• Grade Level: 9
• Length of Course: Year
• Credit: 1
• Prerequisite: 8TH grade Math or Pre-Algebra
• Textbook: Algebra I, Volume I
• ISBN#: 0-07-822847-6
  
• Publisher: Glencoe

COURSE DESCRIPTION
This course consists of a specific set of standards that determine the course content and a set of performance standards that delineate what students should be able to do after successfully completing this course. Math I combines various mathematics topics in one course. Number sense, algebra, geometry, statistics, and logic are presented as tools for investigating problems and exploring new math concepts. Math I is a problem-solving approach to learning mathematics. The appropriate use of technology will enhance the students’ mathematical understanding and improve problem-solving skills. Students successfully completing this course will be ready to advance to Math II. Both Math I and II must be successfully completed to meet the Algebra I requirement.

NUMERATION, NUMBER SENSE, NUMERICAL OPERATIONS

• Learn and use place value, rounding, and estimation
• Represents numbers in different forms: scientific notation, expanded, factored, and exponential
• Find the GCF and LCM of a pair of numbers
• Find equivalent fractions and write fractions in simplest form
• Convert between fractions, decimals, and percents
• Compares, simplifies, and orders fractions, decimals, percents, and square roots
• Compares and orders data containing mixed units of measurement (hours and minutes, feet and inches, metric units)
• Recognizes and applies the properties of addition and multiplication with numbers and variables
• Write and evaluate variable expressions
• Use the order of operations
• Know and use the properties of real numbers
• Use integers to represent points on a number line
• Give the absolute value of an integer
• Read, write, and use ratios and rates to solve problems

MEASUREMENT

• Select and use appropriate systems, units and tools of measurement including estimation
• Accurately measures and draws distances and angles using a ruler or a protractor
• Estimates and converts measurement of length, weight, temperature, time, volume, and capacity within the same system (standard or metric)
• Convert between customary (standard) and metric units
• Solve problems involving rate, distance, time, and scale
• Find dimensions of geometric figures using formulas
• Find perimeter of polygons and solve problems involving perimeter
• Find circumference of circles and solve problems involving circumference

ESTIMATION & COMPUTATION

• Determines whether an estimate is appropriate and whether the estimate is greater or less than the exact answer
• Use the four basic operations (add, subtract, multiply and divide)
• Adds, subtracts, multiplies, and divides numbers in various forms: positive and negative numbers, scientific notation, square roots, fractions, decimals, and percents
• Express numbers in exponential form and scientific notation
• Simplify numbers in exponential form and scientific notation
• Apply the laws of exponents (multiplication, division, and raising an exponent to a power)
• Use zero and negative exponents and scientific notation
• Simplify rates and ratios
• Solves multi-step problems using ratio and proportions
• Calculate percent of increase and decrease
• Rounds numbers appropriately
• Use paper and pencil, mental math, or a calculator to efficiently and accurately solve problems with real numbers (calculators are not permitted on the Exit Exam)

FUNCTIONS & RELATIONSHIPS

• Analyzes and compares lines form graphs, tables, and equations (slope, perpendicular, parallel)
• Analyzes, extends, and applies patterns of numbers or shapes
• Adds, subtracts, and multiplies algebraic expressions
• Uses algebraic expressions to represent or model mathematical relationships
• Recognizes, writes, and applies formulas including terms with exponents
• Describes patterns with algebraic expressions
• Converts representation of data between graphs, tables, and equations
• Solves algebraic equations involving one or more variables
• Solve a formula for a specific value
• Solve one-step and two-step equations and inequalities
• Solve equations and inequalities with variables on both sides
• Graph the solution of an equation or inequality
• Simplify polynomials by gathering like terms
• Multiply monomials and a polynomial by a monomial
• Graph points in a coordinate plane
• Use ordered pairs to graph a linear equation
• Find the slope of a line
• Write equations of lines

GEOMETRY

• Construct draw, measure, transform, compare, visualize, classify, and analyze the relationships among geometric figures
• Identify basic geometric shapes
• Identifies and applies properties of complementary and supplementary angles; parallel, perpendicular, and intersecting lines; polygons and circles
• Classify triangles
• Identify types of quadrilaterals
• Construct a copy of a given angle and line segment
• Construct an angle bisector and a perpendicular bisector of a line
• Draws a geometric figure with specific properties
• Identifies the slope and equation of a line in the coordinate plane
• Find the area of rectangular figures and irregular figures
• Find the area of a parallelogram and triangle
• Find the circumference and area of circles
• Apply the Pythagorean theorem
• Find the volume of a prism, cylinder, pyramid, cone and sphere
• Find the surface area of a prism, cylinder, cone, and sphere
• Identify, draw, and use translations, reflections, and rotations to demonstrate geometric principles
• Identify line symmetry and rotational symmetry
• Visualizes, draws, or describes a three-dimensional figure, such as a box or pyramid, form its two-dimensional view (or vice versa)

STATISITCS/PROBABILITY

• Explains, justifies, and defends statistical conclusions
• Explore methods of collecting, displaying, and analyzing data
• Selects, explains, and uses appropriate scales of graphs
• Read data and predicts trends from tables, graphs, and charts
• Read, analyze, interpret, and construct stem and leaf plots, pictographs, bar graphs, and line graphs
• Identify and calculate mean, median, mode and range
• Chooses between mean, median, and mode as the best representation of data and explains the choice
• Describes the slope of a line as the rate of change
• Find and compute probabilities of dependent and independent events
• Determines the probability of an event
• Use the counting principle to find number of outcomes
• Selects and appropriate sampling group and uses samples to make predictions
• Determine line of best fit and use to predict unknown data values

PROBLEM SOLVING, COMMUNICATION, REASONING, CONNECTIONS

• Uses appropriate vocabulary and symbols to explain, justify, and defend solutions to mathematical problems
• Uses a variety of problem-solving strategies (guess and check, working backwards, diagrams, patterns, etc.)
• Writes expressions and equations from a given problem
• Solves multi-step problems
• Explains answers in written form showing all steps of solving the problem
  

• Grade Level: 10-11
• Length of Course: Year
• Credit: 1
• Prerequisite: Math I or Placement
• Textbook: Algebra I, Volume 2
• ISBN#: 0-07-822849-2
  
• Publisher: Glencoe

COURSE DESCRIPTION
This course consists of a specific set of standards that determine the course content and a set of performance standards that delineate what students should be able to do after successfully completing this course. Math II combines various mathematics topics in one course. Algebra, geometry, statistics, logic, and trigonometry are presented as tools for investigation phenomena, and exploring new math concepts. Math II is a problem solving approach to learning mathematics. This course briefly reviews concepts presented in Math I, then emphasizes more advanced topics in algebra, probability and statistics, and geometry. Students successfully completing Math I and II can advance to Geometry, or other math electives. Math I and II must be successfully completed to meet the Algebra I requirement for graduation.

