MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 8
Unit Description
Big Idea(s)
What enduring
understandings are essential
for application to new
situations within or beyond
this content?
Unit 10
Transformations and Congruence
Suggested Length: 4 weeks
Enduring Understandings
Develop an understanding of two- and three- dimensional space and
figures.
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.
Enduring Skills Rubric measures competency of the following skills:
Use compasses, protractors, and rulers or technology to explore figures
created from translations, reflections, and rotations and understand that
these transformations produce images of exactly the same size and shape
as the pre-image and are known as rigid transformations.
Examine two figures to determine congruency by identifying the rigid
transformation(s) that produced the figures and write statements of
congruency.
Identify resulting coordinates from translations, reflections, and rotations,
recognizing the relationship between the coordinates and the
transformation. Additionally, students recognize the relationship between
the coordinates of the pre-image, the image and the scale factor
following a dilation from the origin.
Understand similar figures have angles with the same measure and sides
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 8
that are proportional and understand that a scale factor greater than one
will produce an enlargement in the figure, while a scale factor less than
one will produce a reduction in size.
Essential Question(s)
What questions will provoke
and sustain student
engagement while focusing
learning?
How can the coordinate plane help me understand properties of
reflections, translations, and rotations?
What is the relationship between reflections, translations, and rotations?
What is a dilation and how does this transformation affect a figure in the
coordinate plane?
How can I tell if two figures are similar?
In what ways can I represent the relationships that exist between similar
figures using the scale factors, length ratios, and area ratios?
What strategies can I use to determine missing side lengths and areas of
similar figures?
Under what conditions are similar figures congruent?
Standards
Curriculum and Instruction
Standards for Mathematical Practice
3. Construct viable arguments and critique the reasoning of others.
In grade 8, students construct arguments using verbal or written
explanations accompanied by expressions, equations, inequalities, models,
and graphs, tables, and other data displays (i.e. box plots, dot plots,
histograms, etc.). They further refine their mathematical communication
skills through mathematical discussions in which they critically evaluate their
own thinking and the thinking of other students. They pose questions like
“How did you get that?”, “Why is that true?” “Does that always work?” They
explain their thinking to others and respond to others’ thinking.
5. Use appropriate tools strategically.
Students consider available tools (including estimation and technology)
when solving a mathematical problem and decide when certain tools
might be helpful. For instance, students in grade 8 may translate a set of
data given in tabular form to a graphical representation to compare it to
another data set. Students might draw pictures, use applets, or write
equations to show the relationships between the angles created by a
transversal.
7. Look for and make use of structure.
Students routinely seek patterns or structures to model and solve problems.
In grade 8, students apply properties to generate equivalent expressions
and solve equations. Students examine patterns in tables and graphs to
generate equations and describe relationships. Additionally, students
experimentally verify the effects of transformations and describe them in
terms of congruence and similarity.
8. Look for and express regularity in repeated reasoning.
In grade, students use repeated reasoning to understand algorithms and
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 8
make generalizations about patterns. Students use iterative processes to
determine more precise rational approximations for irrational numbers.
During multiple opportunities to solve and model problems, they notice that
the slope of a line and rate of change are the same value. Students flexibly
make connections between covariance, rates, and representations
showing the relationships between quantities.
Supporting Standard(s)
Which related standards will
be incorporated to support
and enhance the enduring
standards?
Instructional Outcomes
What must students learn
and be able to do by the
end of the unit to
demonstrate mastery?
Standards for Mathematical Content
Understand congruence and similarity using physical models,
transparencies, or geometry software.
8.G.1 Verify experimentally the properties of rotations, reflections, and
translations:
a. Lines are taken to lines, and line segments to line segments of the
same length.
b. Angles are taken to angles of the same measure.
c. Parallel lines are taken to parallel lines.
8.G.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.3 Describe the effect of dilations, translations, rotations, and reflections
on two‐dimensional figures using coordinates.
8.G.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 two‐dimensional
figures, describe a sequence that exhibits the similarity between them.
