Grade(s): 1012
Length: Two semesters
Prerequisites: Algebra B
Numbers and Operations

 Use models, explanations (verbal & written), number lines, reallife situations, descriptions and illustrations to demonstrate the effects of arithmetic operations on real numbers
 Use models, explanations, number lines, reallife situations to describe and illustrate the use of inverse operations (squaring/square root)
 Apply the rules of order of operations to real numbers and variables
 Use the distributive property with variables.
 Judge whether a strategy will result in an answer greater or less than the exact answer
 Add, subtract, multiply, and divide rational numbers including integers with whole number exponents
 Determine rate by using ratio and proportion
 Explain why one strategy is more appropriate than another and determine why the estimated result is greater or less than the exact number

Measurement

 Convert square and cubic units within the same system and between English or metric systems (using a conversion factor)
 Apply indirect methods, such as the Pythagorean Theorem to find missing dimensions in realworld applications

Statistics & Probability

 Design, collect, organize, display, and explain the classification of data in realworld problems using information from tables or graphs that display two sets of data (or with technology)
 Determine and compare the experimental and theoretical probability of independent or dependent events
 Make predictions about the probability of independent and dependent events and use the information to solve problems
 Design, conduct, analyze, and communicate the results of a probability experiment

Functions & Relationships

 Generalize relationships (linear, quadratic, absolute value) using a table of ordered pairs, a graph, or an equation
 Use a calculator as a tool when describing, extending, representing, or graphing patterns or equations
 Solve literal equations or formulas for a given variable
 Describe in words how a change in one variable in a formula affects the remaining variables

Geometry

 Use a coordinate plane to solve problems involving congruent or similar shapes
 Draw and describe the results of applying transformations (translations, rotations, reflections, or dilations) to figures on a coordinate plane
 Determine the perimeter and area of 2dimensional figures
 Determine the volume and surface area of prisms, cylinders, cones, pyramids, spheres, and compound solids
 Graph or identify (using equations and formulas) the slope of line segments on a coordinate plane
 Identify, analyze, compare, and use properties of plane figures:
 Supplementary, complementary and vertical angles
 Angles created by parallel lines with a transversal
 Sum of interior and exterior angles of a polygon
 Central angles, chords, inscribed angles and arcs of a circle
 Use transformations to show congruence or similarity of figures on a coordinate plane
 Graph a line segment on a coordinate grid and identify its length and midpoint by using formulas
 Draw, measure, and construct geometric models of plane figures (containing parallel and/or perpendicular lines, angles, perpendicular bisectors, congruent angles, and regular polygons)

Problem Solving

 Select, modify, and apply a variety of problemsolving strategies and verify the results
 Apply multistep integrated mathematical problemsolving strategies
 Evaluate, interpret, and justify solutions to problems by using an alternative strategy
 Verify an answer by using an alternative strategy
 Follow and evaluate an argument, judge its validity using inductive or deductive reasoning and logic; or make and test conjectures
 Use methods of informal proof including direct, indirect, and counterexamples to validate conjectures
 Use mathematics in realworld contexts such as science, humanities, among peers, community, national issues, global issues, and careers
 Represent mathematical problems numerically, graphically, and algebraically, communicate math ideas in writing; and use appropriate vocabulary, symbols, or technology to explain, justify, and defend strategies and solutions

Grade(s): 912
Length: Two semesters
Prerequisites: Algebra I
Numbers and Operations

 Use models, explanations (verbal & written), number lines, reallife situations, descriptions and illustrations to demonstrate the effects of arithmetic operations on real numbers
 Use models, explanations, number lines, reallife situations to describe and illustrate the use of inverse operations (squaring/square root, cubing/cube root)
 Apply order of operations rules to real numbers and variables
 Use the distributive property with variables.
 Simplify expressions with positive exponents
 Express square roots in simplest radical form
 Judge whether the strategy will result in an answer greater or less than the exact answer
 Add, subtract, multiply, and divide real numbers including integers with whole number exponents
 Determine rate by using ratio and proportion
 Explain why one strategy is more appropriate than another and determine why the estimated result is greater or less than the exact number

