Title
Suggested Time Frame
Transformations & Congruence
CISD Safety Net Standards: 8.10C
Big Ideas/Enduring Understandings
4th Six Weeks
12 days
Guiding Questions
•
Students will understand how to show or describe the change
in position of a figure.
•
Grade 8 Math
2016-17 Unit 7
How can we best show or describe the change in the position of a
figure?
Vertical Alignment Expectations
*TEKS one level below*
*TEKS one level above*
TEA Vertical Alignment 5th Grade – Algebra I
Sample Assessment Question
Coming soon....
The resources included here provide teaching examples and/or meaningful learning experiences to address the District Curriculum. In order to address the TEKS to the proper
depth and complexity, teachers are encouraged to use resources to the degree that they are congruent with the TEKS and research-based best practices. Teaching using only the
suggested resources does not guarantee student mastery of all standards. Teachers must use professional judgment to select among these and/or other resources to teach the
district curriculum. Some resources are protected by copyright. A username and password is required to view the copyrighted material. Portions of the District Specificity/Examples
are a product of the TEKS Clarifying Documents provided by the Austin Area Math Supervisors.
8th Math Unit 7
Updated November 30, 2016
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Grade 8 Math
2016-17 Unit 7
Ongoing TEKS
Math Processing Skills—To be embedded and used all year long throughout all concept student expectations.
8.01 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The
student is expected to:
(A) apply mathematics to problems arising in everyday life, society, and the
• Focus is on application
workplace;
(B) use a problem-solving model that incorporates analyzing given
information, formulating a plan or strategy, determining a solution,
justifying the solution, and evaluating the problem-solving process and the
reasonableness of the solution;
(C) select tools, including real objects, manipulatives, paper and pencil, and
technology as appropriate, and techniques, including mental math,
estimation, and number sense as appropriate, to solve problems;
•
Students should assess which tool to apply rather than trying
only one or all
•
Students should evaluate the effectiveness of representations
to ensure they are communicating mathematical ideas clearly
Students are expected to use appropriate mathematical
vocabulary and phrasing when communicating ideas
Students are expected to form conjectures based on patterns
or sets of examples and non-examples
(D) communicate mathematical ideas, reasoning, and their implications
using multiple representations, including symbols, diagrams, graphs, and
language as appropriate;
(E) create and use representations to organize, record, and communicate
mathematical ideas;
•
(F) analyze mathematical relationships to connect and communicate
mathematical ideas; and
•
(G) display, explain, and justify mathematical ideas and arguments using
precise mathematical language in written or oral communication
•
8th Math Unit 7
Updated November 30, 2016
Precise mathematical language is expected.
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Grade 8 Math
2016-17 Unit 7
Knowledge and
Skills with Student
Expectations
8.10 Two-dimensional
Shapes. The student
applies mathematical
process standards to
develop
transformational
geometry concepts.
The student is
expected to:
(A) generalize the
properties of
orientation and
congruence of
rotations,
reflections,
translations, and
dilations of twodimensional shapes
on a coordinate
plane.
District Specificity/ Examples
8.10(A)
Be able to identify the transformation based on given coordinates.
8.10(B)
Students must understand that rotations, reflections and translations preserve
congruence but dilations do not unless the scale factor is one.
8.10(C)
Recognize the relationship between the coordinates of the pre-image and the
image to determine the transformation of the image (rotation, reflection, or
translation).
Students identify the transformation based on given coordinates. For example, the
pre-image coordinates of a triangle are A(4, 5), B(3, 7), and C(5, 7). The image
coordinates are A(-4, 5), B(-3, 7), and C(-5, 7). What transformation occurred?
For Clockwise Rotations: algebraic rules
(B) differentiate
• 90 degrees (Counterclockwise 270): (x,y) goes to (y, -x)
between
• 180 degrees (Counterclockwise 180): (x,y) goes to (-x, -y)
transformations that
•
270 degrees (Counterclockwise 90): (x,y) goes to (-y, x)
preserve
• 360 degress: (x,y) stays (x,y)
congruence and
For
Dilations: algebraic rule:
those that do not.
• (x,y) goes to (ax,ay) where a is the scale factor.
Algebraic rule for reflections across an axis:
8th Math Unit 7
Updated November 30, 2016
Vocabulary
• Algebraic
representation
• Clockwise
rotation
• Congruence/
Congruency
• Coordinate plane
• Counterclockwise rotation
• Differentiate
• Dilation
• Ordered pair
• Orientation
• Reflection
• Rotation (90°,
180°, 270°, 360°)
• Transformation
• Translation
• Two-dimensional
shape
• X-axis
• Y-axis
Suggested Resources
Resources listed and categorized
to indicate suggested uses. Any
additional resources must be
aligned with the TEKS.
Textbook Resources
McGraw-Hill
Chapter 8
Lessons 1-4
(Lesson 5 is previously
addressed in Chapter 2.)
Web Resources:
Region XI: Livebinder
NCTM: Illuminations
Khan Academy
Additional Resources:
Patty Paper
Page 3 of 7
*CISD Safety Net*
(C) explain the
effect of
translations,
reflections over the
x- or y-axis, and
rotations limited to
90°, 180°, 270° and
360° as applied to
two-dimensional
shapes on a
coordinate plane
using an algebraic
representation.
• reflection across the y-axis: (x,y) goes to (-x,y)
• reflection across the x-axis: (x,y) goes to (x, -y)
Misconceptions:
Students confuse x and y axis.
Students may not graph ordered pairs correctly.
Students may use the incorrect algebraic representation.
Students may confuse the different transformations.
Grade 8 Math
2016-17 Unit 7
Examples:
8th Math Unit 7
Updated November 30, 2016
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Grade 8 Math
2016-17 Unit 7
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Grade 8 Math
2016-17 Unit 7
8th Math Unit 7
Updated November 30, 2016
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Grade 8 Math
2016-17 Unit 7
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