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G-2D-1-1

Page history last edited by Brenda Butz 6 years, 3 months ago

G.2D.1.1 Apply the properties of parallel and perpendicular lines, including properties of angles formed by a transversal, to solve real-world and mathematical problems and determine if two lines are parallel, using algebraic reasoning and proofs.

In a Nutshell

In this standard students will draw upon their coordinate system knowledge of lines to discover properties about line relationships within a plane and their included angles. This will include that if lines are parallel what angle pair relationships are formed and if given specific conditions are the lines parallel? The integration of conditional statements with these concepts will lead to the beginning of informal proofs.

Student Actions	Teacher Actions
Develop a Deep and Flexible Conceptual Understanding: Students will determine if two lines are parallel or perpendicular based upon knowing information about certain angle pairs (i.e. corresponding angles, supplementary angles, etc.). Develop Strategies for Problem Solving: Students will demonstrate the integration of angle relationships and parallel lines in a variety of problems. Develop Mathematical Reasoning: Students will use their knowledge of parallel lines, transversals and angle relationships to evaluate the reasonableness of a solution. Develop the Ability to Communicate Mathematically: Students will use properties of angles, parallel lines and transversals to communicate mathematically and prove that two lines are parallel.	Teachers will implement tasks with multiple entry points that promote student reasoning and problem solving. Teachers will present multiple representations of lines and transversals that will require student interpretation of the relationships. Teachers will pose purposeful questions to help students make connections between different angle relationships found inside transversals. Teachers will build procedural fluency from conceptual understanding while applying algebra concepts to lines and transversals (i.e. finding missing angles represented by algebraic expressions).
Key Understandings	Misconceptions
Students understand the properties of parallel lines and the angle pair relationships formed by a transversal. Students understand how to determine if two lines are parallel. Students understand how to use properties of perpendicular lines and the angles formed when perpendicular lines are present. Students understand the use the properties of parallel lines and angle pairs to prove that two lines are parallel.	Students believe that all angle pairs are congruent i.e. same side interior angles are actually supplementary, but students will try to say they are congruent. Students don’t understand that lines must be parallel before angle pairs can be assumed congruent or supplementary. Students think that vertical angles and linear pairs prove parallel lines.