NUMERATION, NUMBER SENSE, NUMERICAL OPERATIONS

• Read, write, and find powers and roots of numbers
• Use mathematical symbols to describe sets and relationships between sets
• Identify and graph real numbers
• Represents numbers in different forms: scientific notation, expanded, factored, and exponential
• Compares, simplifies, and orders fractions, decimals, percents, and square roots
• Identify unions and intersections of sets
• Use Venn diagrams to solve problems
• Apply the properties of exponents to evaluate and simplify expressions
• Evaluate variable expressions with negative exponents
• Identify the next terms in a sequence
• Identify relations and domains and ranges
• Add in a different base system
• Converts between fractions, decimals, and percents
• Compares and orders data containing mixed units of measurement (hours and minutes, feet and inches, metric units)
• Recognizes and applies the properties of addition and multiplication with numbers and variables

MEASUREMENT

• Read, write, and calculate measurements to show precision, tolerance, and accuracy
• Accurately measures and draws distances and angles using a ruler or protractor
• Estimates and converts measurements of length, weight, temperature, time, volume, and capacity within the same system (standard or metric)
• Solve problems involving rate, distance, time, and scale
• Finds dimensions of geometric figures using formulas
• Analyze space figures
• Find surface areas and the volume of space figures

ESTIMATION & COMPUTATION

• Perform basic operations on integers and rational numbers
• Add, subtract, multiply, and divide real numbers and expressions: positive and negative numbers, scientific notation, square roots, fractions, decimals, and percents
• Calculates percent of increase and decrease
• Determines whether an estimate is appropriate and whether the estimate is greater or less than the exact answer
• Solves multi-step problems using ratios and proportions
• Rounds numbers appropriately

FUNCTIONS & RELATIONSHIPS

• Analyze and compare lines from graphs, tables, and equations (slope, perpendicular, parallel)
• Analyze, extend, and apply patterns of numbers and shapes
• Add, subtract, and multiply algebraic expressions
• Use algebraic expressions to represent or model mathematical relationships
• Recognize, write, and apply formulas including terms with exponents
• Describe patterns with algebraic expressions
• Convert representation of data between graphs, tables, and equations
• Solve algebraic equations involving one or more variables
• Solve word problems using systems of equations
• Solve systems of equations using determinants and matrices
• Solve systems of inequalities
• Add, subtract, and multiply polynomials by monomials
• Factor polynomials into a monomial factor and polynomial factor
• Multiply binomials
• Factor polynomials by grouping
• Factor perfect square trinomials and differences of perfect squares
• Use factoring to solve quadratic equations
• Factor trinomials
• Identify, graph, and describe the graphs of basic families of functions, including linears, absolute value, quadratic, and exponential using a graphing calculator
• Solve quadratic equations by completing the square
• Solve quadratic equations by using the quadratic formula
• Write equations of circles, parabolas, hyperbolas, and ellipses
• Solve problems with direct and inverse variation
• Graph quadratic inequalities

GEOMETRY

• Apply postulates about points, lines, and planes
• Use shapes to investigate trigonometric functions
• Recognize, classify, and measure lines and angles
• Identify bisectors of angles and segments
• Apply theorems about midpoints, angle bisectors, and vertical angles
• Solve problems using circles, semi-circles, and quarter circles.
• Apply knowledge of lines and angles to problem solving
• Identify and draw three dimensional shapes
• Apply the Pythagorean Theorem, the sine, cosine, and tangent functions to right triangles.
• Use characteristics of 45-45 degree and 30-60 degree right triangles to solve practical problems
• Find the area, surface area, and volume to geometric objects and solids
• Use inductive reasoning to complete patterns
• Identify and evaluate conditional statements
• Identify converses and biconditionals
• Write geometric proofs in two-column format
• Analyze tessellations using properties of polygons
• Identify and sketch altitudes and medians of a triangle
• Identify and sketch perpendicular bisectors of sides of a triangle
• Identifies and draws rotations and mirror images

STATISTICS/PROBABILITY

• Explore methods of collecting, displaying, and analyzing data
• Compute and determine probabilities of dependent and independent events and find experimental and theoretical probability
• Read and create statistical graphs (two-dimensional coordinate graph, bar graph, scatter plot, box-whisker, histograms, stem and leaf, etc.)
• Read data and predict trends from tables, graphs, and charts
• Explain, justify, and defend statistical conclusions
• Identify and calculate mean, median, mode and range
• Choose between mean, median, and mode as the best representation of data and explain the choice
• Compute probabilities of dependent and independent events
• Multiplication rule for independent events
• Create a sample space to illustrate all possible outcomes of a simple or compound event
• Describe the slope of a line as the rate of change
• Selects an appropriate sampling group
• Estimate/calculate a line of best fit for a given set of data
• Predict unknown values using the line of best fit
• Compare probability for simple and compound events
• Find the number of permutations and combinations of a set
• Recognize and analyze the validity of statistical conclusions and the use, misuse, and abuse of data caused by a wide variety of factors
• Find variance and standard deviation
• Find amplitude, wave length, period, phase shift, and frequency of sine waves

TRIGONOMETRY

• Use trigonometric ratios to find an unknown side or angle of a right triangle
• Identify and compute sine, cosine, and tangent ratios in a right triangle
• Use trigonometric ratios to find the lengths of sides of right triangles
• Use trigonometric ratios to find the measures of angles in right triangles
• Solve right triangle using trigonometric ratios and the Pythagorean theorem
• Explore relationships in right triangles 30 degrees, -60 degrees, -90 degrees and 45 degrees, -45 degrees,-90 degrees

PROBLEM SOLVING, COMMUNICATION, REASONING, CONNECTIONS

• Solve problems that involve numbers written as powers and roots
• Use formulas to solve problems
• Solve problems that involve linear equations
• Uses appropriate vocabulary and symbols to explain, justify, and defend solutions to mathematical problems
• Uses a variety of problem-solving strategies (guess and check, working backwards, diagrams, patterns, etc.)
• Explains answers in written form showing all steps of solving the problem
  

• Grade Level: 11-12
• Length of Course: Year
• Credit: 1
• Prerequisite: HSGQE or Placement
• Textbook: Mathematics: Applications and Connections Course 3
• ISBN#: 0-07-822852-2
• Publisher: Glencoe
  

COURSE DESCRIPTION

This course consists of a specific set of standards that determine the course content and a set of performance standards that delineate what students should be able to do after successfully completing this course. Math III is a refresher course for students, who have completed the Math I and Math II or Algebra I requirements for graduation, but have not been successful in passing the High School Graduation Qualifying Exam in Mathematics. This course will cover the topics of basic mathematics, consumer math, statistics and probability, geometry, and algebra. It will be individualized to meet student needs.