Measurement

 Apply indirect methods, such as the Pythagorean Theorem to find missing dimensions in realworld applications
 Convert square and cubic units within the same system and between English or metric systems (using a conversion factor)
 Apply right triangle trigonometry (sine, cosine, and tangent) to find missing dimensions in realworld applications

Statistics & Probability

 Design, collect, organize, display, and explain the classification of data in realworld problems using information from tables or graphs that display two sets of data (or with technology)
 Determine and compare the experimental and theoretical probability of independent or dependent events
 Make predictions about the probability of independent and dependent events and use the information to solve problems
 Design, conduct, analyze, and communicate the results of a probability experiment

Functions & Relationships

 Generalize relationships (linear, quadratic, absolute value) using a table of ordered pairs, a graph, or an equation
 Use a calculator as a tool when describing, extending, representing, or graphing patterns or equations
 Describe in words how a change in one variable in a formula affects the remaining variables
 Describe in words how a change in one variable or constant in an equation affects the outcome of the equation
 Model (graphically and algebraically) and solve situations (including realworld applications) using systems of linear equations or inequalities
 Solve or identify solutions to literal equations or formulas for a given variable involving multisteps

Geometry

 Use a coordinate plane to solve problems involving congruent or similar shapes
 Draw and describe the results of applying transformations (translations, rotations, reflections, or dilations) to figures on a coordinate plane
 Determine the volume or surface area or prisms, cylinders, cones, pyramids, spheres, and compound solids
 Graph or identify (using equations or formulas to determine the slope of line segments) on a coordinate plane
 Draw, measure, or construct geometric models or plane figures (containing parallel and/or perpendicular lines)
 Identify, analyze, compare, or use properties of plane figures:
 Supplementary, complementary and vertical angles
 Angles created by parallel lines with a transversal
 Sum of interior and exterior angles of a polygon
 Central angles, chords, inscribed angles and arcs of a circle
 Use transformations to show congruence or similarity of figures on a coordinate plane
 Graph a line segment on a coordinate grid and/or identify its length or midpoint by using formulas
 Draw, measure, or construct geometric models of plane figures (containing parallel and/or perpendicular lines, angles, perpendicular bisectors, congruent angles, regular polygons)
 Graph a system of equations on a coordinate grid, identify a solution, or determine their relationship (intersecting, parallel, perpendicular)

Problem Solving

 Select, modify, and apply a variety of problemsolving strategies and verify the results
 Apply multistep integrated mathematical problemsolving strategies
 Evaluate, interpret, and justify solutions to problems by using an alternative strategy
 Verify the answer by using an alternative strategy
 Follow and evaluate an argument, judge its validity using inductive or deductive reasoning and logic; or make and test conjectures
 Use methods of formal proof including direct, indirect, and counterexamples to validate conjectures
 Use realworld contexts such as science, humanities, peers, community, careers, national issues, and global issues
 Represent mathematical problems numerically, graphically, and/or symbolically, communicating math ideas in writing; and using appropriate vocabulary, symbols, or technology to explain, justify, and defend strategies and solutions

Grade(s): 912
Length: Two semesters
Prerequisites: Geometry (or equivalent)
Numbers and Operations

 Write equivalent representations of the same exponential expression
 Identify the subsets of complex numbers (natural, whole, integers, rational, irrational, real, and imaginary)
 Simplify expressions with positive and negative exponents
 Express radical expressions in simplest radical form
 Describe and illustrate the effects of arithmetic operations on complex numbers
 Describe and illustrate the use of inverse operations (cubing/cube root)
 Identify and apply commutative, identity, associative, inverse, and distributive properties to complex numbers and variables
 Identify and write the prime factorization of a variable expression using exponents
 Explain why one strategy is more appropriate than another and determine why the estimated result is greater or less than the exact answer
 Apply basic operations with complex numbers using powers

Measurement

 Convert square and cubic units within the same system and English or metric systems (using a conversion factor)

