S1+McKeown,+Sarah

=Stage 1 - Identify Desired Results= Geometric Figures Grades 9 - Diploma 1. Students justify statements about polygons and solve problems. a) Use properties of triangles to prove theorems about figures and relationships among figures. 3. Students understand and use basic ideas of trigonometry. ||
 * **Establish Goals (MLR):** **(G)** ||
 * Maine Learning Results: Mathematics - C. Geometry

//What understandings are desired?//
•the unique properties of right triangles can be used to solve other geometric problems. •the Pythagorean Theorem can only be used in certain conditions and will be able to determine when it is appropriate to use. ||
 * **//Students will understand that://** **(U)** ||
 * •there exist useful relationship between angles and sides of right triangles.

//What essential questions will be considered?//
• Why do the properties unique to right triangles help solve other geometric problems? • How can trigonometry be used to find missing angles and/or sides of triangles? ||
 * **Essential Questions:** **(Q)** ||
 * • How is the Pythagorean Theorem used?

//What key knowledge and skills will students acquire as a result of this unit?//
•Formulas: Pythagorean Theorem, Law of Sines, Law of Cosines, Inverse trigonometric functions, the 45, 45, 90 triangle, the 30, 60, 90 triangles. •Critical Details: Relationship between angles of a triangle. || •Describe a right triangle. •Evaluate the proper situation in which to use the Pythagorean Theorem. •Apply prior knowledge of triangles to new shapes. •Analyze given information to determine missing lengths/angles of triangles and how to solve for those values. •Relate properties and formulas of triangles to properties and formulas of triangles. •Recognize relationships between angles and sides. ||
 * **//Students will know://** **(K)** || **//Students will be able to://** **(S)** ||
 * •Vocabulary: angle, leg, "right" angle, "right" triangle, hypotenuse, sine, cosine and tangent.


 * 2004 ASCD and Grant Wiggins and Jay McTighe.**