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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: 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. Pool Geometry Game Link 2. Conduct Drill and Practice with worksheets. See links in resources. 2. Translation Worksheet 2. Math Drills Worksheets 2. Congruent Triangle Worksheets 2. Triangle Worksheets (More Difficult) www.mathworksheetsland.com o 2. Angle Sum Worksheet 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. 5. Interactive Lesson 7. Play the interactive Congruent Figures Concentration Game. 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. 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. 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 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