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2022 G-2D-1-3

Page history last edited by Brigit Minden 11 months, 2 weeks ago

G.2D.1.3

G.2D.1.3 Apply the properties of angles (corresponding, exterior, interior, vertical, complementary, supplementary) to solve problems using mathematical models, algebraic reasoning, and proofs.

In a Nutshell

Students will be able to define, model, and apply angle pair relationships in a variety of mathematical situations involving parallel lines and transversals.

Student Actions	Teacher Actions
Develop strategies for problem-solving by analyzing diagrams and verbal descriptions and applying angle relationships in a variety of tasks involving parallel lines and transversals. Develop mathematical reasoning by applying algebraic concepts to find solutions to problems presented in geometric relationships and/or real-world situations. Develop the ability to make conjectures, model, and generalize by utilizing patterns in relationships among properties of parallel lines and transversals to develop efficient processes for determining appropriate angle relationships to solve a given situation.	Implement tasks that will promote productive struggle by allowing students to analyze mathematical situations involving parallel lines and transversals and develop appropriate strategies for determining solutions in context. Use and connect representations of the properties of various angle types with algebraic reasoning to construct proofs and solve modeling problems. Build procedural fluency from conceptual understanding by providing students with opportunities to develop and apply efficient procedures to solve problems involving properties of angle pair relationships.
Key Understandings	Misconceptions
Properties of angle pair relationships can be justified and organized through proofs and/or models involving parallel lines and transversals. Properties of angle pair relationships with parallel lines and transversals also apply to intersecting perpendicular lines.	Students think that all angle pairs are congruent such as assuming same side interior angles are congruent when these angles are actually supplementary. Students assume angle pairs are congruent or supplementary before knowing lines are parallel. Students may incorrectly determine an angle pair relationship for a given mathematical situation. Students may apply the incorrect angle pair relationship for a given mathematical situation.
Knowledge Connections
Prior Knowledge	Leads to
Solving problems using angle relationships (middle school)	Solving problems using angle relationships in trigonometry, pre-calculus, and beyond.