Download Standard 4.1 Congruence and Similarity

Curriculum Guide
Grade 8 – Math Standard 4.1
Math.4.1 - Transformations of objects can be used to define the concepts of congruence and similarity.
Related Colorado Department of Education Sample Units:
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Moving Mathematically (Concepts: Volume, formulas, cones, cylinders, spheres, transversal, parallel lines, angles, relationships, rotations,
reflections, translations, congruence, dilations, similarity, coordinates, symbolically, algebraic)
Essential Questions - 21st Century Skills and Readiness Competencies (District):
1. What advantage, if any, is there to using the Cartesian coordinate system to analyze
the properties of shapes?
2. How can you physically verify that two lines are really parallel?
3. What are the properties of rotations, reflections, and translations?
4. What is the effect of dilations, translations, rotations, and reflections on twodimensional figures using coordinates?
5. How do you know if one two-dimensional figure is congruent to another?
6. Describe a sequence of transformation with two congruent figures.
7. How do you know if one two-dimensional figure is similar to another when the
second is obtained from the first by a sequence of rotations, reflections, translations,
and dilations?
Evidence Outcomes (District):
1. Verify experimentally the properties of rotations, reflections, and translations.
2. Describe the effect of dilations, translations, rotations, and reflections on twodimensional figures using coordinates.
3. Demonstrate 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.
4. Given two congruent figures, describe a sequence of transformations that exhibits
the congruence between them.
5. Demonstrate 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.
6. Given two similar two-dimensional figures, describe a sequence of transformations
that exhibits the similarity between them.
7. 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.
Academic Vocabulary (District):
rotations
reflections
translations
dilations
coordinates
congruent
transformations
similar
parallel lines
angle sum
exterior angle
coordinate plane
interior angle
transversal
Assessment (District):
All assessments are found in the suggested activities links, correlating with their
numbers, unless listed below.
1. Game score is the assessment.
2. Use a worksheet or combination of worksheets to assess.
3 & 4. Assessments are built into each activity.
5. Assessment is built into the activity. Allow students to explain the concepts of
translation, reflection, and rotation. The students should share about the places where
the activity was difficult. Ensure that all students understand the three concepts before
moving on to another lesson.
6. No Assessment. This activity is used as an introduction to Translations, Rotations,
Reflections.
7. The game is interactive, so the student score is the assessment.
8. Assessments are built into the lessons.
9. This lesson has both traditional and authentic assessment ideas at the bottom of the
lesson plan.
Suggested Activities/Strategies (District):
For all activities listed below, the links are numbered to correlate with each activity.
1. Play the Pool Geometry Game.
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Pool Geometry Game Link
2. Conduct Drill and Practice with worksheets. See links in resources.
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2. Translation Worksheet
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2. Math Drills Worksheets
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2. Congruent Triangle Worksheets
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2. Triangle Worksheets (More Difficult)
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www.mathworksheetsland.com
o
2. Angle Sum Worksheet
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2. Printable Graph Paper Link
3. If you have a SmartBoard or Airliner, you can find multiple lessons free at Smart
Exchange.
4. Share My Lesson is a website that has several free lessons for these standards. Most
are 21st Century Lessons. Login and search for topics.
5. Use the Interactive Lesson as an introduction to translations, reflections, and
rotations.
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5. Interactive Lesson
7. Play the interactive Congruent Figures Concentration Game.
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7. Congruent Figures Concentration Game
8. Learn Zillion has several lessons on understanding angle sums, exterior angles,
angles created when parallel lines are cut by a transversal, and the angle-angle
criterion for similarity of triangles.
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8. Learn Zillion
9. This Lesson matches the informal argument standard from Youngstown City School
System. In this unit, students will be introduced to parallel lines, transversals, and the
angles created when they cross. From here, students expand their knowledge by using
similar triangles and their properties to create parallel lines and apply the concepts of
this unit while they construct a geometry city.
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9. Lesson on Informal Arguments
Resources/Technology (District):
 Definitions and examples of flips
 Examples of angles and shapes
 PARCC offers instructional and assessment support. Click on the tab "In the
Classroom" and at the model frameworks for math.
 Illustrative Mathematics contains examples of tasks designed by the makers
of the CCSS-M (Common Core State Standards of Mathematics.)
 Inside Mathematics has tasks, rubrics, and discussion questions that correlate
with PARCC and Smarter Balance.
 Math Arizona has explanations and overviews for how the mathematics
strands progress from one year to the next.
 Math Shell is Mathematics Assessment Resource Service (MARS) from the
Shell Centre in Nottingham, England and it contains a number of
performance tasks.
 Achieve the Core is from Student Achievement Partners, a nonprofit
organization that assembles educators and researchers to design actions
based in evidence that will substantially improve student achievement.
 Balanced Assessments is a site with free performance tasks to use in your
classroom.
 Illuminations from NCTM – Great Lessons and Units supporting all grades
levels
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o Multiple Links to Games/Interactives
Link to Site with Games for Geometry
Super Teacher Worksheets
Math is Fun
YouTube Congruent Triangles Video
TeacherTube Video Congruent Figures
Congruent Figures Interactive Game
Definitions of Dilations
Video on Dilations
Site with Multiple Lessons for Informal Arguments
Tangled Web Game
Properties of Transformations
Math.Com
Math Chimp 8th Grade Math Games