NUMERATION, NUMBER SENSE, NUMERICAL OPERATIONS

• Represents numbers in different forms; scientific notation, expanded, factored, and exponential
• Compares, simplifies, and orders fractions, decimals, percents, and square roots
• Converts between fractions, decimals, and percents
• Compares and orders data containing mixed units of measurement (hours and minutes, feet and inches, metric units)
• Recognizes and supplies the properties of addition and multiplication with numbers and variables

MEASUREMENT

• Identify and use metric prefixes
• Accurately measures and draws distances and angles using a ruler or protractor
• Estimates and converts measurements of length, weight, temperature, time, volume, and capacity within the same system (standard or metric)
• Solves problems involving rate, distance, time, and scale
• Finds dimensions of geometric figures using formulas
• Use and convert customary and metric units of measurement
• Convert between metric and customary units of measurement
• Estimate and measure metric units of length
• Change metric units of length
• Change from one customary unit of length to another
• Find measure of length, mass, capacity, area, volume, temperature (metric and customary)
• Know and use the Pythagorean theorem
• Use right triangle trigonometry to solve problems

ESTIMATION and COMPUTATION

• Determines whether an estimation is appropriate and whether the estimation is greater or less than the exact answer
• Adds, subtracts, multiplies, and divides numbers in various forms: positive and negative numbers, scientific notation, square roots, fractions, decimals, and percents
• Calculates percent of increase and decrease
• Solves multi-step problems using ratios and proportions
• Rounds numbers appropriately

FUNCTIONS and RELATIONSHIPS

• Perform algebraic operations on integers, polynomials, and formulas and solve and graph linear equations
• Perform operations on positive and negative numbers (adding, subtracting, multiplying and dividing)
• Adds, subtracts, and multiplies algebraic expressions
• Use properties of equalities
• Define and graph absolute value
• Perform operations on rational expressions
• Perform polynomial operations
• Solve fraction and percent problems using variables
• Solves algebraic equations involving one or more variables
• Use formulas to solve problems
• Recognizes, writes, and applies formulas including terms with exponents
• Graph linear, quadratic, and inequalities in coordinate plane
• Simplify and perform operations with exponential and radical expressions
• Add in different base system
• Identify, describe, and graph functions using a graphing calculator (linear, absolute value, quadratic, and exponential)
• Create and solve linear and quadratic equations and inequalities
• Translate between equivalent representations of the same exponential expressions
• Analyzes, extends, and applies patterns of numbers or shapes
• Describes patterns with algebraic expressions
• Analyzes and compares lines from graphs, tables, and equations (slope, perpendicular, parallel)
• Uses algebraic expressions to represent or model mathematical relationships
• Converts representation of data between graphs, tables, and equations

GEOMETRY

• Construct, draw, measure, transform, compare, visualize, classify, and analyze the relationships among geometric figures
• Draws a geometric figure with specific properties
• Identify, name, and draw points, lines, and planes
• Know and use properties of lines, angles, and triangles (definitions, similar, and congruent)
• Identifies and applies properties of complementary and supplementary angles; parallel, perpendicular, and intersecting lines; and polygons
• Identifies the slope and equation of a line in the coordinate plane
• Use transformations to demonstrate geometric principles (e.g., slides, flips, turns, and shrinking or enlarging)
• Identifies and draws rotations and mirror images
• Name, draw, and measure angles
• Make constructions using a compass and a straightedge
• Identify and name parallel and perpendicular lines
• Identify and use properties of polygons and circles (interior and exterior angles, arcs, chords, secants, and tangents) to solve problems
• Finds circumference and area of circles
• Identify and name various types of triangles
• Identify and name quadrilaterals
• Visualizes, draws, or describes a three-dimensional figure, such as a box or pyramid, from its two-dimensional view (or vice versa)
• Construct geometric models, transformation, and scale drawings using a variety of methods
• Identify and name three-dimensional figures
• Determine slopes of lines
• Create and solve systems of linear equations algebraically and graphically
• Identify and use congruent and similar figures to solve problems

STATISTICS/PROBABILITY

• Use measures of central tendency and graphical representations to analyze data
• Create bar, line, and circle graphs to display data
• Use frequency distributions and measures of central tendency to analyze data
• Calculate probability and odds of an event occurring
• Find the line of best fit and use to predict unknown data values
• Calculate correlation and use to analyze data
• Find and compare theoretical and experimental probability on multiple events
• Selects, explains, and uses appropriate scales of graphs
• Explains, justifies, and defends statistical conclusions
• Reads data and predicts trends from tables, graphs, and charts
• Chooses between mean, median, and modes as the best representation of data and explains the choice
• Analyzes, interprets, and constructs graphs and diagrams to display data
• Describes the slope of a line as the rate of change
• Selects an appropriate sampling group

PROBLEM SOLVING, COMMUNICATION, REASONING, CONNECTIONS

• Solve problems using logical reasoning
• Use appropriate vocabulary and symbols to explain, justify, and defend solutions to mathematics problems
• Use a variety of problem-solving strategies (guess and check, working backwards, diagrams, patterns, etc.)
• Writes expressions and equations from a given problem
• Solves multi-step problems
• Explains answers in written form showing all steps of solving the problem
  

ALASKA MATHEMATICS PERFORMANCE STANDARDS

Course________________________________________ School Year______________

Instructions: Enter date of when the performance standard was introduced, reinforced, or mastered (proficient). Assignments will provided in teacher lesson plans and/or Individual Learning Plans.

• Grade Level: 9th/10th
• Length of Course: Year
• Credit: 1
• Prerequisite: 8th grade math, Pre-Algebra, Math I
• Textbook: Algebra I
• ISBN#: 0-07-822847-6
• Publisher: Glencoe

COURSE DESCRIPTION
This course consists of a specific set of standards that determine the course content and a set of performance standards that delineate what students should be able to do after successfully completing the course. Algebra I covers linear functions, linear inequalities, real numbers, manipulating algebraic symbols, and solving real world problems using algebraic expressions and equations. This course integrates topics from probability, statistics, and trigonometry, which will be employed to motivate, justify, extend, and enhance important concepts of algebra. Appropriate technology, scientific and graphing calculators, graphing software, and spreadsheet software will be integrated throughout Algebra I for instruction and assessment. Students will use the skills of reading, writing, listening, and modeling to investigate, interpret, and evaluate mathematical ideas.

• NUMERATION, NUMBER SENSE, NUMERICAL OPERATIONS
  Read, write, model, order, and define real numbers and subsets
• Classify numbers, as real, irrational, rational, integer, whole, natural
• Compare the differences and similarities among rational, irrational, whole, integral, and natural numbers and represent these relationships using Venn diagrams
• Evaluate absolute value expressions
• Compare and order real numbers using <, <, >, >, -, and =
• Compute a rational approximation for an irrational number
• Use prime factors to find the greatest common factors (GCF) and least common multiple (LCM) of a set of monomial
• Factor quadratic expressions
• Evaluate expressions for specific values of variables
• Evaluate exponential expressions

MEASUREMENT

• Estimate and convert measurements within the same system
• Estimate and convert measurements between different systems of measurement
• Select and use appropriate systems, units, and tools of measurement including estimation

ESTIMATION and COMPUTATION

• Add, subtract, multiply, and divide real numbers in various forms, including scientific notations, powers, and roots
• Add, subtract, multiply, divide, and simplify rational expressions
• Add in a different base
• Add, subtract, multiply, and divide signed numbers and variables
• Convert decimals, fractions, or percents to most useful form in various situations
• Use a calculator to evaluate a numeric expression involving roots and exponents
• Evaluate formulas including the quadratic formula, distance formula, slope and midpoint formulas
• Convert between scientific notation and standard decimal form
• Identify the dimensions of a matrix
• Add and subtract matrices
• Multiply a matrix by a scalar
• Use appropriate units to label solutions to application problems
• Use unit analysis with standard and metric systems
• Evaluate and simplify algebraic expressions using order of operations

