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Curriculum and Instruction Maps Dade County Schools Course:Mathematics I Unit:3 Geometry Gallery Stage 1: Desired Results Standards Assessed/Learning Goals MM1G3. Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons. MM1G2. Students will understand and use the language of mathematical argument and justification. Enduring Understandings -Properties of angles, triangles, quadrilaterals, and polygons are connected. -Geometric ideas are significant in all areas of mathematics such as: algebra, trigonometry, and analysis. -Geometric ideas are appropriate for describing many aspects of our world. Essential Questions -Are there special relationships that govern the measurements of the interior and exterior angles of a convex polygon? -Are there special relationships among the lengths of the sides of any triangle? -Are there special relationships between the lengths of the sides of a triangle and the measures of the angles of a triangle? -What special relationships exist between the exterior and interior angles of a triangle? -What information is sufficient to guarantee that two triangles are congruent? -How can I use congruent triangles to help me solve real-world problems? -How can I determine which quadrilateral(s) can be constructed based on specific information about the diagonals? -How can I identify and verify properties of special quadrilaterals? -How are angle bisectors, perpendicular bisectors, altitudes, and medians of triangles related? -How can I use geometric ideas to solve real-world problems? Knowledge Skills Students will know … -how to model real world situations using geometric applications and be able to solve problems associated with those situations. -how to use the language of mathematical argument and justification. Students will know how to… -Determine the sum of interior and exterior angles in a polygon. -Understand and use the triangle inequality, the sideangle inequality, and the exterior-angle inequality. -Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL). -Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite. -Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid. Curriculum and Instruction Maps Dade County Schools Diagnostic/Prior Knowledge Assessment Math I Pre-Test Stage 2: Evidence of Learning Formative Assessments Questioning, tasks, student presentations, quizzes, homework, ticket out the door, and warm-ups Summative Assessments Unit exams and Benchmark exams Stage 3: Learning Activities Teaching for Meaning, Acquisition, & Higher Order Thinking Levels Transfer Task 1- Robotic Gallery Guards All tasks in this unit require justifying your Task 2-Poor Captain Robot answers based on the given situation. Every Task 3-Constructing Pennants task has several questions that cover a range of Task 4-Constructing with Diagonals DOK levels for DOK 1 to DOK 3. Which includes, Task 5-Middles and Halves remembering, understanding, applying, Task 6 - Centers of Triangles analyzing, evaluating, and creating.