Statistics & Probability

 Design, collect, organize, display, and explain the classification of data in realworld problems, using information from tables and graphs that display two or more sets of data (or with technology)
 Use information from a display to solve a problem or analyze the validity of statistical conclusions
 Use a line of best fit to describe trends and make predictions about data
 Explain in words or identify the difference between experimental and theoretical probability of independent or dependent events
 Analyze data to make predictions about the probability of independent or dependent events as a basis for solving realworld problems
 Design, conduct, analyze, and communicate the results of a multistage probability experiment
 Identify and apply combinations and permutations

Functions & Relationships

 Describe and extend patterns represented in tables, graphs, and in realworld situations using these relations:
polynomial, absolute value, exponential, logarithmic, rational, radical, inverse functions, arithmetic and geometric sequences and series up to the nth term
 Describe in words how a change in one variable or constant in an equation affects the outcome of the equation
 Use a calculator as a tool when describing, extending, representing, or graphing patterns, polynomial, rational, radical, exponential and logarithmic functions
 Represent linear, quadratic and absolute value inequalities using a graph
 Model (graphically and algebraically including matrices) and solve situations (including realworld applications) using systems of linear equations or inequalities
 Select and use the quadratic formula, completing the square or factoring to solve problems
 Solve and identify solutions to literal equations or formulas for a given variable involving multisteps
 Simplify polynomial expressions
 Apply algebraic properties to solve equations (polynomial, rational, radical, exponential, logarithmic)

Geometry

 Use transformations applied to functions to show congruence or similarity of figures on a coordinate plane
 Graph a system of equations or inequalities (linear programming) on a coordinate grid, identify a solution and determine their relationship (intersecting, parallel, perpendicular)

Problem Solving

 Follow and evaluate an argument, judge its validity using inductive or deductive reasoning and logic; and make and test conjectures
 Apply multistep, integrated mathematical problemsolving strategies
 Verify an answer by using an alternative strategy
 Represent mathematical problems numerically, graphically, and algebraically, communicate math ideas in writing; and use appropriate vocabulary, symbols, or technology to explain, justify, and defend strategies and solutions
 Use methods of proof including direct, indirect, and counterexamples to validate conjectures
 Apply mathematics to realworld contexts such as global issues and careers

Grade(s): 810
Length: Two Semesters
Prerequisites: Teacher recommendation
Numbers and Operations

 Convert between a rational number in scientific notation and standard form
 Equate different equivalent representations of the same exponential expression
 Use models, explanations, number lines. reallife situations to describe and illustrate the effects of arithmetic operations on real numbers
 Use models, explanations, number lines, reallife situations to describe and illustrate the use of inverse operations (squaring/square root, cubing/cube root)
 Apply the rules for order of operations to real numbers and variables
 Identify the subsets of real numbers (natural, whole, integers, rational, irrational)
 Simplify expressions with positive and negative exponents
 Express square roots in simplest radical form
 Identify and apply commutative, identity, associative, inverse, and distributive properties to real numbers and variables
 Identify and write the prime factorization of a variable expression using exponents
 Judge whether the strategy will result in an answer greater or less than the exact answer
 Add, subtract, multiply, and divide rational numbers, including integers with whole number exponents
 Determine rate by using ratio and proportion
 Multiply or divide numbers in scientific notation
 Apply basic operations with real numbers using powers
 Solve problems involving percent increase or decrease

Measurement

 Estimate and convert measurements within the English and metric systems in realworld applications, given a conversion factor
 Apply indirect methods, such as the Pythagorean Theorem to find missing dimensions in realworld applications

Statistics & Probability

 Design, collect, organize, display, and explain the classification of data in realworld problems, using information from tables and graphs that display two or more sets of data( or with technology)
 Use information from a display to solve a problem and analyze the validity of statistical conclusions found in the media
 Use and justify range and measures of central tendency to determine the best representation of the data for a practical situation
 Use a line of best fit to describe trends and make predictions about data
 Identify and/or show the meaning of a best fit line
 Determine and compare the experimental and theoretical probability of independent and dependent events
 Explain in words and identify the difference between experimental and theoretical probability of independent and dependent events
 Analyze data to make predictions about the probability of independent and dependent events as a basis for solving realworld problems
 Design, conduct, analyze, and communicate the results of a multistage probability experiment