FUNCTIONS and RELATIONSHIPS

• Solve and simplify expressions, first-degree equations, inequalities, and/or polynomials
• Solve problems containing “and” or “or” statements
• Create and solve linear and quadratic equations and inequalities
• Model and represent situations that involve numerical and variable quantities with expressions, equations, inequalities, and/or polynomials
• Use tables and graphs as tools to interpret and analyze expressions, equations, inequalities, and/or polynomials
• Translate among tabular, symbolic, and graphical representations of a variety of functions and equations
• Use ratios and proportions to model and solve fractions and percent problems with variables
• Identify, graph, and describe the graphs of basic families of functions and equations, including linear, absolute value, quadratic, and exponential
• Graph absolute value in one and two variables
• Write the equation of a line using slope-intercept form, standard form, and/or point slope form
• Find the slope of a line given two points on the line
• Identify the slope of a line, x-intercept, and y-intercept given the equation of the line
• Describe the slope of the line in the context of a problem situation
• Investigate and determine the effects of changes in slope and intercepts on the graph and equation of a line
• Use the distance and midpoint formula
• Create and solve systems of equations, algebraically, graphically, and by using technology
• Use function notation and evaluate functions
• Identify domain and range from the graph of a function, relation, or a set of ordered pairs
• Write an equation or rule for a set of paired data
• Describe polynomials using appropriate terminology
• Classify polynomials by degree and by number of terms
• Simplify polynomial expressions, including factoring
• Use a variety of techniques to factory polynomial expressions, including the greatest common factor, difference of two squares, perfect square trinomial, grouping, and trial and error
• Add, subtract, multiply, and divide with polynomials
• Evaluate polynomials
• Apply the Pythagorean theorem

GEOMETRY

• Apply the properties of equality and proportionality to solve problems involving congruent or similar shapes
• Graph and describe the results of transformations including translations (slides) and dilations (shrinking or enlarging)
• Use coordinate geometry to represent and interpret relationships defined by equations and formulas including distance and midpoint
• Use geometric formulas such as area, surface area, volume, and circumference to solve problems
• Apply geometric concepts to solve problems in algebra by solving systems of equations through graphing, analyzing range, domain, intercepts, by finding an equation of a line given a graphical representation, and by exploring number sentence relationships to coordinate graphs (numerical coefficients, slopes, and the y and x intercepts
• Identify situations requiring the Pythagorean theorem, and analyze how and why the theorem is used
• Use the Pythagorean theorem and theorem’s converse to solve real world scenario problems involving right triangles
• Predict characteristics of unseen faces of three-dimensional figures
• Describe, extend, and express algebraically a wide variety of geometric patterns

TRIGONOMETRY

• Studying triangles, trigonometric ratios, and triangle measurements, applying triangle properties, and solving right triangle problems
• Find either the sine, cosine, or tangent of right triangles by utilizing a table of trigonometric ratios
• Find six trigonometric ratios and their relationships
• Solve right triangles using trigonometric ratios and the Pythagorean theorem
• STATISTICS/PROBABILITY
• Construct tables, chars, scatter plots, and graphs from given data
• Describe the central tendency and distribution of a given set of data, including a box-and-whisker plot
• Make predictions based on data from a table, chart or graph
• Compute mean, median, and mode for set of data
• Compute the range of a set of data
• Represent data in a matrix
• Estimate/calculate a line of best fit for a given set of data
• Predict unknown values using the line of best fit
• Create a sample space to illustrate all possible outcomes of a simple or compound event
• Compare probability for simple and compound events
• Solve probability problems represented as area models
• Find and compare results of experimental and theoretical probability
• Experiment using simulations such as random number generators

PROBLEM SOLVING, COMMUNICATION, REASONING, CONNECTIONS

• Use various problem solving strategies including estimation, systematic lists, diagrams, patterns, guess and check, working backward, and solving simpler problem
• Check the reasonableness of answers using estimation
• Write equations and inequalities to represent word problems
• Graph and compare functions with and without a graphing calculator
• Enter and run a simple program using a graphing calculator or computer
• Create a spreadsheet(such as a table of function values) to display information
• Select and use appropriate method for computing: estimation, mental math, pencil and paper, calculator, and computer
• Develop an appropriate graph and use it to prove a point or communicate an idea
• Use appropriate vocabulary, symbols, and technology to explain, justify, and defend mathematical solutions
• Use informal deductive and inductive reasoning in both concrete and abstract contexts
• Understand that a physical or mathematical model can be used to estimate the probability of real-world events
• Apply mathematical skills and processes to other disciplines (e.g. measurement in science, data analysis in social studies research)
  

• Grade Level: 10th-12th
• Length of Course: Year
• Credit: 1
• Prerequisite: Algebra I or Math I and Math 2
• Textbook: Geometry
• ISBN#: 0-07-822880-8
• Publisher: Glencoe

COURSE DESCRIPTION
This course consists of a specific set of standards that determine the course content and a set of performance standards that delineate what students should be able to do after successfully completing this course. Students will move from an inductive approach to deductive methods of proof in their study of geometric figures. Geometry covers Euclidean geometry concepts of solving right triangles, developing the unit circle, and working with vectors. This course develops the relationships between two-dimensional and three-dimensional figures. Two- and three-dimensional reasoning skills will be emphasized and students will broaden their use of coordinate plane to include transformations of geometric figures. Appropriate technology, from manipulatives to calculators and graphics software, will be used regularly for instruction and assessment.

NUMERATION, NUMBER SENSE, NUMERICAL OPERATIONS

Perform operations with real numbers to solve problems in a geometric unit

• Validate numerical solutions for application problems
• Describe the number “Pi” and its relationship to circles, cylinders, and spheres
• Determine the surface area and volume of cylinders and spheres
• Sketch diagrams that represent given information about measures of segments and angles
• Determine limitations and boundaries of variables representing angles and lengths
• Explain restrictions on variables representing angles and lengths

MEASUREMENT

• Use measurement tools with accuracy and precision
• Measure angles using a protractor
• Model and measure basic geometric figure using a variety of methods including paper folding, compass, straight edge, protractor, and technology
• Use a variety of methods for basic constructions and models (e.g., paper folding, compass, straight edge, protractor, technology)
• Use appropriate unit labels in solutions of application problems

ESTIMATION and COMPUTATION

• Simplify expressions involving radicals and exponents
• Simplify complex fractions when the appear in proportions and formulas
• Evaluate formulas relevant to geometry including distance, midpoint, area, perimeter, volume, Pythagorean theorem, and quadratic formula
• Set up and solve proportions involving similar figure
• Use trigonometric ratios to compute measures of unknown parts of a right triangle
• Compute measures of unknown parts of a right triangle using the sine, cosine, and tangent ratios

