S1+Doran,++Christopher

=Stage 1 - Identify Desired Results= Functions and Relations (4) Grades: 9-Diploma Students understand and interpret the characteristics of functions using graphs, tables, and algebraic techniques. ||
 * **Establish Goals (MLR):** **(G)** ||
 * Maine Learning Results: Mathematics - D. Algebra

//What understandings are desired?//
• all sorts of functions are used in real world problems every day. • concepts such as rate of change, increasing/decreasing over intervals, and intercepts are used to identify graphs. ||
 * **//Students will understand that://** **(U)** ||
 * • there are multiple types of graphs, functions, and the techniques used to identify them.

//What essential questions will be considered?//
• How will real world situations use these functions in their applications? • Why do different algebraic techniques affect the function and its graph? ||
 * **Essential Questions:** **(Q)** ||
 * • How to recognize the different types of functions based on the graphs shown and vice-versa?

//What key knowledge and skills will students acquire as a result of this unit?//
• Definitions: Function, limit, rate of change, x-intercept, y-intercept, asymptote, matrix, vector, position, velocity, acceleration • Terminology: Variable, distributive property, associative property,commutative property || • demonstrate the concepts involved in identifying graphs. • illustrate the multiple types of graphs. • create a real world situation involving algebraic functions. • analyze real world applications of algebraic functions. • consider the different concepts that help identify graphs. • recognize the multiple types of graphs. ||
 * **//Students will know://** **(K)** || **//Students will be able to://** **(S)** ||
 * • Formulas: Quadratic formula, slope formula, distance formula, midpoint formula


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