Functions & Relationships

 Describe and extend patterns (families of functions: linear, quadratic, absolute value, square root) up to the nth term, represented in tables, equations, graphs, and realworld situations
 Generalize equations and inequalities (linear, quadratic, absolute value, square root) using a table of ordered pairs or a graph
 Describe in words how a change in one variable or constant in an equation affects the outcome of the equation
 Use a calculator as a tool when describing, extending, representing, or graphing patterns, linear equations, and quadratic equations
 Model (graphically and algebraically) and solve problems (including realworld applications) using systems of linear equations or inequalities
 Solve and identify solutions to multistep linear equations of the form ax ± b = cx ± d, where a ,b, c, are rational numbers and a ≠ 0, c ≠ 0
 Solve and identify solutions to literal equations and formulas for a given variable involving multisteps

Geometry

 Determine the slope of a line using equations, formulas, tables, and graphs on a coordinate plane
 Draw, measure, and construct geometric models or plane figures containing parallel and/or perpendicular lines
 Graph a line segment on a coordinate grid and identify its length and midpoint by using formulas

Problem Solving

 Select, modify, and apply a variety of problemsolving strategies and verify the results
 Apply multistep integrated mathematical problemsolving strategies
 Evaluate, interpret, and justify solutions to problems by using an alternative strategy
 Represent mathematical problems numerically, graphically, and algebraically, communicate math ideas in writing ; and use appropriate vocabulary, symbols, or technology to explain, justify, and defend strategies and solutions
 Follow and evaluate an argument, judge its validity using inductive or deductive reasoning and logic; or make and test conjectures
 Explain why one strategy is more appropriate than another and determine why the estimated result is greater or less than the exact answer
 Use methods of informal proof including direct, indirect, and counterexamples to validate conjectures
 Apply mathematics to realworld contexts such as science, humanities, peers, community, careers, national issues, and global issues

Grade(s): 911
Length: Two semesters
Prerequisites:
Numbers and Operations

 Converts between a rational number in scientific notation and standard form
 Equate different equivalent representatives of the same exponential expression
 Use models, explanations, number lines and reallife situations to describe and illustrate the effects of arithmetic operations on real numbers
 Use models, explanations, number lines and reallife situations to describe and illustrate the use of inverse operations (squaring/square root)
 Identify and apply commutative, identity, associative, inverse, and distributive properties to real numbers and variables
 Judge whether a strategy will result in an answer greater or less than the exact answer
 Add, subtract, multiply, and divide rational numbers including integers with whole number exponents
 Multiply and divide numbers in scientific notation
 Apply basic operations with real numbers using powers

Measurement

 Estimate or convert measurements between the English and metric systems in realworld applications, given a conversion factor
 Apply indirect methods to find missing dimensions in realworld applications

Statistics & Probability

 Design, collect, organize, display, or explain the classification of data in realworld problems, using information from tables and graphs that display two sets of data( or with technology)
 Use information from a variety of displays and analyze the validity of statistical conclusions found in the media
 Use range and measures of central tendency to determine the best representation of the data for a practical situation
 Use a best fit line to describe trends and make predications about data
 Identify and/or show the meaning of a best fit line
 Determine or compare the experimental and/or theoretical probability of independent or dependent events
 Design, conduct, analyze, and communicate the results of a multistage probability experiment
 Make predictions about the probability of independent or dependent events and use the information to solve problems

Functions & Relationships

 Determine rate by using ratio and proportion
 Generalize relationships (linear) using a table of ordered pairs, a graph, and an equation
 Use a calculator as a tool when describing, extending, representing, and graphing patterns
 Solve or identify solutions to multistep linear equations of the form ax ± b = cx ± d, where a ,b, c, are rational numbers and a ≠ 0, c ≠ 0
 Solve and identify solutions to literal equations or formulas for a variable involving multisteps
 Introduce linear functions represented in tables, equations, graphs, and in realworld situations
 Introduce the movement between words, graphs, tables, and equations for linear relationships