FUNCTIONS, RELATIONSHIPS, ALGEBRA

• Use slopes to determine if two lines are parallel or perpendicular
• Write the equation of a line parallel or perpendicular to a given line through a given point
• Graph linear equations
• Find equations of and graph conic sections
• Transform (translate, reflect, rotate, dilate) polygons in the coordinate plane; describe the transformation in simple algebraic form
• Solve problems using the inequality relationship between the sides and angles of a triangle
• Identify and use patterns from right triangles, including 30 degree –60 degree –90 degree, 45 degree –45 degree –90 degree, and Pythagorean triples to solve application problems
• Identify and describe patterns that emerge from two-dimensional and three-dimensional geometric figures (e.g. Euler’s formula for vertices, edges, and faces; altitudes and slant height of solids, etc.)
• Write and solve equations that model geometric relationships
• Simplify and solve equations that result from formulas including distance, midpoint, and the Pythagorean Theorem
• Solve application problems that result from formulas

GEOMETRY

THEORY

• Communicate orally and in writing using correct geometric vocabulary and notation
• Explain the difference among definitions, postulates/axioms, and theorems
• Explain the importance of the Parallel Postulate in Euclidean geometry
• Classify problems as classical Euclidean geometry, coordinate geometry, or transformational geometry
• Explain the difference between inductive and deductive reasoning

DEDUCTION

• State the converse, inverse and contrapositive of a conditional statement and determine the validity of each
• Rewrite and “if and only if” statement into two conditional statements and vice versa
• Prove conjectures related to geometric figures using paragraph proofs, indirect proof, two-column proofs, and coordinate geometry proofs
• Prove triangles are congruent using SSS, SAS, ASA, AAS, and HL
• Use definitions of terms related to triangles (i.e. altitude, median, angle bisector, isosceles, etc.) to deduce other properties of triangles
• Develop and explain the properties of trapezoids, parallelograms, rectangles, rhombuses, kites, and squares using the definitions of the various quadrilaterals
• Prove two triangles are similar and write a valid proportion showing the relationship between the corresponding sides
• Prove conjectures related to angles, parallel lines, and planes
• DIAGRAMS and MODELS
• Select appropriate theorems to prove or disprove conjectures related to geometric figures
• Identify, classify, and draw two-dimensional and three-dimensional figures
• Draw and label triangles illustrating the congruency relationships of SSS, SAS, ASA, AAS, and HL
• Identify and label corresponding parts of overlapping triangles
• Identify and label congruent non-coplanar triangles in a three-dimensional diagram
• Draw and label similar figures showing the correct relationship between corresponding parts
• Solve problems involving triangles, quadrilaterals, and other polygons using appropriate terminology and properties
• Identify and label angles, segments, and lines as they relate to circles, and use the properties to solve problems
• Explain the difference among alternate interior angles, alternate exterior angles, corresponding angles, supplementary angles, and vertical angles formed by two lines and a transversal
• Model and explain parallel, perpendicular, skew, and oblique lines
• Describe the relationships of planes in space
• Find interior and exterior angle measures of regular polygons
• Confirm the validity of conjectures or provide a counter example using appropriate technology and software

STATISTICS/PROBABILITY

• Use length, area, and volume to solve problems involving probability
• Construct a sample space illustrating all outcomes of a particular event
• Solve probability problems involving geometric models
• Create scatter plots and find lines of best fit to predict outcomes

PROBLEM SOLVING, COMMUNICATION, REASONING, CONNECTIONS

• Recognize and formulate mathematical problems from within and outside the field of mathematics
• Apply multi-step, integrated, mathematical problem-solving strategies, persisting until a solution is found or it is clear no solution exists
• Verify the reasonableness of an answer by using an alternative strategy
• Develop an appropriate graph and use it to prove a point or communicate an idea
• Use numerical, graphic, and symbolic representations to support oral and written communication about mathematical ideas
• Justify and defend mathematical ideas, solutions, and methods to various audiences
• Use appropriate technology to present information and ideas
• Follow and evaluate an argument, judging its validity using reasoning and logic
• Make and test conjectures
• Use methods of methods (e.g. direct, indirect, counterexamples, paragraph) to validate conjectures
• Use the connections among mathematical topics to develop multiple approaches to problems
• Relate procedures in one representation of a problem to procedures in an equivalent representation (e.g., writing an equation given a set of ordered pairs, writing an equation given a graph of the line
• Apply mathematical skills and processes to other disciplines (e.g. measurement in science, data analysis in social studies research)
• Describe how mathematics can be used in careers
  

• Grade Level: 10th-12th
• Length of Course: Year
• Credit: 1
• Prerequisite: Algebra I & Geometry
• Textbook: Algebra II
• ISBN#: 0-07-822887-5
• Publisher: Glencoe

COURSE DESCRIPTION
This course consists of a specific set of standards that determine the course content and a set of performance standards that delineate what students should be able to do after successfully completing this course. Algebra II continues the students’ study of advanced algebraic concepts including solving and graphing second-degree equations, solving systems of linear equations, complex numbers, matrices, determinants, synthetic division, polynomial, exponential, and logarithmic functions. It also incorporates data analysis, geometry, statistics, and business applications. Emphasis should be placed on practical applications and modeling. Students will use technology from manipulatives to calculators and application software to further explore topics and build conceptual understanding.

NUMERATION, NUMBER SENSE, and NUMERICAL OPERATIONS

Use estimation to check reasonableness of answers

• Select appropriate scales when graphing application problems
• Set an appropriate window when graphing with a graphing calculator
• Estimate an equation for a line or curve that models the scatter plot for a given set of data
• Identify and classify subsets of the complex number system as natural, whole, integer, rational, irrational, real, or imaginary
• Determine appropriate domain and range for application problems
• Determine restrictions for variables appearing in rational and radical expressions so that the statement will be meaningful
• Use appropriate units to label solutions of application problems
• Define and use properties of the complex number system
• Identify and use closure, identity, inverse, associative, and commutative properties
• Identify and use reflexive, symmetric, and transitive properties

PATTERNS & RELATIONSHIPS

Develop a rule for a sequence and represent that rule recursively, explicitly, or verbally

• Identify a sequence as arithmetic, geometric, or neither
• Factor polynomial expressions using a variety of patterns including difference of two squares, sums or differences of two cubes, perfect square trinomials, and grouping
• Use Pascal’s triangle to find the coefficients for a binomial expansion
• Use the Binomial theorem to find a particular term of binomial expansion
• Determine if two variables vary directly or inversely and, if applicable, find the constant variation

ALGEBRA & FUNCTIONS

Identify the Fundamental Theorem of Algebra (all polynomial equations can be solved using complex numbers, even those with imaginary coefficients)

