16
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The
student will construct the perpendicular bisector of a line
segment and an angle bisector.
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6.17
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The
student will sketch, construct models of, and classify solid
figures (rectangular prisms, cones, cylinders, and pyramids).
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Patterns, Functions, and Algebra
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6.21
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The
student will recognize, describe, and extend a variety of
numerical and geometric patterns.
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Grade 7
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Number and Number Sense
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7.3
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The student will simply
expressions by using order of operations, mental mathematics,
and appropriate tools. Exponents will be included.
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Measurement
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7.7
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The
student, given appropriate dimensions, will
·
Estimate and find the area of polygons by
subdividing them into rectangles and right triangles; and
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Apply perimeter and are formulas in practical
situations.
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7.8
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The
student will investigate and solve problems involving the
volume and surface area of rectangular prisms and cylinders,
using concrete materials and practical situations to develop
formulas.
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Geometry
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7.9
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The student will compare and contrast the following
quadrilaterals: a parallelogram, rectangle, square, rhombus,
and trapezoid. Deductive reasoning and inference will be used
to classify quadrilaterals.
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7.11
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The
student will identify and draw the following polygons:
pentagon, hexagon, heptagon, octagon, nonagon, and decagon.
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Patterns, Functions, and Algebra
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7.22
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The
student will investigate and describe functional
relationships, including the number of sides of a regular
polygon and the sum of the measures of the interior angles.
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Grade 8
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Measurement
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8.6
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The
student will verify by measuring and describe the
relationships between vertical angles, supplementary angles,
and complementary angles and will measure and draw angles of
less than 360°
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Geometry
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8.11
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The
student will verify the Pythagorean Theorem by measuring and
then applying the Pythagorean Theorem to find the missing
length of a side of a right triangle when the lengths of the
other two sides are given.
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Geometry
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G3
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The
student will solve practical problems involving complementary,
supplementary,
and congruent angles that include vertical angles, angles
formed
when
parallel lines are cut by a transversal, and angles in
polygons.
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G7
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The
student will solve practical problems involving right
triangles by using the
Pythagorean
Theorem, properties of special right triangles, and right
triangle
trigonometry.
Solutions will be expressed in radical form or as decimal
approximations.
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G9
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The
student will use measures of interior and exterior angles of
polygons to solve
problems.
Tessellations and tiling problems will be used to make
connections to
art,
construction, and nature.
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G10
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The
student will investigate and solve practical problems
involving circles, using
properties
of angles, arcs, chords, tangents, and secants. Problems will
include
finding
arc length and the area of a sector, and may be drawn from
applications of
architecture,
art, and construction.
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G11
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The
student will construct a line segment congruent to a given
line segment, the
bisector
of a line segment, a perpendicular to a given line from a
point not on the
line,
a perpendicular to a given line at a point on the line, the
bisector of a given
angle,
and an angle congruent to a given angle.
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VISUAL ARTS STANDARDS OF LEARNING
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Grade 5
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Visual Communication and Production
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5.1
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The
student will synthesize information to create works of art.
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5.2
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The
student will use primary colors and black and white to mix a
variety of hues, shades, and textures to create works of art.
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5.3
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The
student will use the elements of art – line, shape, form,
color, value, texture, and space – to express ideas, images
and emotions.
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5.4
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The
student will create repeating patterns, using translations
(slides), reflection (flip), and rotation (turn).
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5.5
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The
student will use the principles of design, including
proportion, rhythm, balance, emphasis,
variety,
contrast, and unity, to express ideas and create images.
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The
student will develop ideas for works of art by brainstorming,
conducting research,
and
making preliminary sketches.
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5.9
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The
student will demonstrate an understanding of symbolic meanings
by incorporating
symbols
in a work of art.
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5.10
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The
student will use linear perspective in a work of art.
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5.11
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The
student will use linear perspective in a work of art.
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5.12
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The
student will express ideas through artistic choices of media,
techniques, and subject matter.
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5.13
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The
student will use technology to produce a work of art.
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Cultural
Context and Art History
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5.19
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The
student will identify the influences of historic events,
subject matter, and media in works of art.
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5.20
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The
student will research artists from a variety of cultures and
the works of art they
have
produced.
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5.22
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The
student will research, compare, and contrast the art of two
cultures, using
contemporary
technology.
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Judgment
and Criticism
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5.24
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The
student will discuss an artist’s point of view based on
evidence from written
sources.
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5.26
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The
student will analyze works of art based on visual properties
and historical context.
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5.27
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The
student will apply specific criteria to assess a finished
product.
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Aesthetics
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5.28
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The
student will discuss the role of art and artists in society.
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5.31
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The
student will articulate reasons for establishing preferences
among works of art,
using
appropriate art vocabulary.
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GRADE 6
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Visual Art and Production
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The
student will solve design problems, using color relationships
selected from the color
wheel.
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6.2
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The
student will use the principles of design, including
proportion, rhythm, balance, emphasis, variety, and unity, to
express ideas and create images.
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6.5
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The
student will use visual memory skills to produce a work of
art.
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6.6
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The
student will use appropriate art media and techniques to
create both visual and
tactile
textures in works of art.
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6.9
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The
student will utilize fantasy as a means of expression in works
of art.
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6.10
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The
student will use computer graphics and computer-generated text
to create original
works
of art.
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Cultural
Context and Art History
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6.12
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The
student will identify the components of an artist’s style,
including materials,
design,
technique, and subject matter.
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6.13
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The
student will identify major art movements in American culture
from 1877 to the
present,
with emphasis on relating these movements to changes in
science and
technology.
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6.14
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The
student will identify how artists contribute to society.
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Judgement
and Criticism
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6.15
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The
student will discuss the ways that art can be persuasive.
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6.17
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The
student will demonstrate inquiry skills and appropriate art
vocabulary for
1.
describing
works of art;
2.
responding
to works of art;
3.
interpreting
works of art; and
4.
evaluating
works of art.
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6.18
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The
student will interpret the ideas and emotions expressed in
works of art.
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6.19
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The
student will identify the relationship between art processes
and final solutions.
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Aesthetics
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6.22
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The
student will generate philosophical questions regarding
meanings in works of art.
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6.24
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The
student will explain orally and in writing the means by which
visual art evokes
sensory
and emotional responses.
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GRADE 7
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Visual
Art and Production
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7.4
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The
student will use line variations, including directionality,
width, and implied line, to create contrasting qualities in a
composition.
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7.5
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The
student will communicate information and ideas through
illustration.
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7.7
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The
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