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December 2002 Charles City Community School Calculus I=Introduce, D = Develop, A=Access, M= Maintain MC/GF = Multicultual Gender Fair Approaches; CE=Career Education; GE=Global Education ITBS/ITED Standard 1: Effectively uses a variety of strategies in the problem-solving process MC/GF CE Classifies problem-solving strategies or problem types by AM underlying general characteristics Constructs and describes simple algorithms for solving problems M that take several steps Uses inductive reasoning to make conjectures and tests the M conjectures using deductive reasoning to construct with a logical verification of a counter example M Writes and equation to represent a problem situation Provides simple valid arguments as justification for solutions to M specific problems and for algorithms constructed for various purposes GE Standard 2: Understands and applies basic and advanced properties of concept of numbers MC/GF CE GE M Understands the basic characteristics of the real-number system and its subsystems AM Understands the basic characteristics of roots AM Understands the basic characteristics of exponents DA Models numbers using three-dimensional regions M Demonstrates an understanding of relative magnitude by expressing and comparing very small and very large numbers in scientific notation M Has an understanding of the concept of inequalities Standard 3: Uses basic and advanced procedures while performing the process of computation MC/GF CE GE M Adds and subtracts, multiplies and divides algebraic expressions AM Solves real-world problems involving roots and exponents Uses rounding, inputs, and the types of operations to analyze the AM reasonableness of answers derived from calculator, computer, and pencil and paper computations December 2002 Standard 4: Understands and applies basic and advanced properties of the concept of measurement MC/GF CE GE Uses length, area, and volume appropriately in problem-solving DA situations Has a basic understanding of the concept of velocity, acceleration, DA other unit rates and how they are measured AM Determines precision and accuracy of measurements Standard 5: Understands and applies basic and advanced properties of the concepts of geometry MC/GF CE GE DA Describes relationship in geometric terms DA Solves real-world problems involving the Pythagorean relationship DA Uses geometric models, diagrams, and graphs to solve realworld problems DA Uses coordinates and vectors to represent geometric figures and properties algebraically AM Uses properties of lines to describe figures algebraically DA Knows the characteristics and properties of conic sections DA Understands that when the size of a linear shape changes by some factor, its area and volume change disproportionately; area changes in proportion to the square of the factor and volume changes in proportion to the cube of the factor DA Understands the relationship between surface area and volume for rectangular Standard 6: Understands and applies basic and advanced concepts of data analysis and probability MC/GF CE GE DA Understands basic generalizations about the nature of graphs; the position of any point on a surface can be described by two numbers; a graph represents all the values that satisfy an equation; and the point at which two graphs intersect represents the values that will satisfy the two equations represented by the graphs December 2002 Standard 7: Understands and applies basic and advanced properties of relationships, functions, and algebra MC/GF DA AM A A AM A AM Uses appropriate terminology and notation to define functions and their properties, including domain, range, function composition, and inverses Understands the characteristics and uses of basic trigonometric functions Compares and applies the numerical, symbolic, and graphical properties of a variety of functions Solves systems of equations and inequalities graphically and algebraically, and using matrices Uses a variety of algebraic and graphical methods to solve polynomial equations with real and complex roots Understands functional relationships for which the rate of change of one variable is dependent on how much there is of another variable Represents real-world problems using algebraic functions and graphs of those functions CE GE