• Determine whether a given relation is a function
• Identify the domain and range of a function
• Find the inverse of a function if it exists and describe it graphically
• Add, subtract, multiply, divide, and compose functions, and identify the domain and range of the new function
• Graph a piecewise function (piecewise function has different rules for different parts of its domain)
• Perform operations on matrices (add, subtract, multiply, inverse, determinants, and scalar multiplication)
• Simplify rational expressions and radicals
• Solve problems that contain radicals and rational expressions
• Simplify expressions involving fractional exponents
• Add, subtract, multiply, and divide complex numbers, and simplify the results
• Solve quadratic equations that have complex roots
• Identify the conic sections and use completing the square to rewrite them in standard form
• Write equations of and graph conic sections
• Solve problems involving “and” and “or” statements
• Solve literal equations and formulas for a given variable
• Solve a system of three equations in three unknowns using the substitution method and/or addition method
• Use matrices and a graphing calculator to solve systems of linear equations
• Solve systems of non-linear equations
• Use the rational root theorem and the factor theorem to find rational roots of equations of degree three or more
• Use synthetic division to divide a polynomial by a binomial of the form x-a
• Solve inequalities using number lines and coordinate planes
• Represent a series using sigma notation
• Find partial sums of arithmetic and geometric series
• Calculate the sum of an infinite geometric series with lrl< 1
• Identify, solve, and graph exponential and logarithmic functions
• Simplify expressions involving logarithms
• Solve equations by applying the properties of logarithms
• Solve for an unknown exponent using logarithms
• Find common and natural logarithms and antilogarithms
• Apply algebra concepts and skill to solve real world problems
• Solve application problems using appropriate technology

TRIGONOMETRY

• Use the unit circle to find values of trigonometry functions
• Find values of trigonometric functions (exact and decimal approximation)
• Apply right triangle trigonometry to problems
• Apply law of cosines and sines to problems
• Graph trigonometric functions (amplitude, period, and phase shift)
• Identify trigonometric identities

STATISITCS & PROBABILITY

• Read and interpret data displayed in a table, chart or graph
• Organize and display data using stem-and-leaf plots, box-and-whisker plots, histograms, and scatter plots
• Determine a line or curve of best fit for a given set of data
• Use regression equation that models a set of data to make predictions
• Determine the mean, median, mode, and range for a set of data
• Determine the percentile rank of a data point
• Explain the difference between percentile and percentage
• Calculate the standard deviation for a set of data that is normally distributed
• Determine the reasonableness of statistical conclusions applied to real-world situations
• Explain the difference between combinations and permutations
• Select and use appropriate formulas to solve problems involving combinations and permutations
• List all possible outcomes for a particular event
• Explain the difference among independent, dependent, and mutually exclusive events
• Compute probabilities for simple and compound events
• Solve problems involving conditional probability
• Explain the difference between experimental probability and theoretical probability

GEOMETRY & MEASUREMENT

• Graph linear functions accurately with pencil and paper given slope-intercept form
• Graph quadratic functions accurately with pencil and paper given vertex form
• Label a geometric figure using algebraic expressions and write a valid relationship involving the expressions
• Identify and graph parent functions including constant, linear, quadratic, cubic, absolute value, exponential, logarithmic, and reciprocal
• Transform parent functions using translation, reflection, stretching and/or shrinking
• Graph equations having discontinuities such as asymptotes and/or holes
• Identify and explain types of symmetry
• Sketch the graphs of circles, ellipses, hyperbolas, and parabolas given in standard form
• Use the formulas of coordinate geometry including slope, midpoint, distance, and equations of lines from memory
• Explain the geometric interpretation of real zeros of a function

PROBLEM SOLVING, COMMUNICATION, REASONING, CONNECTIONS

• Identify the elements within a story problem
• Uses appropriate vocabulary and symbols to explain, justify, and defend solutions to mathematical problems
• Uses a variety of problem-solving strategies
• Writes expressions and equations from a given problem
• Solves multi-step problems
• Explains answers in written form showing all steps of solving the problem
• Recognize and formulate mathematical problems from within and outside the field of mathematics
• Follow and evaluate an argument, judging its validity using inductive or deductive reasoning and logic
• Use methods of proofs including direct, indirect, and counterexamples, to validate conjectures
• Apply mathematical skills and processes to global issues
• Describe how mathematics can be used in knowing how to prepare for careers

• Grade Level: 11th-12th
• Length of Course: Year
• Credit: 1
• Prerequisite: Geometry & Algebra II

COURSE DESCRIPTION
Functions, Analysis, and Trigonometry is a course designed to pull together and extend the students’ mathematical knowledge base. Particular emphasis is placed on trigonometric functions, to provide students with a solid foundation for further study in mathematics. It includes an in-depth coverage of the concepts of functions, including linears, polynomial, exponential, logarithmic, and trigonometric functions. This course also covers analytic geometry, vectors, sequences, series, and curve fitting. Descriptive and inferential statistics, elementary combinatorics and probability are included. Scientific graphing calculators are used extensively to facilitate visualization of graphs and to perform statistical analysis of data, while traditional methods of graphing and data analysis without the use of technology are still stressed.

NUMBER SENSE, OPERATIONS, COMPUTATION

• Identify sets and use properties of sets
• Union, intersection, disjoint, and mutually exclusive
• Work with open sentences and conditional sentences
• Recognize the properties of real numbers and irrational numbers
• Describe irrational numbers
• Find the position or irrational numbers on the number line in decimal and radical form
• Explain the relationship of the sets of the rational and irrational numbers to the set of real numbers
• Understand the number line and its use with inequalities
• Understand absolute value and be able to use it
• Know the subsets of real numbers (rational numbers, integers, natural numbers and irrational numbers)
• Use complex numbers
• The number i
• Square roots of negative numbers
• Operations with complex numbers
• Conjugate factors
• Use complex numbers to illustrate properties, solve equations using trigonometric forms, and use De Moivre’s Theorem
• Sketch graphs of complex numbers in Argand (complex) plane

PATERNS & RELATIONSHIPS; ALGEBRA & FUNCTIONS

• Understand the concept of a relation and know when a relation is a function
• Determine that the domain and range of a relation and function
• Understand functions as mappings
• Understand transformations of linear functions
• Understand matrices and the properties and operations dealing with matrices
• Evaluate a determinant and know its relationship to linear systems
• Solve systems of linear equations
• Add, subtract, and multiply matrices
• Find the inverse of a matrix
• Use matrices in problem solving and applications
• Sketch a graph of a polynomial with real coefficients
• Sketch a rational equation
• Work with and understand exponential functions
• Understand logarithmic functions and their application
• Logarithm of 1, Logarithm of a Product, Logarithm of a Quotient, Logarithm of a Power
• Logarithm function with base b
• Logarithm of x to the base b
• Understand vectors and their use in navigation, force, work, and energy
• Demonstrate an understanding of mathematical induction
• Demonstrate the binomial theorem and Pascal’s triangle
• Work with arithmetic and geometric sequences and series
• Find limits of sequences

STATISTICS, DATA ANALYSIS, and PROBABILITY

• Model problem situations using vector representations
• Utilize curve fitting to predict data
• Choose the exponential curve on the power curve to fit a situation
• Fit an appropriate trigonometric function to cyclical data
• Use mathematical modeling to describe real world phenomena
• Count the number of paths in small block diagrams
• Compute the number of additions required to solve problems involving small block diagrams
• Find the quickest route(s) in small block diagrams
• Estimate the number of paths in large block diagrams
• Use probability to solve problems involving uncertainty
• Use conditional probabilities to solve problems with partial information
• Determine whether or not two events are independent