Geometry

 Determine the area and perimeter of 2dimensional figures
 Graph onedimensional solutions to linear equations and inequalities

Problem Solving

 Select, modify, and apply a variety of problemsolving strategies and verify the results
 Evaluate, interpret, and justify solutions to problems by using an alternative strategy
 Represent mathematical problems numerically, graphically, and algebraically, translate among these alternative representations; and use appropriate vocabulary, symbols, or technology to explain, justify, and defend strategies and solutions
 Follow and evaluate an argument, judge its validity using inductive or deductive reasoning and logic; and make and test conjectures
 Describe in words how a change in one variable in a formula affects the remaining variables
 Describe in words how a change in one variable or constant in an equation affects the outcome of the equation

Grade(s): 1012
Length: Two semesters
Prerequisites: Algebra A
Numbers and Operations

 Identify the subsets of real numbers (natural, whole, integers, rational, irrational)
 Simplify expressions with positive and negative exponents
 Describe and illustrate the effects of arithmetic operations on real numbers
 Describe and illustrate the use of inverse operations (cubing/cube root)
 Identify and apply commutative, identity, associative, inverse, and distributive properties to real numbers and variables
 Identify and write the prime factorization of a variable expression using exponents
 Apply basic operations with real numbers using powers
 Solve and identify solutions to literal equations or formulas for a given variable involving multisteps

Measurement

 Use dimensional analysis to convert from one unit to another within and between English and metric systems in realworld applications
 Apply indirect methods, such as the Pythagorean Theorem to find missing dimensions in realworld applications

Statistics & Probability

 Design, collect, organize, display, and explain the classification of data in realworld problems, using information from tables and graphs that display two or more sets of data( or with technology)
 Use information from a display to solve a problem and analyze the validity of statistical conclusions found in the media
 Use and justify range and measures of central tendency to determine the best representation of the data for a practical situation
 Use a line of best fit to describe trends and make predictions about data
 Explain in words or identify the difference between experimental and theoretical probability of independent or dependent events
 Analyze data to make predictions about the probability of independent or dependent events as a basis for solving realworld problems
 Design, conduct, analyze, and communicate the results of a multistage probability experiment

Functions & Relationships

 Generalize equations and inequalities (linear, quadratic, absolute value) using a table of ordered pairs and a graph
 Use a calculator as a tool when describing, extending, representing, or graphing patterns, linear equations, or quadratic equations
 Model (graphically and algebraically) and solve problems (including realworld applications) using systems of linear equations and inequalities
 Select and use the quadratic formula or factoring to solve quadratic equations
 Solve problems involving percent increase or decrease
 Introduce and move between quadratic and absolute value functions as a table, graph and equation

Geometry

 Determine the slope of a line using equations, formulas, tables, and graphs on a coordinate plane
 Draw, measure, and construct geometric models or plane figures containing parallel and/or perpendicular lines
 Graph a line segment on a coordinate grid and identify its length and midpoint by using formulas

Problem Solving

 Apply multistep integrated mathematical problemsolving strategies
 Verify the answer by using an alternative strategy
 Represent mathematical problems numerically, graphically, and algebraically, communicate math ideas in writing ; and use appropriate vocabulary, symbols, or technology to explain, justify, and defend strategies and solutions
 Use methods of informal proof including direct, indirect, and counterexamples to validate conjectures
 Explain why one strategy is more appropriate than another and determine why the estimated result is greater or less than the exact answer

Grade(s): 9th
Length: Two semesters
Prerequisites: Teacher recommendation
Numbers and Operations

 Identify, describe, and illustrate equivalent representations of rational numbers (fractions, decimals, and percents including integers)
 Express products of numbers using exponents of rational numbers (fractions, decimals, and percents including integers)
 Apply the rules for order of operations to rational numbers
 Apply the rules for order of operations to real numbers and variables
 Identify and write the prime factorization of a number using exponents
 Use the distributive property with real numbers and variables
 Judge whether the strategy will result in an answer greater or less than the exact answer
 Add, subtract, multiply, and divide integers or positive rational numbers
 Use percents and percentages
 Convert between equivalent fractions, decimals, or percents
 Determine rate by using ratios and proportions

