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Wentzville School District
Curriculum Development Template
Stage 1 – Desired Results
Unit Ten - Congruence, Similarity, and Transformations
Unit Title: Congruence, Similarity, and Transformations
Course: Pre-Algebra
Brief Summary of Unit: Students will learn how to determine congruence and similarity. In addition, students will use
the properties that exist in and between intersecting lines, triangles, and other polygons to solve problems. Finally,
students will use transformations to describe the relationships between objects and use them to determine if figures
are similar or congruent.
Textbook Correlation: Glencoe Math Accelerated Chapter 11
Time Frame: 3.5 weeks
WSD Overarching Essential Question
Students will consider…
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How do I use the language of math (i.e. symbols,
words) to make sense of/solve a problem?
How does the math I am learning in the classroom
relate to the real-world?
What does a good problem solver do?
What should I do if I get stuck solving a problem?
How do I effectively communicate about math
with others in verbal form? In written form?
How do I explain my thinking to others, in written
form? In verbal form?
How do I construct an effective (mathematical)
argument?
How reliable are predictions?
Why are patterns important to discover, use, and
generalize in math?
How do I create a mathematical model?
How do I decide which is the best mathematical
tool to use to solve a problem?
WSD Overarching Enduring Understandings
Students will understand that…
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Mathematical skills and understandings are used
to solve real-world problems.
Problem solvers examine and critique arguments
of others to determine validity.
Mathematical models can be used to interpret and
predict the behavior of real world phenomena.
Recognizing the predictable patterns in
mathematics allows the creation of functional
relationships.
Varieties of mathematical tools are used to
analyze and solve problems and explore concepts.
Estimating the answer to a problem helps predict
and evaluate the reasonableness of a solution.
Clear and precise notation and mathematical
vocabulary enables effective communication and
comprehension.
Level of accuracy is determined based on the
context/situation.
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How do I effectively represent quantities and
relationships through mathematical notation?
How accurate do I need to be?
When is estimating the best solution to a
problem?
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Using prior knowledge of mathematical ideas can
help discover more efficient problem solving
strategies.
Concrete understandings in math lead to more
abstract understanding of math.
Transfer
Students will be able to independently use their learning to…
Reason and solve problems about two-dimensional objects by knowing the attributes of geometric figures.
Meaning
Essential Questions
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How can you determine congruence and
similarity?
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Understandings
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Geometric shapes have specific attributes
that are used to describe and solve problems
about the shape..
What tools could best be used to draw
geometric shapes?
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Triangles can be classified by angles and/or
sides.
How can knowing the properties of polygons
help us find missing measurements?
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Polygons are classified using characteristics
about their sides and angles.
How can angle relationships help us solve for
unknown angle measurements?
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The relationships between the angles made
by intersecting lines can be used to solve
problems.
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Angle relationships can be used to find
unknown angle measurement in a figure.
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A transformation maps an original geometric
figure onto a new figure by sliding
(translation), flipping (reflection), or turning
(rotation) it.
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Dilated figures result in an enlarged or
reduced figure that is similar to the original.
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Congruency can be determined by
performing a series of transformations.
How can angle measurements be determined
without using a protractor?
What patterns are there in the measures of the
angles that are formed when lines intersect?
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How are supplementary, complementary,
vertical, and adjacent angles similar? How are
they different?
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How can a coordinate plane be used to solve
problems about transformations?
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Similarity can be determined by performing a
dilation alone or with another transformation.
Acquisition
Key Knowledge
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Vertical angles
Adjacent angles
Complementary angles
Supplementary angles
Perpendicular lines
Parallel lines
Transversal
Alternate interior angles
Alternate exterior angles
Corresponding angles
║ is read is parallel to
⊥ is read is perpendicular to
m∠ABC is read measure of angle ABC
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Line segment
Triangle
Vertex
Interior angle
Exterior angle
Congruent
∆XYZ is read triangle XYZ
Triangle Sum Theorem (p. 503)
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Key Skills
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Examine relationships between pairs of angles
and solve problems using those relationships.
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Examine relationships of angles formed by
parallel lines and a transversal and solve
problems using those relationships.
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Find missing measures of a geometric figure.
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Write and solve equations to find the
measures of unknown angles.
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Identify angle relationships and apply facts
about them to solve multi-step problems (i.e.
use Triangle Sum Theorem to find an angle,
then use that measure to solve for a
supplementary variable).
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Classify geometric shapes according to their
properties (angles and sides).
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Use protractors, rulers, and technology to
create specified geometric shapes.
Polygon
Diagonal
Regular polygon
Tessellation
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Determine the sum of the measures of the
interior angles of a polygon.
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Define and identify transformations.
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Transformation
Image
Congruent
Translation
Reflection
Line of reflection
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Draw translations and reflections on a
coordinate plane.
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Define, identify, and draw rotations.
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Rotation
Center of rotation
Rotational symmetry
Determine if a figure has rotational symmetry,
and if it does describe the rotational symmetry.
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Identify congruency by using transformations.
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Dilation
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Graph dilations on a coordinate plane.
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(x, y) → (kx, ky) means the dilation of (x, y)
has a scale factor of k
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Find the scale factor of a dilation.
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Use a series of transformations to identify
similar figures.
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Use a scale factor to create similar figures.
Standards Alignment
MISSOURI LEARNING STANDARDS
Draw, construct, and describe geometrical figures and describe the relationship between them.
(7.G.2) Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given
conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions
determine a unique triangle, more than one triangle, or no triangle.
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
(7.G.5) Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step
problems to write and solve simple equations for an unknown angle in a figure.
MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.
MP.7 Look for and make use of structure.
MP.8 Look for and express regularity in repeated reasoning.
SHOW-ME STANDARDS
Goals:
1.1, 1.4, 1.5, 1.6, 1.7, 1.8
2.2, 2.3, 2.7
3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8
4.1, 4.4, 4.5, 4.6
Performance:
Math 1, 2, 5