GEOMETRY, MEASUREMENT and SPACIAL SENSE

• Demonstrate an understanding of the Cartesian coordination system
• Find the midpoint of a segment and use the distance formula
• Graph a line, find its slope, and intercepts
• Graph the conic sections by using the mathematical graphing tools
• Find the intersection of conic sections
• Recognize connections between vectors in their algebraic, geometric and trigonometric forms
• Sketch graphs of vectors as complex numbers
• Apply properties of vectors in modeling physical application such as navigation, force and work
• Apply the double-angle and half-angle formulas in problem solving

TRIGONOMETRY

• Identify a unit circle and be able to evaluate basic trigonometry functions
• Find amplitude, period, and phase
• Graph circular functions
• Demonstrate and understanding of inverses of circular functions
• Sketch a polar graph, using polar coordinates
• Convert from polar coordinates to rectangular coordinates and vice versa
• Apply complex numbers and limits
• Inverses of three trigonometric functions
• Determine the inverse of the sine, cosine, and tangent functions
• Graph the inverse of these three functions
• Identify the relationship between the graphs of the functions and their inverse
• Evaluate the inverse functions using a calculator
• Apply common identities
• Establish new identification based on other identification

PROBLEM SOLVING, COMMUNICTAION, REASONING, CONNECTIONS

Solve trigonometric equations using appropriate techniques and technology

• Apply mathematical skills and processes to global issues
• Describe how mathematics can be used in knowing how to prepare for careers
• Recognize and formulate mathematical problems from within and outside the field of mathematics
  

• Grade Level: 10th-12th
• Length of Course: Year
• Credit: 1
• Prerequisite: Geometry & Algebra II
• Textbook: Advanced Math Concepts
• ISBN#: 0-02-834175-4
• Publisher: Glencoe

COURSE DESCRIPTION
Pre-calculus completes the formal study of the elementary functions taught in Algebra I and Algebra II. Pre-calculus is designed to provide a solid preparation for calculus. It includes an in-depth coverage of functions (linear, polynomial, exponential, logarithmic, and trigonometric), as well an introduction to sequences and series. The use of technology and problem solving are emphasized in units covering data analysis, circular functions, and trigonometric inverses and identities.

NUMBER SENSE, OPERATIONS, and COMPUTATION

Evaluate determinants

• Find inverses of matrices
• Approximate real zeros of a polynomial function
• Find numerical values of trigonometric functions
• Convert from polar coordinates to rectangular coordinates and vice versa
• Add, subtract, multiply, and divide complex numbers in rectangular form
• Change complex numbers from rectangular form to polar form and vice versa
• Evaluate expressions with irrational exponents
• Use logarithms to compute powers and roots
• Solve problems using the properties of logarithms

PATTERNS and RELATIONSHIPS; ALGEBRA and FUNCTIONS

• Understand and use polynomial factoring
• Find composite functions
• Identify an odd function and an even function
• Solidify understanding of exponents and radicals
• Develop the complex number system and demonstrate facility with its operations
• Sketch the graphs of the basic functions (linear, quadratic, cubic, square root, absolute value, reciprocal, trigonometric, exponential, logarithmic, and greatest integer)
• Graph transformations and combinations of transformations for all basic functions
• Analyze a function by decomposing it into simpler functions
• Identify maximum and minimum points on a graph
• Explore the limits of sequences using an area model
• Identify maximum and minimum functions
• Use informal methods to find the sum of an infinite sequence
• Investigate maximum and minimum areas of squares and rectangles with given perimeters
• Graph second degree functions and identify their maximum and minimum values within given parameters
• Explain the end behavior of a function
• Find the maxima and minima for quadratic functions
• Recognize discontinuities in functions
• Use rectangular approximations to determine the areas under curves
• Introduce the concept of the limit of a function
• State whether or not an infinite geometric series has a limit, and if so, determine the limit
• Describe the surface of revolution by rotating a set of points
• Find the maximum and minimum of a polynomial function
• Determine roots of polynomial equations
• Apply the Fundamental Theorem of Algebra
• Identify all possible rational roots of a polynomial equation by using the Rational Root Theorem
• Solve problems involving simple harmonic motion
• Relate the limit behavior of a function to its graph and find equations for its asymptotes
• Determine the end behavior of a function
• Evaluate a finite ore infinite geometric series
• Calculate the rate of change
• Compute average rates of change
• Interpret rates of change as they apply to phenomena such as inflation, spread of disease, population growth, tax brackets, pollution, etc.
• Use the definition of derivative to compute derivatives
• Explore limits of perimeter and area using problems similar to the “snowflake” problem
• Solve inequalities using an appropriate technology

STATISITICS, DATA, and PROBABILITY

• Determine the probability of events
• Determine the probability of two events
• Determine the probability of two mutually exclusive events
• Recognize dependent vs. independent events
• Know and apply the Binomial Probability Theorem to real world situations
• Draw and analyze scatter plots
• Compute curves of best fit
• Compute correlation values to determine accuracy of fit
• Find the z-scores for a set of data
• Analyze graphical data gathered by technical equipment including combinations of graphs, periodic phenomena, and relative rates of change

PROBLEM-SOLVING, COMMUNICATION, REASONING, CONNECTIONS

• Apply a multitude of integrated problem-solving strategies to solve problems with and outside mathematics
• Recognize and formulate problems from situations
• Apply the process of mathematical modeling to real-world problem situations
• Express mathematical ideas orally and in writing
• Reflect upon and clarify their thinking about mathematical ideas and relationships
• Read written presentations of mathematics with understanding
• Make and test conjectures
• Formulate counter examples
• Relate procedures in one strategy to procedures in another appropriate strategy
• Use and value the connections among mathematical topics

TRIGONOMETRY

• Solve applies problems using the Law of Sines and the Law of Cosines
• Apply trigonometry to problem situations involving triangles
• Explore periodic real-world phenomenon using the sine and cosine functions
• Apply graphing techniques to trigonometric functions
• Solve trigonometric equations and verify trigonometric identities
• Evaluate inverse trigonometric functions
• Write equations for inverses of trigonometric functions
• Graph inverses of trigonometric functions
• Use the sum and difference identities for sine, cosine, and tangent functions
• Use the double- and half-angle identities for the sine, cosine, and tangent functions
• Solve trigonometric equations and inequalities either algebraically or using an automatic grapher
• Prove and apply DeMoivre’s Theorem to find roots and powers of complex numbers

SEQUENCES and SERIES

Demonstrate and understanding of sequences by representing them recursively and explicitly

• Represent patterns using arithmetic and geometric sequences and series including the use of sigma notation to represent series
• Determine whether a given series converges or diverges
• Find the sum of an infinite series that converge
• Find the sum of an infinite geometric series
• Apply sequences and series to solve problems including sums, binomial expansion, the Binomial Theorem, combinations, and Pascal’s Triangle
• Prove statements about sequences and series using the Principle of Mathematical Induction

DISCRETE MATHEMATICS

• Represent problem situations using discrete structures such as finite graphs, matrices and sequences
• Represent and solve problems using linear programming

CONCEPTUAL UNDERPINNINGS OF CALCULUS

• Determine the maximum and minimum points of a graph and interpret the results in problem situations
• Investigate limiting processes by examining infinite series and areas under curves
• Understand the concept of slope of a tangent line and it’s application in other disciplines
• Analyze the graphs of polynomial, rational, radical and transcendental functions

• Grade Level: 10th-12th
• Length of Course: Year
• Credit: 1
• Prerequisite: Geometry & Algebra II

COURSE DESCRIPTION

This course integrates concepts of calculus with trigonometry and functions. Calculus emphasizes conceptual understanding; a multirepresentational approach to calculus (graphical, numerical, analytic, verbal); the use of technology; and unifying themes which include derivatives, integrals, limits, applications and modeling, and approximation. Both application and formal proof are emphasized. Emphasis is placed on derivation of theorems and properties, as well as techniques for evaluating real world problems using calculus.

