2015 – 2016 Curriculum Thematic Unit
Grade: 9th – 10th
Course: CCR Geometry
Approximate Time Frame:
Unit Name: Geometric Transformations
2 Week Plan ---- (10 days)
Essential Question(s): What impact does each type of
transformation have on the location, size, and orientation
of geometric objects? How might each of the geometric
transformations be represented algebraically? What is the
relationship between transformations the produce similar
figures and those that produce congruent figures?
Unit Overview: The study of geometric transformations gives students a visual perspective of the
outcome of performing translations, rotations, dilations, and reflections. In the unit, students will
build on their eighth grade experiences to help connect geometric and algebraic representations
by using the coordinate system to verify geometric relationships and prove geometric theorems.
They also apply reasoning to complete geometric constructions and explain why they work.
Essential Vocabulary: preimage, image, dilation, center
of dilation, isometry, symmetry, scale factor or magnitude,
reflection, translation, rotation, angle of rotation, center of
rotation, transformation, composition of transformations,
geometric proof, construction, similarity, congruence
Unit Skills: Identify polygons as represented on the coordinate plane and verify their properties;
Calculate distances, areas, and perimeters on the coordinate plane using Pythagorean theorem
and/or the distance formula; Investigate parallel and perpendicular slopes; Construct parallel and
perpendicular lines; Describe translations, reflections, rotations, and dilations; Transform figures
in the coordinate plain using multiple tools; Use multiple methods to prove theorems; Develop
definitions for similarity and congruence and use them to verify properties of figures.
Standards:
Suggested Activities:
Resources:
G-CO.1 Know precise definitions of angle, circle, parallel
line, perpendicular line, and line segment, based on the
undefined notion of point, line, distance along a line, and
distance around a circular arc.
Students complete a modeling intersections activity by labeling
two index cards according to a set of given instructions. It may
be more helpful to give students a visual of the directions. They
cut the cards along the dotted line, slide cards together, and
answer a set of questions.
Teacher/Student Textbooks
G-CO.2 Represent transformations in the plane using, e.g.,
transparencies and geometry software; describe
transformations as functions that take points in the plane
as inputs and give other points as outputs. Compare
transformations that preserve distance and angle to those
that do not (e.g., translation versus horizontal stretch).
G-CO.3 Given a rectangle, parallelogram, trapezoid, or
regular polygon, describe the rotations and reflections
that carry it onto itself.
G-CO.4 Develop definitions of rotations, reflections, and
translations in terms of angles, circles, perpendicular
lines, parallel lines, and line segments.
G-CO.5 Given a geometric figure and a rotation, reflection,
or translation, draw the transformed figure using e.g.,
graph paper, tracing paper, or geometry software. Specify
a sequence of transformations that will carry a given
figure onto another.
 When the cards aren’t together, what is the intersection of
lines 𝐴𝐵 and 𝐶𝐷 ?
 With the cards together, what is the intersection of 𝐶𝐷 and
𝐸𝐹 ?
 What is the intersection of Plane M?
 Are 𝐶𝐷 and 𝐸𝐹 coplanar? Explain.
Students work in grounds to investigate translations using patty
paper and verify results with geometry software such as Mira or
Sketchpad.
Students work in pairs to check understanding of the geometric
definitions. Students are able to earn energy points and badges
for answering several questions in a row. The questions take
the form of multiple guess, matching, and true and false with
interactive hints. They watch a video lesson if they get stuck.
https://www.khanacademy.org/math/geometry/intro_euclid
/e/geometric-definitions
Illustrative Mathematics Tasks
o Is This a Rectangle?
https://www.illustrativemat
hematics.org/contentstandards/tasks/1302
o Unit Squares & Triangles
https://www.illustrativemat
hematics.org/contentstandards/tasks/918
o A Midpoint Miracle
https://www.illustrativemat
hematics.org/contentstandards/tasks/605
o Dilating a Line
https://www.illustrativemat
hematics.org/contentstandards/tasks/602
2015 – 2016 Curriculum Thematic Unit
Grade: 9th – 10th
Course: CCR Geometry
Approximate Time Frame:
Unit Name: Geometric Transformations
2 Week Plan ---- (10 days)
G-CO.6 Use geometric descriptions of rigid motions to
transform figures and to predict the effect of a given rigid
motion on a given figure; given two figures, use the
definition of congruence in terms of rigid motion to decide
if they are congruent.
G-CO.9 Prove theorems about lines and angles.
Theorems include: vertical angles are congruent;
when a transversal crosses parallel lines, alternate
angles are congruent and corresponding angles
are congruent.
G-CO.11 Prove theorems about parallelograms.
Theorems include: opposite sides are congruent,
opposite angles are congruent, the diagonals of a
parallelogram bisect each other, and conversely,
rectangles are parallelograms with congruent
diagonals.