Measurement

 Convert measurements within the same system (English or metric)
 Estimate or convert measurements between the English and metric systems in realworld applications, given a conversion factor
 Apply indirect methods, such as, Pythagorean Theorem to find missing dimensions in realworld applications
 Model the conversion within the same system
 Measure accurately using English and metric systems

Statistics & Probability

 Design, collect, organize, display, and explain the classification of data in realworld problems using histograms, scatter plots, and box and whisker plots with appropriate scale (or with technology)
 Design, collect, organize, display, and explain the classification of data in realworld problems using information from tables or graphs that display two sets of data (or with technology)
 Use information from a variety of displays or analyze the validity of statistical conclusions found in the media
 Determine and justify a choice of range, mean, median, or mode as the best representation of data for a practical situation
 Identify and show the meaning of a best fit line
 Determine and compare the experimental and theoretical probability of simple events
 Use a systematic approach to finding sample spaces or to make predictions about the probability of independent events and use the information to solve realworld problems
 Design and conduct a simulation to study a problem and communicate the results

Functions & Relationships

 Describe and extend patterns (linear) up to the nth term represented in tables, sequences, graphs, or in problem situations
 Generalize relationships (linear) using a table, ordered pairs, a graph, or an equation
 Describe in words how a change in one variable in a formula affects the remaining variables (how changing the length affects the area of quadrilaterals and volume of a rectangular prism)
 Use a calculator as a tool when describing, extending, and representing patterns
 Translate a written phrase to an algebraic expression
 Solve or identify solutions to twostep linear equations of the form ax ± b = c, where a ,b, and c, are rational numbers and a ≠ 0; translating a story problem into an equation of similar form; or translating a story problem into an equation of similar form and solving it

Geometry

 Use the attributes and properties or regular polygons to sketch regular or irregular polygons
 Use attributes and properties of solid figures (vertices, length and alignment of edges, shape and number of bases) to identify and describe cylinders and cones
 Use 2dimensional nets to create 3dimensional objects (prisms and cylinders)
 Identify, analyze, compare, and use properties of angles (including supplementary or complementary) or circles (degrees in a circle)
 Use proportionality to solve realworld problems involving similar shapes
 Determine the circumference and area of a circle
 Draw, measure, and construct geometric figures(polygons, perpendicular bisectors, or perpendicular or parallel lines)

Problem Solving

 Select, modify, and apply a variety of problemsolving strategies ( charts, graphing, inductive and deductive reasoning, Venn diagram, and making a simpler problem) and verify the results
 Evaluate, interpret, and justify solutions to problems
 Represent mathematical problems numerically, graphically, and symbolically, translating among these alternative representations; and use appropriate vocabulary, symbols and technology to explain, justify, and defend strategies and solutions
 Generalize from patterns of observations (inductive reasoning) about mathematical problems and testing using a logical verification (deductive reasoning); and justify and defend the validity of mathematical strategies and solutions using examples and counterexamples
 Use realworld contexts such as science, humanities, peers, community, and careers

Grade(s): 1012
Length: Two semesters
Prerequisites: Advanced Algebra (or equivalent)
Numbers and Operations

 Identify numbers as complex, real, irrational, rational, integers, whole, or natural
 Simplify expressions with complex numbers, positive and negative exponents, and rational exponents
 Write expressions in simplest radical form
 Describe and illustrate the affects of arithmetic operations on complex numbers
 Describe and illustrate the use of inverse operations
 Identify and apply commutative, associative, distributive, identity and inverse properties to complex numbers and variables
 Apply basic operation on matrices

