Download Understand congruence and similarity using physical models

Grade/Course: Grade 8
Instructional Unit 1: Congruence and Similarity
Instructional Schedule: First Nine Weeks (suggested for 20 days)
( Bold text is new content )
Adapted from Timothy Kanold Scope-and-Sequence documents
Standards:
Evidence Of Standard:
(student should be able to…)
Understand congruence and
similarity using physical models,
transparencies, or geometry
software.
(BA 3.3) Verify experimentally the properties of rotations, reflections,
and translations:
a. Lines are taken to lines, and line
-Construct:
segments to line segments of the
1. An image from pre-image, using
same length.
geometric tools.
2. A rotation.
3. A reflection.
4. A translation.
-Understand image and pre-image are
congruent in:
1. Translations.
2. Reflections.
3. Rotations.
-Explore and justify figures created
from transformations using
compasses, protractors, and rulers or
technology.
b. Angles are taken to angles of the
- Defend whether or not two figures
same measure.
are congruent given the graph of a
figure and its transformation using:
1. Translation.
2. Rotation.
3. Reflection.
Prerequisite Knowledge:
(standards linked to content taught in
previous grades)
Assessment Tools:
(formative assessments, quizzes,
mastery tasks/activities)
c. Parallel lines are taken to parallel
lines.
(BA 3.4) Use coordinates to describe
the effect of dilations, translations,
rotations, and reflections on twodimensional figures.
(PASS 3.1) Construct models, sketch,
and classify solid figures such as
rectangular solids, prisms, cones,
cylinders, pyramids, and combined
forms.
-Recognize the angles formed by two
parallel lines and a transversal.
-Justify why angles (formed by parallel
lines and a transversal) are congruent
using angle relationships.
-Determine if two figures are
congruent by identifying the
transformation used to produce the
figures.
-Write congruent statements.
-Recognize the congruent symbol.
-Define congruent.
-Write statements that justify the
process of transformation as well as
the conclusion.
-Describe the sequence of
transformations from one figure to
another.
-Identify the new coordinates of:
1. A translation.
2. A reflection.
3. A rotation.
4. A dilation.
-Understand image and pre-image are
similar in dilations.
-Given two similar figures describe the
sequence of rotations, reflections,
translations, and dilations.
-Create a figure congruent to a given
figure by:
1. Applying knowledge of translation.
2. Applying knowledge of reflection.
3. Applying knowledge of rotation
(90, 180, 270 degrees) both clockwise
and counterclockwise.
- Construct models, sketch, and
classify solid figures such as
rectangular solids, prisms, cones,
cylinders, pyramids, and combined
forms.
(PASS 4.3) Identify basic 2dimensional figures from a composite
figure. Find the area of composite
figures.
-Separate composite figures into basic
2-dimensional figures (rectangle,
square, triangle, trapezoid).
-Calculate the area of each 2dimensional figure and combine to
find the area of the complete
composite figure.
(BA 4.4) Understand that a two-Define congruent.
dimensional figure is congruent to
-Recognize the congruent symbol.
another if the second can be
-Write congruent statements.
obtained from the first by a sequence -Determine if two figures are
of rotations, reflections, and
congruent by identifying the
translations. Describe a sequence
transformation used to produce the
that exhibits the congruence
figures.
between two different figures.
- Write statements that justify the
process of transformation as well as
the conclusion.
- Describe the sequence of
transformations from one figure to
another.
(BA 4.5) Understand that a two-Create similar figures using dilations
dimensional figure is similar to
and transform them.
another if the second can be
-Comprehend and describe that the
obtained from the first by a sequence angles of similar figures are congruent
of rotations, reflections, translations, and the sides of similar figures are
and dilations; given two similar two- proportional.
dimensional figures, describe a
-Produce similar figures from dilations
sequence that exhibits the similarity
using scale factors.
between them.
-Interpret the meaning of similar
figures and describe their similarities.
-Describe the list of steps that would
produce similar figures when given
the scale factors (dilation).
-Differentiate between scale factor
that would enlarge a figure’s size and
one that would reduce it.
(PASS 4.2) Set up and solve for
- Set up and solve for missing side
missing side lengths of similar
lengths of similar geometric shapes
geometric shapes using ratios and
using ratios and proportions.
proportions.
(BA 4.6) Use informal arguments to
establish facts about the angle sum
and exterior angle of triangles, about
the angles created when parallel
lines are cut by a transversal, and the
angle-angle criterion for similarity of
triangles. For example, arrange three
copies of the same triangle so that
the sum of the three angles appears
to form a line, and give an argument
in terms of transversals why this is
so.
-Find the measures of missing angles.
-Make conjectures about
relationships between angles.
-Construct parallel lines and a
transversal to:
1. Examine and determine the
relationships between created angles.
2. Explore and justify relationships
that exist between angles created
when parallel lines are cut by a
transversal.
-Apply knowledge of vertical,
adjacent, and supplementary angles
to identify other pairs of congruent
angles.
-Find a missing angle and and/or
exterior angle of a triangle.
-Find the missing angle measure when
given two similar triangles.
Resources/Exemplar Tasks:
( list possible task/activities students could engage in within this unit)
Standards for Mathematical Practice:
(highlight practice standards to be emphasized in the instructional unit)
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of instruction.
8. Look for and express regularity in repeated reasoning.
( BA: Broken Arrow rigor standard; PASS: Priority Academic Student Skills standard; BA/PASS: Combination standard )