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FAYETTE COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 8
Topic 8G
Big Idea(s)
What enduring understandings are
essential for application to new
situations within or beyond this
content?
Essential Question(s)
What questions will provoke and
sustain student engagement while
focusing learning?
Enduring Standard(s)
Which standards provide
endurance beyond the course,
leverage across multiple
disciplines, and readiness for the
next level?
Transformations, Similarity & Congruence
Transformations:
Translations
Reflections
Rotations
Dilations
Similar Figures
Parallel Lines Congruence
Understand congruence and similarity using physical models,
transparencies, or geometry software.
What do transformations represent?
How can I use a model to show congruencies exist when parallel lines
are cut by a transversal?
Enduring Understandings
 Coordinate geometry can be a useful tool for understanding
geometric shapes and transformations.
 Reflections, translations, and rotations are actions that produce
congruent geometric objects.
 A dilation is a transformation that changes the size of a figure, but
not the shape.
 The notation used to describe a dilation includes a scale factor
and a center of dilation. A dilation of scale factor k with the center
of dilation at the origin may be described by the notation (kx, ky).
 If the scale factor of a dilation is greater than 1, the image resulting
from the dilation is an enlargement. If the scale factor is less than 1,
the image is a reduction.
 Two shapes are similar if the lengths of all the corresponding sides
are proportional and all the corresponding angles are congruent.
 Two similar figures are related by a scale factor, which is the ratio of
the lengths of the corresponding sides.
 Congruent figures have the same size and shape. If the scale
factor of a dilation is equal to one, the image resulting from the
dilation is congruent to the original figure.
 When parallel lines are cut by a transversal, corresponding,
alternate interior and alternate exterior angles are congruent.
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
Curriculum and Instruction
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FAYETTE COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 8
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Supporting Standard(s)
Which related standards will be
incorporated to support and
enhance the enduring standards?
Instructional Outcomes
What must students learn by the
end of the unit?
Curriculum and Instruction
Standards for Mathematical Content
Geometry
Understand congruence and similarity using physical models,
transparencies, or geometry software.
8.G.A.1 Verify experimentally the properties of rotations, reflections,
and translations:
8.G.A.1a Lines are taken to lines, and line segments to line segments of
the same length.
8.G.A.1b Angles are taken to angles of the same measure.
8.G.A.1c Parallel lines are taken to parallel lines.
8.G.A.2 Understand that a two-dimensional figure is congruent to
another if the second can be obtained from the first by a sequence of
rotations, reflections, and translations; given two congruent figures,
describe a sequence that exhibits the congruence between them.
8.G.A.3 Describe the effect of dilations, translations, rotations, and
reflections on two-dimensional figures using coordinates.
8.G.A.4 Understand that a two-dimensional figure is similar to another if
the second can be obtained from the first by a sequence of rotations,
reflections, translations, and dilations; given two similar twodimensional figures, describe a sequence that exhibits the similarity
between them.
8.G.A.5 Use informal arguments to establish facts about the angle sum
and exterior angle of triangles, about the angles created when
parallel lines are cut by a transversal, and the angle-angle criterion for
similarity of triangles. For example, arrange three copies of the same
triangle so that the sum of the three angles appears to form a line, and
give an argument in terms of transversals why this is so.
I can…
 determine if one object is a transformation of another.
 transform a figure using rotations, reflections, translations.
 determine a sequence of transformations between two
congruent figures.
 dilate, translate, rotate, and reflect a figure in the coordinate
plane.
 describe the effects of a dilation, reflection, rotation, or
translation on the coordinates of a figure in the coordinate
plane.
 determine the sequence of transformations between two similar
objects.
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FAYETTE COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 8
calculate the angle sum of a triangle(polygon).
calculate the measure of an exterior angle of a
triangle(polygon).
 find the angles formed when parallel lines are cut by a
transversal.
 determine if two triangles are similar.
Students who demonstrate understanding can…
 verify experimentally the properties of rotations, reflections, and
translations.
 understand and describe a sequence of transformations to
create congruent figures.
 describe the effects of rotations, reflections, translations and
dilations of two dimensional congruent and similar figures using
coordinates.
 determine the angle sum and exterior angles of triangles.
 describe and determine angles created when parallel lines are
cut by a transversal.
 describe similarity of triangles using the angle-angle criterion.
Essential Vocabulary


Performance Expectations
What must students be able to do
by the end of the unit to
demonstrate their mastery of the
instructional outcomes?
Essential Vocabulary
What vocabulary must students
know to understand and
communicate effectively about
this content?
adjacent angles - Two angles that share both a side and a vertex.
Alternate Interior Angles - When two lines are crossed by another line
(which is called a transversal), the pairs of angles on opposite sides of
the transversal but inside the two lines are called alternate interior
angles.
corresponding angles - When two lines are crossed by a transversal,
the angles in matching corners are called corresponding angles.
congruent - Two plane or solid figures are congruent if one can be
obtained from the other by rigid motion (a sequence of rotations,
reflections, and translations). Having the same size and shape.
dilation - A transformation that moves each point along the ray
through the point emanating from a fixed center, and multiplies
distances from the center by a common scale factor.
exterior angle - An exterior angle is the angle between one side of a
polygon and the extension of an adjacent side. An exterior angle of a
triangle is equal to the sum of the opposite interior angles.
interior angle - An angle whose sides are determined by two
consecutive sides of a polygon.
line of symmetry - A line across the figure such that the figure can be
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FAYETTE COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 8
folded along the line into matching parts; Line that divides a
geometric figure into two congruent portions.
parallel lines - Coplanar lines that do not intersect.
perpendicular lines - A line that forms a right angle with another line or
segment.
reflection - A transformation resulting from a flip.
rotation - A transformation in which a figure is rotated through a given
angle, about a point.
scale factor - A number which multiples some quantity; the ratio of any
two corresponding lengths in two similar geometric figures.
similar polygons - Two polygons are similar if their corresponding sides
are proportional.
supplementary - Two angles are supplementary if their sum is 180
degrees.
transformation - A change in the position, shape, or size of a geometric
figure.
translation - A transformation, or change in position, resulting from a
slide with no turn.
transversal - A line that intersects two other lines.
vertical angles - A pair of opposite angles that is formed by
intersecting lines.
Supporting Vocabulary
alternate exterior angles
angle of rotation
enlargement
image
line of reflection
reduction
reflection symmetry
rotational symmetry
Common Core Glossary
Curriculum and Instruction
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FAYETTE COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 8
http://www.corestandards.org/Math/Content/mathematicsglossary/glossary/
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Subject and Grade Level
Unit Title
Summative Assessment of
Learning
Mathematics 8G
Transformations, Similarity, and Congruence
In what way will students meet the
performance expectations to
demonstrate mastery of the
standards?
Instructional Outcomes
How will the instructional outcomes
be sequenced into a
progression of learning?
Learning Activities
What well-designed progression of
learning tasks will intellectually
engage students
in challenging content?
Formal Formative Assessments
What is the evidence to show
students have learned the lesson
objective and are progressing
toward mastery of the instructional
outcomes?
Integration Standards
What standards from other
disciplines will enrich the learning
experiences for the students?
Resources
Resources
What resources will be utilized to
enhance student learning?
Curriculum and Instruction
2014-2015
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