Download Calculus - Charles City Community School District

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