NUMBER SENSE, OPERATIONS, COMPUTATION

• Evaluate determinants
• Find inverses of matrices
• Approximate real zeros of a polynomial function
• Find numerical values of trigonometric functions
• Convert from polar coordinates to rectangular coordinates and vice versa
• Add, subtract, multiply, and divide complex numbers in rectangular form
• Change complex numbers from rectangular to polar form and vice versa
• Evaluate expressions with irrational exponents
• Use logarithms to compute powers and roots
• Solve problems using the properties of logarithms
• Numerical integration: trapezoidal rule

PATTERNS and RELATIONSHIPS; ALGEBRA and FUNCTIONS

Represent real world situations involving change with variable quantities and expressions

• Solve real world problems involving change with equations and inequalities
• Define functions and demonstrate a knowledge of functions through evaluations and graphs
• Graph functions using maximum, minimum, and reflection points, concavity, asymptotes, and zeros
• Use Taylor series in power expansions of functions
• Given the graph of a function, graph its inverse and other reflections or translations
• The Mean Value Theorem and its geometric consequences
• Recognize the relationship between limits, continuity, and the existence of a derivative
• Limits and continuity
• Understand continuity in terms of limits
• Continuous functions
• Sandwich Theorem and (sin x) / x
• Derivatives
• Slopes, tangent, lines and derivative
• Numerical derivatives
• Differentiation rules
• Velocity, speed and other rates of change
• Chain Rule
• Implicit differentiation and fractional powers
• Linear approximation and differentials

STATISTICS / PROBABILITY/ DATA

• Draw and analyze scatter plots
• Analyze scatter graphs to find the dependent variable with the strongest relationship to an independent variable
• Compute curves of best fit
• Compute correlation values to determine accuracy of fit
• Use integration methods to investigate the area under a curve of normal distribution
• Generate discrete probability distribution, e.g. binomial distribution
• Find the z-scores for a set of data
• Compare and contrast assumptions of two different statistical distributions, e.g. normal, binomial, Chi square
• Use linear and multiple regression procedures to make predictions of real world situations

GEOMETRY

Geometry for a synthetic perspective

• Model an infinite sequence with concrete materials
• Geometry from an Algebraic perspective
• Recognize rotations of plane figures around lines and axes
• Geometric understanding of graphs of continuous functions (Intermediate Value Theorem and Extreme Value Theorem)

TRIGONOMETRY

• Use the basic trigonometry identities to verify other identities and to solve problems
• Evaluate inverse trigonometric functions
• write equations for inverses of trigonometric functions
• Graph inverses of trigonometric functions
• Use the sum and difference identities for sine, cosine, and tangent functions
• Use the double- and half-angle identities for the sine, cosine, and tangent functions

DISCRETE MATHEMATICS

Use a calculator or computer for discrete simulations of concept of derivative and integral (e.g. Reimann sums or trapezoidal approximations)

• Concept of Riemann sum over equal subdivision
• Computation of Riemann sums using left, right, and midpoint evaluations
• Definite integral as a limit of Riemann sums

PROBLEM-SOLVING, COMMUNICATION, REASONING, CONNECTIONS

• Solve related rates and maxima minima problems in real world situations
• Use math modeling to address real world situations
• Use computer or calculator assisted modeling to solve problems derived from real world situations
• Interpret and use appropriate symbolism, notation, and vocabulary
• Explain in oral or written form, the application of the derivative to real world situations
• Explain the behavior of a function given a graph of its derivative and explain the behavior of the derivative
• Use mathematical proof of derive identity relations
• Compare the graphs of functions and their derivatives to test hypotheses
• Identify the limit of the secant to a curve as the tangent to the curve
• Recognize the slope of a curve is the slope of the tangent at a point on the curve
• Recognize that the product rule is extendable to n functions
• Recognize the quotient rule is an extension of the product rule
• Recognize the application of the derivative as a rate of change to other disciplines
• Apply techniques of calculus to problems of exponential growth and decay from other disciplines
• Use and value the connections among mathematical topics, particularly between calculus, algebra and trigonometry

CONCEPTUAL UNDERPINNINGS OF CALCULUS

• Use theorems to evaluate limits
• Apply the Fundamental Theorem of Integral Calculus
• Use integration to find areas under a curve, length of a curve, and volume of rotating a curve about a line
• Use integration in pressure, mass, moment, centroid, and work problems
• Informal exploration of calculus concepts from both a graphical and a numerical perspective so that all students can
• Determine the maximum and minimum of points of a graph and interpret the results in problem situations
• Investigate limiting processes by examining infinite sequences and series and areas under curves
• Understand the conceptual foundations of limit, the area under a curve, the rate of change, and the slope of a tangent line, and their Applications in other disciplines
• Analyze the graphs of polynomial, radical, and transcendental functions
• Find the derivatives and integrals of trigonometric, inverse, exponential, and logarithmic functions
  

MATH WITH APPLICATIONS

• (Personal Finance)
• Grade Level: 11-12
• Length of Course: Year
• Credit: 1
• Prerequisite:
• Textbook: Business and Personal Finance
• ISBN#: 0-02-644128-4
• Publisher: Glencoe

COURSE DESCRIPTION
This course emphasizes mathematics used in business and economics. Topics in finance, credit, investing, business operation, and an introduction to probability and statistics will be covered to show the application of algebra in business. Students will demonstrate management of money by investigating financial situations such as personal earning power, budgets, insurance, income, sales, taxes, credit cards, consumer credit, purchase homes and cars, loans, mortgages, investments, present value and future value, annuities, banking, break-even analysis, amortization’s of loans, and consumerism.

NUMERATION

• Recognize and use properties of the real number system
• Simplify real expressions, that include variables, constants, and exponents

ESTIMATION &COMPUTATION

• Compute with real numbers including powers and roots
• Solve fraction problems that contain variables

FUNCTIONS & RELATIONSHIPS

• Add, subtract, multiply, and divide rational expressions
• Use proportions to solve variable expressions
• Create and solve simple systems of equations, algebraically and graphically, using a graphing calculator
• Recognize, create, extend, and generalize patterns, sequences and iterations
• Describe linear and quadratic equations and inequalities
• Manipulate expressions, formulas, equations, and inequalities to model mathematical situations

STATISTICS/PROBABIL