S1+Emery,+Jordan

=Stage 1 - Identify Desired Results= Functions and Relations Grades 9-Diploma Students understand and interpret the characteristics of functions using graphs, tables, and algebraic techniques. a. Recognize the graphs and sketch graphs of the basic functions ||
 * **Establish Goals (MLR):** **(G)** ||
 * Maine Learning Results: Mathematics - D. Algebra

//What understandings are desired?//
• functions have various real-world applications. • there are many techniques used in order to solve functions and change the appearance of functions. ||
 * **//Students will understand that://** **(U)** ||
 * • functions can be expressed in several ways.

//What essential questions will be considered?//
• How can functions apply to the real world? • Why are a variety of techniques used to solve functions and change the appearance of functions? ||
 * **Essential Questions:** **(Q)** ||
 * • How are functions expressed in different ways?

//What key knowledge and skills will students acquire as a result of this unit?//
• Formulas: the quadratic formula. • Techniques: substitution, factoring, the quadratic formula, properties of logarithms, the vertical line test, horizontal stretch, vertical stretch, reflection over x-axis, reflection over y-axis. || • express a variety of functions through graphs and algebraic equations. • translate functions of graphs according to equation manipulations. • solve functions using a variety of methods. • compare methods of solving functions to determine which is appropriate for the problem being solved. • consider the role functions play in real-world problem solving. • a. recognize the graph and sketch graphs of basic functions. ||
 * **//Students will know://** **(K)** || **//Students will be able to://** **(S)** ||
 * • Definitions of: domain, range, ordered pair, function, polynomial, and degree.


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