Trigonometry

 Use graphs of the unit circle and circular functions to explain, illustrate and calculate trigonometric values
 Express angle displacement in revolutions, degrees and radians
 Use graphs of circular functions to explain, illustrate, and calculate trigonometric solutions
 Apply right triangle trigonometry to solve right triangles
 Apply Law of Sines and Law of Cosines to solve oblique triangles
 Verify equivalent trigonometric expressions using trigonometric identities
 Find exact trigonometric values using trigonometric identities (sum, difference, half angles and double angles)
 Apply trigonometric identities to simplify and solve trigonometric equations
 Apply trigonometric relationships to solve vector problems
 Apply properties of the unit circle to solve trigonometric relationships and equations

Statistics & Probability

 Collect, design, organize, display, and explain data in realworld contexts: science, humanities, among peers, community, and careers
 Use information from tables, graphs, and displays with multiple sets of data to solve problems

Functions & Relationships

 Generalize equations and inequalities involving polynomial, rational, trigonometric, exponential and logarithmic, square root, absolute value, step, radical and piecewise functions
 Use technology including graphing calculators and computers to describe, extend, represent, and graph patterns of polynomial, rational, trigonometric, logarithmic, and exponential equations
 Identify, graph, model and find equations for the conic sections
 Identify and graph points in both rectangular and polar coordinate systems.
 Describe the characteristics of a graph of a function:
intercepts
maximums and minimums
asymptotes using limits
symmetry
end behavior
continuity
domain and range

Problem Solving

 Explain why one strategy is more appropriate than another
 Find alternative methods for solving problems
 Communicate solutions and strategies using appropriate vocabulary and mathematical units
 Use methods of proof to validate conjectures, including direct, indirect and counterexamples
 Apply multistep integrated mathematical problem solving strategies
 Verify solutions using alternative strategies
 Represents problems in a mathematical format using numbers, graphs, tables, illustrations, and symbols
 Use appropriate technology to analyze, solve, justify, and explain strategies and solutions

Grade(s): 1112
Length: Two semesters
Prerequisites: 2 years of high school math
Numbers and Operations

 Read, write model and order real numbers, explaining percents.
 Translate between equivalent representations of the same number. Select a representation that is appropriate for the situation.
 Describe and model the relationship of fractions to decimals, percents, ratios, and proportions.
 Use estimation to solve problems and to check the accuracy of solutions; state whether the estimation is greater or less than the exact answer.
 Apply basic operations efficiently and accurately, using estimation to check the reasonableness of results.
 Add, subtract, multiply and divide rational numbers in various forms including fractions, decimals, and percents.
 Solve problems using ratio and proportion.
 Select, convert, and apply an equivalent representation of a number for a specified situation.

Measurement

 Estimate and convert measurements within systems.
 Apply various measurement systems to describe situations and solve problems.
 Apply information about elapsed time to solve problems.

Statistics & Probability

 Determine and justify a choice of mean, median, or mode as the best representations of data for a practical situation.

Geometry

 Estimate and determine volume and surface areas of solid figures using formulas.

Problem Solving

 Analyze and summarize a problem using the relationship between the known facts and unknown information.
 Recognize and formulate mathematical problems from within and outside the field of mathematics.
 Apply multistep, integrated, mathematical problemsolving strategies, persisting until a solution is found or it is clear that no solution exists.
 Evaluate, interpret, and justify solutions to problems.

Communication

 Represent a problem numerically, graphically, and symbolically; translate among these alternate representations.
 Use appropriate vocabulary, symbols, and technology to explain, justify, and defend mathematical solutions.

Connections

 Apply mathematical skills and processes to global issues.
 Describe how mathematics can be used in knowing how to prepare for careers.

