1. science
2. mathematics
3. geometry

Unit #:
2
Subject(s): Math II
Grade(s): 9-12
Designer(s): Kristen Fye, Ashley Pethel, Kim Stilwill, Andrea Harkey
STAGE 1 – DESIRED RESULTS
Unit Title: Transformations
Transfer Goal(s):
 Students will be able to independently use their learning to accurately describe and model transformations that occur in the real world.
Enduring Understanding:
Essential Questions:
Students will understand that…
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Transformations (rotations, reflections, translations, dilations) can be
described and performed through movements in the coordinate plane.
Transformations can be represented in a variety of ways.
Isometric movements can be achieved in a variety of transformations
or a combination of transformations.
Transformations have the ability to change an object’s size, but not its
shape.
Transformations have real world applications.
Lines can be isometric through dilations if the line passes through the
origin.
Lines that are dilated that do not pass through the origin map to a line
parallel to itself.
There is a connection between changes in the constants and
coefficients in a function and the graphical representation of that
same function.
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Where can you apply transformations in the real world?
What are the connections between transformations and spatial
reasoning?
How do points, lines, and angles influence transformations of 2dimensional figures?
How do you describe isometry in terms of transformations?
How do you represent and describe a transformation?
How can you transform a line that is parallel to itself?
What transformations can be represented by changes in the constants
and coefficients of a parent function?
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last revision 10/9/14
1
Unit #:
2
Subject(s): Math II
Grade(s): 9-12
Students will know:
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Geometric vocabulary
Geometric and algebraic symbols
Transformations are changes to size or location
Properties of isometric figures
The effects of the coefficients and constants on transformations of
linear and quadratic functions.
Vertex form of a quadratic function
Designer(s): Kristen Fye, Ashley Pethel, Kim Stilwill, Andrea Harkey
Students will be able to:
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Graph on the coordinate plane
Perform transformations graphically and algebraically
Identify transformations as isometric
Identify transformations of linear and quadratic functions based
function structure.
Describe transformations in geometric terms
Derive algebraic rules for transformations
Represent transformations in the plane
Compare and contrast transformations
Specify transformations that map figures onto similar figures or onto
themselves.
Vertically stretch and compress linear and quadratic functions.
Vertically and horizontally translate linear and quadratic functions.
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last revision 10/9/14
2
Unit #:
2
Subject(s): Math II
Grade(s): 9-12
Designer(s): Kristen Fye, Ashley Pethel, Kim Stilwill, Andrea Harkey
STAGE 1– STANDARDS
F.BF.3
G.CO.2
G.CO.3
G.CO.4
Common Core State Standard(s)
Build a function that models a relationship between two
quantities.
Identify the effect on the graph of replacing f(x) by f(x)+k, k f(x), f(kx)
and f(x+k) for specific values of k (both positive and negative); find
the value of k given the graphs. Experiment with cases and illustrate an
explanation of the effects on the graph using technology. Include
recognizing even and odd functions from their graphs and algebraic
expressions for them.
Note: At this level, extend to quadratic functions and k f(x).
Experiment with transformations in the plane.
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).
Given a rectangle, parallelogram, trapezoid, or regular polygon,
describe the rotations and reflections that carry it onto itself.
Develop definitions of rotations, reflections, and translations in terms
of angles, circles, perpendicular lines, parallel lines, and line segments.
ACT Standards
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G.CO.5
G.CO.6
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.
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Understand congruence in terms of rigid motions.
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 motions
to decide if they are congruent.
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Interpret and use information from graphs in the coordinate
plane
Recognize special characteristics of a parabola (ex. the vertex
of a parabola)
Identify characteristics of graphs based on a set of conditions
or on a general equations such as y = ax2 + c
Interpret and use information from graphs in the coordinate
plane
Apply properties of 30° - 60° - 90°; 45° - 45° - 90°; similar,
and congruent triangles
Apply properties of 30° - 60° - 90°; 45° - 45° - 90°; similar,
and congruent triangles
Identify characteristics of graphs based on a set of conditions
or on a general equations such as y = ax2 + c
Solve problems integrating multiple algebraic and/or
geometric concepts
Draw conclusions based on a set of conditions
Solve multistep geometry problems that involve integrating
concepts, planning, visualization, and/or making connections
with other content areas
Interpret and use information from graphs in the coordinate
plane
Solve multistep geometry problems that involve integrating
concepts, planning, visualization, and/or making connections
with other content areas
Interpret and use information from graphs in the coordinate
plane
Apply properties of 30° - 60° - 90°; 45° - 45° - 90°; similar,
and congruent triangles
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last revision 10/9/14
3
Unit #:
G.GPE.6
G.SRT.1a
G.SRT.1b
G.MG.11
G.MG.31
2
Subject(s): Math II
Grade(s): 9-12
Designer(s): Kristen Fye, Ashley Pethel, Kim Stilwill, Andrea Harkey
Use coordinates to prove simple geometric theorems algebraically.
Find the point on a directed line segment between two given points
that partitions the segment in a given ratio.
Understand similarity in terms of similarity transformations
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.
Understand similarity in terms of similarity transformations
Verify experimentally the properties of dilations given by a center and
a scale factor:
b. The dilation of a line segment is longer or shorter in the ratio given
by the scale factor.
Apply geometric concepts in modeling situations
Use geometric shapes, their measures, and their properties to describe
objects (e.g., modeling a tree trunk or a human torso as a cylinder).
Apply geometric concepts in modeling situations
Apply concepts of density based on area and volume in modeling
situations (e.g., persons per square mile, BTUs per cubic foot).
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last revision 10/9/14
4
Unit #:
2
Subject(s): Math II
Performance Tasks:
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Grade(s): 9-12
Designer(s): Kristen Fye, Ashley Pethel, Kim Stilwill, Andrea Harkey
STAGE 2 – ASSESSMENT EVIDENCE
Other Evidence: There may not be an assessment of each type listed below for
each unit. Examples of other types of assessment may include:
Representing and Combining Transformations
Academic Prompts
Quiz and Test Items
Informal Checks for Understanding
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Unit 2 - Transformation Test
Click here to access the other evidences described above.
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last revision 10/9/14
5
Unit #:
2
Subject(s): Math II
Grade(s): 9-12
Designer(s): Kristen Fye, Ashley Pethel, Kim Stilwill, Andrea Harkey
STAGE 3 – RESOURCES FOR THE LEARNING PLAN
District Resources:
Supplemental Resources:
When designing the learning plan, these resources are intended to be a
These are considered additional resources that are recommended by the
primary resource used by all teachers.
Curriculum Writing Teams. Those resources with an asterisk (*) may be
purchased by each individual school.
Additional resources can be found using these digital tools:
 Defined Stem (main site)
 Math I, II, and III Topical Guide
 Discovery Education (main site)
Click here to access the resources listed above.
 iCurio (main site)
Considerations for Differentiating Instruction (AIG, EL, EC, etc.):
These resources are intended to be used when differentiating instruction
to meet the varied needs of students in your classroom.
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ACT Example:
The graph of a certain hyperbola, y = h(x), is shown in the standard (x,y)
coordinate plane below.
None at this time.
Among the following graphs, which best represents y = –h(x) ?
A.
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last revision 10/9/14
6
Unit #:
2
Subject(s): Math II
Grade(s): 9-12
Designer(s): Kristen Fye, Ashley Pethel, Kim Stilwill, Andrea Harkey
B.
C.
D.
E.
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last revision 10/9/14
7