Essential Questions: What are various representations of a function and how can they be interpreted? How are key features of a function identified and explained in relation to the context? How are functions and their properties including the increasing or decreasing (positive or negative) behavior, relative maximums and minimums, symmetries, and end behavior compared? What determines the type of sequence or function is represented in a situation? What are the different ways an exponential function be represented? What are the key features of a function or graph and how is it best modeled? How is the domain of a rational function related to its graph? How can rewriting the equation of a rational function (using long division of polynomials) give further information about its graph? Student will be able to: Define the domain (from one function set) and range (from another function set), assigning each element of the domain to exactly one element of the range. Use f(x) to denote the output of function f corresponding to the or domain and the graph of function f is the graph of f(x). Use appropriate function notation, evaluating functions for inputs in their domains and interpreting statements that use function notation in terms of a context. Determine and use the appropriate sequence or function (sometimes recursive) that best models a real world situation. Model a relationship between functional quantities, interpreting key features of the function graphs and tables in terms of the quantities. Draw a graph expressed symbolically and show key features of the graph, by hand in simple cases and/or using technology for more complicated cases. Compare two functions each represented either algebraically, graphically, given tables or by a verbal description in terms of their domains, their intercepts, their increasing and decreasing behavior, their relative maximums and minimums, their symmetries, and their end behaviors. Calculate, estimate, or interrupt the average rate of change from multiple representations of a function. Represent, interpret, and graph various representations of a function (e.g., the square root function, the cubic function, the piecewise function, the polynomial function, the rational, exponential and logarithmic function) by the process of factoring and completing the square to show zeros, extreme values, and symmetry of the graph, interpreting these concepts in terms of a context.
35 36 37 38 39 40 41 42 43 44 45 46 $2,050,000 $1,900,000 $2,100,000 $2,250,000 $2,400,000 $2,500,000 $2,600,000 $2,700,000 $3,000,000 $2,800,000 $3,100,000 $3,500,000 Learning Activities: (Interventions for students who are not progressing, instructional strategies, differentiated instruction, re-teaching options) Peer teaching through group work Interactive technology as assigned by instructor to support instruction such as: Plato Learning Technology– lessons by objective/ NRS level, interactive websites/illustrations, Study Stack – vocabulary support out loud (demonstrate how to think about a problem) Provide students with a typed set of notes from their classmates Provide support around math specific and general vocabulary Additional practice with concepts and procedures in different contexts Universal Design for Learning protocols such as additional time, modified lesson for disabilities (i.e., enlarged print, drills, flashcards) List of Instructional Materials: Bowl Activity sheet Overhead projector Rulers Calculators List of Technology Resources: Plato Learning Environment Purple Math Building Functions (BF) 6.F.BF.1 / 6.F.BF.2 / 6.F.BF.3 / 6.F.BF.4 / 6.F.BF.5 Essential Understandings: Functions with a domain that are a subset of the integers and can be identified by the constant difference between consecutive terms (arithmetic sequences).