Philosophy:
Students do best when they have an understanding of the conceptual underpinnings of Calculus. Rather than making the course a long list of skills that students have to memorize, the “why” behind the major ideas must be stressed. As we develop the major concepts, we will explain how the mechanics go along with the topics and apply them to real life situations.
Students enrolled in this class must have a graphing calculator that meets the AP College Board calculator requirements. The calculator will be required on some assessments and used as a tool to help students develop an intuitive feel for the concepts.
Unit 1: Precalculus Review
In order to be successful in Calculus, students need a firm grasp on the prerequisite topic. Therefore to assist the students in this requirement 2 3 weeks will be spent reviewing the following topics
 Lines
 Slope as a rate of change
 Parallel and perpendicular lines
 Equations of lines
 B. Functions and graphs
 Functions
 Domain and range
 Families of functions
 Piecewise functions
 Composition of functions
 C. Exponential Growth and Logarithmic functions
 Exponential growth and decay
 Inverse functions
 Logarithmic functions
 Properties of logarithms
 D. Trigonometric Functions
 Graphs of basic trigonometric functions
 Domain and range
 Transformations
 Inverse trigonometric functions
 Applications
Calculus is made up of 4 main concepts: Limits, Derivatives, Indefinite Integrals and Definite Integrals. The 4 concepts will be explored numerically, graphically, algebraically and verbally. The calculator will have an integral part in the study of these concepts.
Unit 2: Limits and Continuity (3 weeks)
 Rates of change and Limits
 Average and instantaneous speed
 Definition of limit
 Properties of limit
 Onesided and twosided
 Squeeze theore
 Limits involving infinity
 Asymptotic and end behavior
 Visualizing limits
 Continuity
 Continuity at a point
 Continuous functions
 Discontinuous functions
 Removable discontinuity
 Jump discontinuity
 Infinite discontinuity
 Intermediate Value Theorem
 Rates of change and Tangent lines
 Average rate of change
 Tangent to a curve
 Slope of a curve
 Normal to a curve
Unit 3: Derivative (5 weeks)
 Derivative of a function
 Definition of a derivative
 Notation
 Relationship between the graphs of _{} and _{}
 Graphing the derivative from data
 B. Differentiability
 Local linearity
 Numeric derivatives using the calculator
 Differentiability and continuity
 Intermediate Value Theorem for derivatives
 Rules for differentiation
 Applications to velocity and acceleration
 Derivatives of trigonometric functions
 Chain rule
 Implicit differentiation
 Derivatives of inverse trigonometric functions
 Derivatives of logarithmic and exponential functions
Unit 4: Applications of the Derivative (4 weeks)
 Extreme values
 Local (relative) extrema
 Global (absolute) extrema
 Applying the derivative
 Mean Value Theorem
 Physical interpretatio
 Rolle’s Theorem
 Increasing and decreasing function
 Analysis of graphs using the first and second derivatives
 Critical values
 First derivative test for extrema
 Concavity and points of inflection
 Second derivative test for extrema
 Modeling and optimization problems
 Linearization models
 Related rates
Unit 5: The Definite Integral (3 weeks)
 Approximation of Area
 Riemann sums
 Trapezoidal rule
 Geometrically
 Definite integrals
 Terminology and notation
 Definite integral and area
 Integrals on the calculator
 Definite integrals and antiderivatives
 Properties of definite integrals
 Average value of a function
 Mean Value Theorem
 Connecting differential and integral calculus
 The Fundamental Theroem of Calculus
 Fundamental Theorem Part 1
 Graphing the function _{}
 Fundamental Theorem Part 2
 Analyzing antiderivatives graphically
Unit 6: Differential Equations and Mathematical Modeling (34 weeks)
 Slope fields
 Differential Equations
 Antiderivatives by substitution
 Indefinite integrals
 Substitution in indefinite integrals
 Substitution in definite integrals
 Exponential growth and decay
 Separable differential equations
 Continuously compounded interest
 Modeling growth with other bases
Unit 7: Applications of Definite Integrals (3 weeks)
 Integral as net change
 Linear motion
 General strategy
 Consumption over time
 Net change from data
 Work
 Areas in the plane
 Volumes
 Volumes of solids with known cross sections
 Volumes of solids of revolution (Disk and Shell methods)
Unit 8: Review for AP Exam (4 5weeks)
Finney, Ross L., Franklin D. Demana, Bert Waits, and Daniel Kennedy.
Calculus – Graphical, Numerical, Algebraic. 3rd ed. Boston Massachusetts: Pearson Prentice Hall, 2007.