None
I am learning to…
• Define & Identify rotations, reflections, and translations.
• Understand prime notation to describe an image after a translation,
reflection, or rotation.
• Identify center, direction and degree of rotation.
• Identify line of reflection.
• Identify corresponding sides and corresponding angles.
• Define and identify symbols for congruency.
• Define dilations as a reduction or enlargement of a figure.
• Identify scale factor of the dilation.
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 8
• Derive a rule using the change in coordinates for each transformation
(rotation, reflections, translation, and dilation).
• Verify the properties of transformations experimentally using
manipulatives, transparencies, or geometry software.
• Recognize that similar triangles have congruent angles and
corresponding proportional sides.
• Apply properties of angles to create similar triangles.
Essential Vocabulary
What vocabulary must
students know to
understand and
communicate effectively
about this content?
Resources/Activities
What resources could we
use to best teach this unit?
Curriculum and Instruction
Essential Vocabulary
Transformations, translations, rotations, reflections, line of reflection, center
of rotation, clockwise, counterclockwise, congruence, prime notation,
similarity, dilations, pre-image, image, rigid transformations, scale factor
Supporting Vocabulary
Coordinate system, shape/figure, left, right, up, down, slide, turn, flip, shrink,
enlarge, reduce
Resources/Activities
www.estimation180.com
www.visualpatterns.org
101Questions
http://www.101qs.com/
Dan Meyer’s Website
http://blog.mrmeyer.com/
Dan Meyer has created many problem-based learning tasks. The tasks
have great hooks for the students and are aligned to the standards.
Andrew Stadel
https://docs.google.com/spreadsheet/ccc?key=0AkLk45wwjYBudG9LeX
Rad0lHM0E0VFRyOEtRckVvM1E#gid=0
Andrew Stadel has created many problem-based learning tasks using
the same format as Dan Meyer.
Robert Palinsky
http://robertkaplinsky.com/lessons/
Robert Palinsky has created many tasks that engage students with real
life situations.
Geoff Krall’s Emergent Math
http://emergentmath.com/my-problem-based-curriculum-maps/
Geoff Krall has created a curriculum map structured around problembased learning tasks.
Mathematics in Movies
http://www.math.harvard.edu/~knill/mathmovies/
Short movie clips related to a variety of math topics.
Mathematical Fiction
http://kasmana.people.cofc.edu/MATHFICT/browse.php
Plays, short stories, comic books and novels dealing with math.
The Shodor Educational Foundation
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 8
http://www.shodor.org/interactivate/lessons/byAudience/
This website has extensive notes, lesson plans and applets aligned with
the standards.
NEA Portal Arkansas Video Lessons on-line
http://neaportal.k12.ar.us/index.php/9th-12th-grades-mathematics/
The NEA portal has short videos aligned to each standard. This resource
may be very helpful for students who need review at home.
Learnzillion
http://learnzillion.com/common_core/math/hs
This is another good resource for parents and students who need a
refresher on topics.
Math Words
http://www.mathwords.com/
This is a good reference for math terms.
National Library of Virtual Manipulatives
http://nlvm.usu.edu/en/nav/vlibrary.html
Java must be enabled for this applet to run. This website has a wealth of
virtual manipulatives helpful for use in presentation. Listed by domain.
Geogebra Download
http://www.geogebra.org/cms/download
Free software similar to Geometer’s Sketchpad. This program has
applications for algebra, geometry & statistics.
Remember there are other sources in your school that may not be listed
on this common resources list due to variation in each individual
school. Examples of other great resources your school may have
access to include: Everyday Math Games, Investigations, Everyday
Partner Games, AVMR file folders, Ongoing Assessment Project, etc. The
Kentucky Numeracy Project is also a great resource that can be
searched by AVMR strand, CCSS, and grade level. Find this resource at
http://knp.kentuckymathematics.org/#!/page_knphome. Kentucky
teachers can use it for free. Just put in your school email address and the
username “mathfun”, and password is “859”.
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