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6-GM-2-1

Page history last edited by Brenda Butz 6 years, 2 months ago

6.GM.2.1 Solve problems using the relationships between the angles (vertical, complementary, and supplementary) formed by intersecting lines.

In a Nutshell

Students have previous knowledge about what an angle is and how to compare angles according to size. Sixth grade is the first year students start to use angle relationships and applying angle relationships to find missing angles. Intersecting lines create angles that share vertices, sides, or sometimes both. Vertical angles are opposite each other, and have equal measurement. When two lines intersect, any two adjacent angles, which are angles that share a side and common vertex, form a linear pair and are by definition, supplementary. When more than two lines intersect, if any two adjacent angles form a right angle, they are by definition complementary. Application of these rules can be used to solve for a missing angles when at least one measure for the pair is known.

Student Actions	Teacher Actions
Develop mathematical reasoning while exploring angle relationships including vertical, complementary, and supplementary angles and developing strategies for finding missing angles, such as solving an equation. Develop the ability to communicate mathematically through discussion and writing about angle relationships using appropriate vocabulary to describe angles such as adjacent, vertical, complementary, and supplementary angles.	Implement tasks that promote reasoning about angle relationships including vertical, complementary, and supplementary angles and engage students in developing strategies for finding missing angle measures using these relationships. Pose purposeful questions to assess students’ understanding about missing angle problems involving angle relationships including vertical, complementary, and supplementary angles. (Ex. Is it possible for two angles to be described as vertical angles and supplementary angles? If so, what would the angle measures be to satisfy these conditions?)
Key Understandings	Misconceptions
That two angles whose measures have a sum of 90° are complementary angles. That two angles whose measures have a sum of 180° are supplementary angles. That angles do not have to be adjacent in order to be complementary or supplementary angles. That vertical angles share a common vertex, but do not share a common side. That vertical angles are congruent.	Confuse the terms for complementary and supplementary angles. Believe that complementary and supplementary angles must be adjacent.