G-CO.12 Make formal geometric constructions with a
variety of tools and methods (compass and straightedge,
string, reflective devices, paper folding, dynamic
geometric software, etc.).
G-SRT.1 Verify experimentally the properties of dilations
given by a center and a scale factor:
a. A dilation takes a line not passing through the
center of the dilation to a parallel line, and leaves a
line passing through the center unchanged.
b. The dilation of a line segment is longer or shorter in
the ratio given by the scale factor.
G-SRT.2 Given two figures, use the definition of similarity
in terms of similarity transformations to decide if they are
similar; explain using similarity transformations the
meaning of similarity for triangles as the equality of all
corresponding pairs of angles and the proportionality of
all corresponding pairs of a sides.
Lead a discussion with students about reflections in a mirror.
Cut out different geometric figures one at a time, and position
them so that the students can see them in the mirror. Break the
students into groups and have them to answer questions about
the similarities and differences in the sizes and orientations of
the figures and their reflection images.
 Also ask about the distance of the figure from the mirror
and the perceived distance of the image from the mirror.
 Move the figure closer to or farther from the mirror so that
students understand that the figure and its image appear to
be the same distance from the mirror.
 Be sure that the students understand the terms “image” and
“equidistant” at this time.
Students use the concept of symmetrical motion in a live plane
by designing and/or performing a dance routine. Metaphors of
Flip, Turn, Slide, Spin, Shrink, and Stretch will be used initially
in place of the geometric transformation vocabulary. Students
will work cooperatively in groups of 3-4. Students will evaluate
the performance of others using a teacher scoring rubric.
Students use a square to investigate other polygonal shapes
that can be formed. Students work with these polygons to make
designs that will later constitute cooperatively designed quilts.
The quilts will be made by translating, rotating, or reflecting a
thirty-six patch design. The completed quilts will then be used
for a discussion of area and perimeter.
Have the students perform a translation, reflection, and rotation
with their names.
Students work in pairs to complete a BrainPOP adventure, in
which Tim and Moby present a geometry lesson on symmetry
and transformation by translating, rotating, and reflecting in the
kitchen! Tim shows students how to describe each of type of
transformation using measurements of distance, direction, and
angle, and by identifying the center point and axis.
http://educators.brainpop.com/bp-topic/transformation/
o Are They Similar?
https://www.illustrativemat
hematics.org/contentstandards/tasks/603
o Midpoint of the Sides of a
Parallelogram
https://www.illustrativemat
hematics.org/contentstandards/tasks/35
o Building a Tile Pattern by
Reflecting Hexagon
https://www.illustrativemat
hematics.org/contentstandards/tasks/1338
o Building a Tile Pattern by
Reflecting Octagons
https://www.illustrativemat
hematics.org/contentstandards/tasks/1337
Content Connections:
2015 – 2016 Curriculum Thematic Unit
Grade: 9th – 10th
Course: CCR Geometry
Approximate Time Frame:
Unit Name: Geometric Transformations
3 Week Plan ---- (10 days)
G-GBE.4 Use coordinates to prove simple geometric
theorems algebraically. (For example, prove or disprove
that a figure defined by four given points in the coordinate
plane is a rectangle.)
G-GBE.5 Prove the slope criteria for parallel and
perpendicular lines and use them to solve geometric
problems (e.g., find the equation of a line parallel and
perpendicular to a given line that passes through a given
point).
G-GBE.7 Use coordinates to compute perimeters of
polygons and areas of triangles and rectangles, e.g.,
using the distance formula.
Students are asked to create a game using the transformations
and series of transformations as a real-world extension of the
study of congruent transformations.
Students use patty paper to fold different types of triangles and
demonstrate medians, altitudes, and bisectors.
Students use patty paper, compasses, and straightedges to do
constructions of angles, angle bisectors, segments, segment
bisectors, perpendicular bisectors, altitudes, and other figures.
Students work in pairs to investigate the perimeter and area of
a square formed with string. They measure a side of the square
and calculate its perimeter and area. Cut the string in half and
repeat procedure. The results are recorded to determine the
relationship between change in perimeter and resulting area.
o Reflected Triangles
https://www.illustrativemat
hematics.org/contentstandards/tasks/31
o Tessellations of the Plane
https://www.illustrativemat
hematics.org/contentstandards/tasks/1125
Patty Paper, Protractors, and
Rulers
GeoBoards and Rubberbands
Teacher & Student iPads with
Insight 360 Software
Create jumbled proofs. On index cards, write statements and
reasons to a two column proof (one per card). Shuffle cards,
distribute them, and then have students put in logical order.
Students construct a moveable model of parallel lines cut by a
transversal from three strips of tag board fastened together with
brads. They measure the different angles and show the
relationship among the angles.
Students investigate designs by Escher and other tessellation
sites and use them to create original tessellations.
Content Connections: