course title: kindergarten mathematics€¦ · course title: grade 1 mathematics prerequisite: n/a...

SY 2010 - 2011

COURSE TITLE: Kindergarten Mathematics

PREREQUISITE: N/A

DESCRIPTION: The kindergarten mathematics program uses the Scott Foresman Addison Wesley Investigations

series along with Mathematics Their Way program of instruction. Through a hands-on approach,

kindergarten students are introduced to basic number concepts and operations that include:

counting, matching, sorting, estimating, measuring, time and temperature, and simple addition and

subtraction. They recognize basic shapes, coins, patterns, and fractions.

MAIN TOPICS: Reasoning and solving problems

Communicating mathematically

Making connections between concepts in mathematics and other academic areas

Number and Number Sense

Count to 100 by ones, fives, and tens

Count back from 10

Write numerals

Compare the number of objects in sets

Indicate ordinal positions (first through tenth)

Identify unit fractions from a representation

Computation and Estimation

Add and subtract whole numbers using models

Measurement and Geometry

Recognize coins and determine the value of several coins

Tell time

Identify measurement instruments (i.e., ruler, scale)

Compare measurable attributes (i. e., length, mass) of two objects

Identify and describe plane figures (i. e.,triangle, square)

Describe relative locations of objects (i.e., above, next to)

Probability and Statistics

Gather, display, and answer questions about data

Patterns, Functions, and Algebra

Classify objects by attributes

Identify and extend patterns

SY 2010 - 2011

COURSE TITLE: Grade 1 Mathematics

PREREQUISITE: N/A

DESCRIPTION: First graders move from the concrete to the symbolic level of essential mathematics concepts and

operations. Key areas of study include numeration (cardinal and ordinal numbers), addition,

subtraction, measurement using non-standard units, time, money, shapes and fractions. Problem-

solving strategies include using sorting, patterning, graphing, and simulating daily life, such as

solving problems involving play money and telling time.





Count (and skip count) to 100 and write the numerals

Identify fractions from a representation

Develop an understanding of place value using models

Identify ordinal positions, first through tenth (2001 SOL)


Recall and use in context (magnitude) basic addition and subtraction facts through sums of 18


Count money

Tell time (clock and calendar)

Measure length, weight/mass, and volume

Compare weight/mass and volumes

Identify and describe plane figures and match them to models in the environment


Collect, display, and interpret data


Classify objects according to attributes

Identify and extend growing and repeating patterns

Understand equality (= sign)

SY 2010 - 2011


PREREQUISITE: N/A

DESCRIPTION: Second graders build upon essential mathematics concepts using a combination of manipulative

and mental processes. Key areas of study include numeration, addition and subtraction as inverse

operations, inequalities ( , ), ordinal numeration, multiplication, measurement, time, money,

estimation, polygons, perimeter, and fractions. Critical thinking skills are further developed

through mental arithmetic, making change, visualization, record keeping, data collection, and

graphing.





Understand place value, round, and compare the values of numbers

Identify and write ordinal positions (first through twentieth)

Identify and compare fractions in representations and write the fractions

Count and skip count to at least 100 and recognize even and odd numbers


Recall and use in context basic addition and subtraction facts through sums of 20

Estimate and then find sums and differences of whole numbers (sums of 100 or less)

Use related addition and subtraction facts to construct understanding of inverse operations in

context


Count money and use symbols associated with money

Measure length, weight/mass, and volume in U.S. Customary and metric units

Tell time (clock and calendar)

Read temperature from a thermometer

Identify symmetric figures and lines of symmetry

Identify, describe, compare and contrast plane and solid figures

Estimate then find perimeter and area (2001 SOL)


Collect, display, and analyze data


Identify and extend repeating and growing patterns

Solve equations derived from basic addition and subtraction facts

Understand = and ≠

SY 2010 - 2011


PREREQUISITE: N/A

DESCRIPTION: Third graders enhance their mathematics foundation and move toward more consistent use of

mental computation using supplements such as Math 24. Key areas of study include place value,

rounding, developing fluency with multiplication and division facts, area, time, money, solid

shapes, lines, angles, congruence, and addition and subtraction of fractions and decimals using

manipulatives. Experimentation, simulation, modeling, extending patterns, and logical deduction

processes expand problem solving capabilities. Students relate mathematics to other areas of

curriculum and identify real life applications of mathematics concepts, such as making change,

telling time, and reading thermometers.





Understand place value and use the concepts to round numbers

Compare numbers (whole and fractions) and use comparison symbols (<, >, =) appropriately

Use models/manipulatives/representations to name and write fractions

Compare values of fractions using models (2001 SOL)

Read and write decimals using models (2001 SOL)


Recall and use in context basic multiplication and division facts through factors of 12

Use models/manipulatives to represent multiplication and division

Estimate and then find sums and differences of whole numbers

Develop understanding of adding and subtracting fractions by using models and manipulatives

Develop understanding of adding and subtracting decimals by using models and manipulatives

(2001 SOL)


Count money and make change

Develop understanding of area and perimeter using models and manipulatives

Measure length, liquid volume, weight/mass, area, and perimeter in U.S. Customary and metric

units

Tell time (clock and elapsed) and determine equivalences between periods of time

Read temperature from a thermometer

Identify, describe, compare and contrast plane and solid figures

Identify and draw representations of points, lines, line segments, angles, and rays

Identify congruent figures and compare and contrast congruence and non-congruence


Investigate questions by designing experiments, collecting and organizing data, analyzing data,

and representing data in appropriate displays

Develop understanding of probability as chance


Identify and extend a wide variety of patterns

Investigate properties of real numbers

Understand = (2001 SOL)

SY 2010 - 2011


PREREQUISITE: N/A

DESCRIPTION: Students learn comparison and place value of numbers through millions, rounding to hundred

thousands, comparison of fractions, identification of equivalent fractions, rounding decimals,

division, addition of fractions, estimation and measurement of weight/masses, lengths, and

volumes, measurement of perimeter, identification of rays, points, and segments, parallel and

perpendicular lines, and the use of rules (or functions) in solving problems. Supplements to the 4th

grade program include Math 24 and Fraction Bars Kit.






Compare rational numbers and use comparison symbols (<, >, =) appropriately

Model equivalent fractions and decimals


Add, subtract, multiply, and divide whole numbers

Add and subtract fractions and decimals

Develop understanding of multiples and factors


Estimate and measure weight/mass, length and liquid volume in U.S. Customary and metric units

Use U.S. Customary and metric equivalents between units

Identify and describe representations of plane figures and intersection, parallelism, and

perpendicularity

Investigate geometric transformations and congruence of transformed figures

Identify and name polygons

Determine elapsed time

Investigate and find perimeter and area (2001 SOL)

Compare and contrast plane and solid figures (2001 SOL)

Identify the ordered pair for points on a coordinate plane (2001 SOL)


Represent probability as a number p, 0 ≤ p ≤ 1and predict the likelihood of an event

Collect, organize, display, and interpret data


Identify and extend complex numerical and geometric patterns


Demonstrate the concept of equality in an equation

SY 2010 - 2011


PREREQUISITE: N/A

DESCRIPTION: Students learn place value of decimals through ten-thousandths, division with two-digit divisors,

measures of center, checking results with calculators, dividing decimal numbers, operations with

mixed fractions, finding areas of various geometric shapes, identifying radius, chord, and

circumference, and how to select appropriate measuring tools. Students distinguish area from

perimeter, classify angles, learn to solve simple equations (using Hands On Equations), determine

elapsed time, locate points in a coordinate plane, and make tree diagrams for events with multiple

outcomes.






Recognize benchmark fractions and decimals

Compare rational numbers and use comparison symbols (<, >, =) appropriately

Investigate prime and composite numbers, and even and odd numbers


Add, subtract, multiply, and divide rational numbers expressed in decimal notation and use the

operations to solve problems

Add and subtract rational numbers expressed in fraction notation

Investigate the order of operations and use it to evaluate expressions


Measure perimeter, area, and volume (and length, weight/mass, and temperature) (2001 SOL)

Identify equivalent measures in the metric system

Determine elapsed time

Measure and classify angles and classify triangles

Identify measurable attributes of circles

Analyze properties of plane and solid figures (2001 SOL)

Investigate symmetry (2001 SOL)

Recognize figures resulting from geometric transformations (2001 SOL)

Investigate congruence and similarity (2001 SOL)


Construct sample spaces to determine probabilities

Compare and contrast measures of center

Collect, organize, and interpret data

Represent probability as a number p, 0 ≤ p ≤ 1and predict the likelihood of an event (2001 SOL)


Describe and analyze numeric and geometric patterns (2001 SOL)

Investigate the idea of variable and equations


SY 2010 - 2011


PREREQUISITE: N/A

DESCRIPTION: Grade 6 Mathematics students are transitioning from whole number arithmetic in the elementary

grades to foundations of algebra. Emphasis is on rational numbers. Students will use ratios to

compare data sets; recognize representations of rational numbers (fractions, decimals, and

percents) as rations, solve problems using rational numbers, and gain a foundation in the

understanding of integers. Students will solve equations, inequalities, and use the vocabulary of

algebra.





Identify, compare, order, and demonstrate equivalent relationships between integers, fractions,

decimals, and percents

Investigate concepts of exponents and perfect squares

Represent, order, and compare integers and describe the absolute value of integers

Find common multiples and factors, including LCM and GCF (2001 SOL)

Identify and describe prime and composite numbers and even and odd integers (2001 SOL)


Identify, compare and perform the four basic operations and solve problems relating to rational

numbers (fractions, decimals, and percents)

Evaluate expressions using order of operations

Measurement

Solve problems relating to perimeter and area of polygons and circumference and area of circles

Determine area, volume, surface area, and perimeter of various geometric figures

Make ball park comparisons between measurements in U. S. Customary and metric systems

Select the appropriate metric or standard measurement tools and measure length, weight/mass,

and volume (2001 SOL)

Measure and draw right, acute, and obtuse angles (2001 SOL)

Geometry

Identify, classify, and describe characteristics of plane figures (2001 SOL) (quadrilaterals 2009

SOL)

In the coordinate plane, identify coordinates of a point and graph ordered pairs

Construct the perpendicular bisector of a line segment (2001 SOL)


Create, read, and interpret graphs, charts, and tables

Investigate dependent and independent events and determine probabilities

Describe mean as balance point

Describe the mean, median, mode, and range for a set of data (2001 SOL)

Determine the probability of an event from a sample space (2001 SOL)


Investigate, describe and extend numerical and geometric patterns

Solve equations and graph inequalities


SY 2010 - 2011


PREREQUISITE: N/A

DESCRIPTION: Grade 7 Mathematics students continue to emphasize the foundations of algebra. Students will

study proportional reasoning, integer computation, solving equations and recognizing multiple

representations for relationships among and between sets of data. Students will apply the

properties of the real numbers to solve equations and inequalities, and use data analysis techniques

to make inferences, conjectures, and predictions.





Compare, order, and determine equivalent relationships between rational numbers

including those written in scientific notation (positive and negative exponents)

Determine the square roots and absolute value of rational numbers

Represent arithmetic and geometric sequences

Simplify expressions that contain rational numbers and positive exponents (2001 SOL)


Use models to formulate rules for the basic operations with integers

Use proportions to solve problems

Solve practical and consumer application problems using rational numbers, integers, percents,

and involving tips, discounts, sales tax, and simple interest (2001 SOL)

Measurement

Find the area of polygons and volume and surface area of rectangular prisms and

cylinders in real-life applications

Determine if figures are similar and write proportions to express relationships between side

lengths

Geometry

Compare and contrast quadrilaterals

Represent transformations (translation, reflection. rotation, dilation) of a polygon in a coordinate

plane

Graph ordered pairs in the coordinate plane (2001 SOL)


Investigate and describe experimental and theoretical probability

Describe the number of possible arrangements of several objects (Fundamental Counting

Principle)

Collect, analyze, display, and interpret data in graphs

Create and solve problems using mean, median, mode, and range of a set of data (2001 SOL)


Identify and apply the properties of operations with real numbers

Solve linear equations and inequalities

Represent relationships with tables, graphs, and symbols

Translate verbal expressions into symbols

SY 2010 - 2011


PREREQUISITE: N/A

DESCRIPTION: The grade 8 mathematics students will address content that extends concepts and skills learned in

previous grades, as well as new content that prepares students for more abstract concepts in

algebra and geometry. Students will gain proficiency in computation with rational numbers and

will use proportions to solve a variety of problems. New concepts include solving multistep

equations and inequalities, graphing linear equations, visualizing three-dimensional shapes

represented in two-dimensional drawings, and applying transformations to geometric shapes in the

coordinate plane. Students will verify and apply the Pythagorean Theorem and represent relations

and functions, using tables, graphs, and rules.

MAIN TOPICS: Reasons and solves problems

Communicates mathematically

Makes connections between concepts in mathematics and other academic areas


Simplify expressions involving positive exponents and evaluate algebraic expressions for given

replacement values of the variables

Compare and order decimals, fractions, percents, and numbers written in scientific

notation

Describe the relationships between the subsets of the real numbers


Investigate square numbers and square roots

Investigate open-ended and practical problems involving rational numbers, including calculating

tax rate, discounts, and sale prices

Measurement

Investigate and describe the relationships among vertical, supplementary, complementary, and

adjacent angles

Measure angles

Investigate volume and surface area of prisms, cylinders, cones, and pyramids

Geometry

Verify and apply the Pythagorean Theorem

Solve open-ended and practical area and perimeter problems

Investigate transformations (translations, reflections, dilations, and rotations) of plane figures


Determine the probability of dependent and independent events

Gather, organize, analyze, and interpret statistical data using simulations and appropriate

technology

Use matrices to organize and interpret data (2001 SOL)


Represent relations using tables, graphs, and algebraic symbols

Solve equations and inequalities and graph the solutions

Use the properties of operations and the real numbers to justify steps in solving equations and

inequalities

Use proportional reasoning to solve problems

SY 2010 - 2011

COURSE TITLE: Math 7 Honors

PREREQUISITE: N/A

DESCRIPTION: Mathematics 7 Honors students are transitioning from whole number arithmetic in the elementary

grades to foundations of algebra. Emphasis is on rational numbers and generalizing patterns of all

types, using multiple representations. Students will use ratios to compare data sets; and recognize

representations of rational numbers (fractions, decimals, and percents) as rations, solve problems

using rational numbers. Students will solve equations, inequalities, and use the vocabulary of

algebra. Students will study proportional reasoning, integer computation, and recognizing

multiple representations for relationships among and between sets of data. Students will apply the

properties of the real numbers to solve equations and inequalities, and use data analysis techniques

to make inferences, conjectures, and predictions.





Investigate concepts of exponents

Compare, order, compare, and determine equivalent relationships between rational numbers

(fractions, decimals, percents, and integers) including those written in scientific notation (positive

and negative exponents)

Investigate perfect squares, square roots, and absolute value

Represent arithmetic and geometric sequences symbolically

Find common multiples and factors, including LCM and GCF (2001 SOL)

Identify and describe prime and composite numbers and even and odd integers (2001 SOL)

Simplify expressions that contain rational numbers and positive exponents (2001 SOL)


Use models to formulate rules for the basic operations with integers

Identify, compare and perform the four basic operations and solve problems relating to rational

numbers (fractions, decimals, percents, and integers)

Evaluate expressions using order of operations

Use proportions to solve problems

Solve practical and consumer application problems using rational numbers, integers, percents,

and involving tips, discounts, sales tax, and simple interest (2001 SOL)

Measurement

Solve problems relating to perimeter and area of polygons and circumference and area of circles

Determine volume and surface area of rectangular prisms, cylinders, pyramids, and cones

Make ball park comparisons between measurements in U. S. Customary and metric systems

Determine if figures are similar and express relationships between side lengths as proportions

Select the appropriate metric or standard measurement tools and measure length, weight/mass,

and volume (2001 SOL)

Measure and draw angles (2001 SOL)

Geometry

Identify, classify, and describe characteristics of plane figures (2001 SOL) (Compare and contrast

quadrilaterals 2009 SOL)

Represent transformations (translation, reflection. rotation, dilation) of a polygon in a coordinate

plane

Graph ordered pairs in the coordinate plane (2001 SOL)

Construct the perpendicular bisector of a line segment (2001 SOL)

SY 2010 - 2011


Describe mean as balance point

Compare and contrast dependent and independent events and determine probabilities

Compare and contrast experimental and theoretical probability

Describe the number of possible arrangements of several objects (Fundamental Counting

Principle)

Collect, analyze, display, and interpret data in graphs

Create and solve problems using mean, median, mode, and range of a set of data (2001 SOL)

Describe the mean, median, mode, and range for a set of data (2001 SOL)

Determine the probability of an event from a sample space (2001 SOL)


Investigate, describe and extend numerical and geometric patterns

Represent relationships with tables, graphs, and symbols

Translate verbal expressions into symbols


Solve equations and inequalities and graph the solutions

Identify and apply the properties of operations and real numbers to justify solving equations and

inequalities

CREDIT INFO: N/A

SY 2010 - 2011

COURSE TITLE: Algebra I

PREREQUISITE: Math 7 Honors, Grade 7 Mathematics, or Grade 8 Mathematics

DESCRIPTION: In Algebra I, students continue to develop algebraic thinking and proportional reasoning skills

necessary to solve problems. Concepts and skills will be developed sequentially by using concrete

materials to assist students in making the transition from the arithmetic to the symbolic

representations. Students use algebra as a tool for representing and solving a variety of practical

problems. Tables and graphs, will be used to interpret algebraic expressions, equations, and

inequalities, and to analyze behaviors of functions. Throughout the course, students will be

encouraged to engage in discourse about mathematics, use the language and symbols of

mathematics in representations and communication, discuss problems and problem solving, and

develop confidence in themselves as mathematics students.

MAIN TOPICS Reasons and solves problems



Expressions and Operations Represent verbal quantitative situations algebraically and evaluate expressions

Perform operations on polynomials including applying laws of exponents and factoring

Simplify radical expressions

Equations and Inequalities

Solve equations (linear and quadratic) and inequalities in two variables using a variety of

strategies and graph solutions

Justify steps in the solutions of equations and inequalities

Solve systems of equations and systems of inequalities

Functions

Investigate and analyze function families and their characteristics both algebraically and

graphically

Make connections among multiple representations of functions

Investigate direct and inverse variation

Statistics

Interpret variation in real-world contexts

Compare and contrast multiple univariate data sets

Use mathematical models to solve real-world problems

Use matrices to organize and manipulate data (2001 SOL)

Incorporate the use of technology when appropriate.

CREDIT INFO: This course may provide a standard unit of credit for a Standard, Standard Technical, Advanced

Technical, or Advanced Studies Diploma.

SY 2010 - 2011

COURSE TITLE: Algebra Foundations

PREREQUISITE: None

DESCRIPTION: Algebra Foundations students have increased opportunities to build foundational mathematics

skills required for success in Algebra I. Practical applications of mathematics are emphasized

throughout the course. Topics studied include simplifying and evaluating algebraic expressions;

solving equations and inequalities; using ratios and proportions to solve problems; reading,

interpreting, and constructing a variety of graphs. When appropriate, calculators, computers, and

manipulatives will be used. Students will learn to communicate their mathematical thinking

coherently and clearly and use the language of mathematics to express mathematical ideas

precisely.




Perform the four basic operations with whole numbers, integers, fractions, and decimals

Simplify expressions involving positive exponents and evaluate algebraic expressions for given

replacement values of the variables. Recognize and represent numbers expressed in scientific

notation. Compare and order decimals, fractions, percents, and numbers written in scientific

notation

Generalize arithmetic concepts to algebra

Translate and/or solve algebraic expressions, equations, and inequalities into mathematical

expressions

Apply the relationship between decimals, fractions, and percentages to determine which

representation is appropriate

Use ratios, proportions, and percents to solve problems

Use measuring tools and formulas to analyze real-world objects

Read, interpret, and construct a variety of graphs

Solve simple and multi-step equations

Solve and graph linear equations and inequalities

Incorporate the use of technology when appropriate

CREDIT INFO: This course does not provide a standard credit in mathematics toward a standard or advanced studies

diploma. Algebra Foundations must be taken with Algebra I as a daily (double-blocked) course. Upon successful completion

of the course, students will take the SOL test in Algebra I, receive a mathematics credit for Algebra I and an elective credit

for Algebra Foundations.

.

SY 2010 - 2011

COURSE TITLE: Algebra I, Parts 1 and 2**

PREREQUISITE: Grade 8 Mathematics

DESCRIPTION: Algebra I, Parts 1 and 2 are academic courses designed for students who need extended time to

complete Algebra I. The series of two courses covers the same content as Algebra I by presenting

the basic concepts of Algebra I in the first year, and then expanding the concepts in the second

year.




Expressions and Operations Represent verbal quantitative situations algebraically and evaluate expressions

Perform operations on polynomials including applying laws of exponents and factoring

Simplify radical expressions


Solve equations (linear and quadratic) and inequalities in two variables using a variety of

strategies and graph solutions

Justify steps in the solutions of equations and inequalities

Solve systems of equations and systems of inequalities

Functions

Investigate and analyze function families and their characteristics both algebraically and

graphically

Make connections among multiple representations of functions

Investigate direct and inverse variation

Statistics

Interpret variation in real-world contexts

Compare and contrast multiple univariate data sets

Use mathematical models to solve real-world problems

Use matrices to organize and manipulate data (2001 SOL)


CREDIT INFO: **For students who are in the ninth grade before the 2010-2011 school year, these courses may

provide 2 standard credits in mathematics toward a high school diploma if both courses are

completed satisfactorily. For students who are entering the ninth grade for the first time in the

2010-2011 school year, Algebra I Part 1 may not be used as a standard unit of credit for high

school graduation.

SY 2010 - 2011

COURSE TITLE: Geometry

PREREQUISITE: Algebra I or Algebra I, Parts 1 & 2

DESCRIPTION: Geometry is the study of the inter-relationships and properties of points, lines, planes, and space

figures. Emphasis is placed on systematic and logical reasoning. This course includes the

deductive axiomatic method of proof to justify theorems and to determine whether conclusions are

valid. The method of justification includes proofs, flow charts, and verbal arguments. Inductive

and intuitive approaches are used. Calculators, computers, and graphing utilities will be used

where feasible.




Reasoning, Lines, and Transformations

Construct and judge the validity of a logical argument

Perform basic Euclidean constructions using various tools. Classify and study polygons and their

properties

Determine whether two lines are parallel and use the relationships between pairs of angles formed

by two parallel lines and a transversal to solve problems

Use coordinate methods to determine transformations, slope, distance, and midpoint

Triangles

Apply the properties of right triangles and trigonometry

Prove triangles congruent and similar

Develop and apply the Pythagorean Theorem

Use the triangle inequality to order sides by length angles by measure, and determine if a triangle

exists.

Polygons and Circles

Recognize properties of circles and demonstrate their applications

Write the equation of a circle

Verify properties of quadrilaterals and use the properties to solve problems

Three-Dimensional figures

Calculate the surface area and volume of solid figures.

Investigate how a change in one dimension of an object affects area and/or volume

Compare ratios between side lengths, perimeters, areas, and volumes of tow- or three-dimensional

objects

The student will make a model of a three-dimensional figure from a two-dimensional drawing and

make a two-dimensional representation of a three-dimensional object (2001 SOL)




SY 2010 - 2011

COURSE TITLE: Functions, Algebra, and Data Analysis

PREREQUISITE: Algebra I or Algebra I, Parts 1 & 2

DESCRIPTION: Functions, Algebra and Data Analysis students study functions and their behaviors, systems of

inequalities, probability, experimental design and implementation, and analysis of data within the

context of mathematical modeling. Data will be generated by applications arising from science,

business, and finance. Students will strengthen conceptual understandings of mathematics and

further develop connections between algebra and statistics.

MAIN TOPICS: Algebra and Functions

Investigate and analyze function families and their characteristics

Use knowledge of transformations to write an equation, given the graph of the functions

Collect data and generate the equation of a curve of best fit

Analyze multiple representations of functions

Determine optimal values in authentic situations using linear programming techniques

Data Analysis

Calculate probabilities for conditional events, and dependent and independent events

Analyze the normal distribution and use its characteristics to determine probabilities of authentic

events

Design and conduct experiemnts




SY 2010 - 2011

COURSE TITLE: Algebra II

PREREQUISITE: Algebra I and Geometry

DESCRIPTION: Algebra II students extend the concepts of Algebra I. A thorough study of advanced algebraic

concepts is provided through the exploration of functions, polynomials, rational expressions,

sequences and series, complex numbers, and matrices. Students will create graphs using

translation, reflection, dilation, and rotation.




Expressions and Operations


Functions

Statistics

Identify field properties, axioms of equality and inequality, and properties of order for the sets of

real and complex numbers and matrices.

Perform operations with rational expressions. Perform operations with expressions containing

rational exponents. Write radical expressions as expressions containing rational exponents.

Factor polynomials completely.

Solve quadratic equations over the set of complex numbers. Solve equations containing rational

expressions and equations containing radical expressions.

Recognize and convert between multiple representations of functions. Find the domain, range,

zeros, and inverse of a function; the value of a function for a given element; and the composition

of multiple functions. Investigate and describe the relationship between solutions, zeros, x-

intercepts, and factors.

Multiply matrices and use systems of linear equations and inequalities to solve practical problems.

Solve non-linear systems of equations algebraically and graphically.

Recognize and explore the general shape of polynomial, exponential, and logarithmic functions.

Investigate and apply the properties of arithmetic and geometric sequences and series.

Perform operations on complex numbers and simplify the results.

Identify and sketch graphs of conic sections.

Identify, create, and solve problems involving inverse and direct variation.



SY 2010 - 2011

COURSE TITLE: Algebra II and Trigonometry

PREREQUISITE: Algebra I and Geometry

DESCRIPTION: Algebra II & Trig. students extend the concepts of Algebra I. This is a faster paced course, which

does a thorough study of advanced algebraic concepts and starts the study of trigonometry. It

provides thorough exploration of functions, polynomials, rational expressions, sequences and

series, complex numbers, matrices, and the introduction to trigonometry. Students will create

graphs using translation, reflection, dilation, and rotation.





Identify field properties, axioms of equality and inequality, and properties of order for the sets of

real and complex numbers and matrices.

Perform operations with rational expressions. Perform operations with expressions containing

rational exponents. Write radical expressions as expressions containing rational exponents.

Factor polynomials completely.

Solve quadratic equations over the set of complex numbers. Solve equations containing rational

expressions and equations containing radical expressions.

Recognize and convert between multiple representations of functions. Find the domain, range,

zeros, and inverse of a function; the value of a function for a given element; and the composition

of multiple functions. Investigate and describe the relationship between solutions, zeros, x-

intercepts, and factors.

Multiply matrices and use systems of linear equations and inequalities to solve practical problems.

Solve non-linear systems of equations algebraically and graphically.

Recognize and explore the general shape of polynomial, exponential, and logarithmic functions.

Identify and sketch graphs of conic sections.

Investigate and apply the properties of arithmetic and geometric sequences and series.

Perform operations on complex numbers and simplify the results.

Identify, create, and solve problems involving inverse and direct variation.

Define and compare definitions of the six trigonometric functions using right triangle

trigonometry and circular trigonometry. Identify and graph trigonometric functions. Apply

trigonometric identities to solve problems.



SY 2010 - 2011

COURSE TITLE: Personal Living and Finance

PREREQUISITE: One year of High School Mathematics

DESCRIPTION: Personal Living and Finance is a calculator-based course that applies computational skills in

solving everyday problems that a student will encounter as a consumer. Areas of the consumer

world considered are job search, income, transportation, food, clothing, housing, budgeting,

taxation, consumer credit, banking, insurance, and investments. Skills in gathering and

interpreting data are also emphasized.





Apply banking and credit procedures to personal finances.

Understand the concepts of income and employment.

Complete federal and state income tax forms.

Create a personal budget.

Understand options for purchasing and operating motor vehicles.

Investigate the options for housing, including furnishings and maintenance.

Explore investment options.

Examine insurance alternatives.

Understand the finances involved in traveling and merchandising.

Manage debt, including retail and credit card debt. Complete a loan application and compute

simple and compound interest rates.

Identify consumer rights and responsibilities. Communicate with salespersons and merchants,

analyze simple contracts, and contest an incorrect bill.

CREDIT INFO: This course may provide a standard unit of credit for a Modified Standard Diploma.

SY 2010 - 2011

COURSE TITLE: Computer Mathematics

PREREQUISITE: Algebra II (or may be taken at the same time as Algebra II)

DESCRIPTION: This course is an elective beyond the Algebra II level and is designed to introduce the student to

the use of interpreted and compiled programming languages. In Computer Mathematics students

are introduced to the JAVA programming language and the concept of Object Oriented

Programming. This course is designed to be a compliment to previous mathematics subjects.

The students will learn to use graphics interfaces, write Web browser applets and create their own

games using the principles of OOP (Object Oriented Programming) using user defined objects,

encapsulation of data, libraries and shared objects.




Apply a program development cycle to practical problems in consumer mathematics, algebra and

geometry. This will include defining the problem, planning a solution, carrying out the plan,

debugging the program, and providing program documentation.

Identify the major hardware and software components of a computer system, their relationship to

one another and the roles of each within the system.

Recognize the ethical and social implications of computer use and examine the scope of JAVA, its

initial development to its relationship to the Internet.

Use a compiled programming language to demonstrate programming techniques.

Demonstrate the use of classes, constructors and methods and as integral parts of OOP

programming and make extensive use of graphical user interfaces – windows, buttons, scrollbars

etc.

Use the graphics system commands supplied in the Java JDK and accessed from within the

programs to a generate Graphical User Interface (gui) that include images, buttons, textfields and

labels.

Recognize the difference between assignment statements, branching statements and iterative

statements and know how and when they are used.

Combine sequence, selection, repletion and graphics classes together to solve a substantial

problem.

Learn and utilize several interfaces in communicating with the computer program. Learn to

translate the raw input data into usable native types and display the output data in a clear and

appropriate manor.

Learn to write and call methods that create and return objects.

Use data structures such as arrays and strings to tract and sort complex applications.

Develop a major program that incorporates all aspects of the programming process to solve a

problem in algebra, geometry, consumer mathematics or physical science.

CREDIT INFO: This course provides one of the elective credits required for a Standard or Advanced Studies

Diploma.

SY 2010 - 2011

COURSE TITLE: Advanced Placement Computer Science

PREREQUISITE: Computer Mathematics

DESCRIPTION: This course follows the course outline for Advanced Placement Computer Science, is an elective

beyond the Algebra II level and is designed to introduce the student to the use of interpreted and

compiled programming languages. In AP Computer Science, students use the Java programming

language concentrating on the AP Java subset. Students will focus the Marine Biology Case

Study.




Apply a program development cycle that includes defining the problem, planning a solution,

carrying out the plan, debugging the program, and providing program documentation to practical

problems.

Understand the Java programming environment and its features.

Use Object Modeling to design Object Oriented solutions to real problems.

Write, compile and execute Java applications and applets.

Demonstrate knowledge of Object Oriented Programming concepts (abstraction, encapsulation,

inheritance, polymorphism, etc.).

Use appropriate programming structures for looping and branching through the use of conditionals

and counters.

Read and write data using I/O streams.

Work cooperatively to solve problems and agree on common solutions.

Demonstrate the ability to use objects, primitive types and control structures.

Identify and correct errors using debugging techniques.

Design and implement complex data structures to include stacks, queues, linked lists and trees.

Design and implement coding which requires recursive solutions.

Recognize the ethical and social implications of computer use.

CREDIT INFO: This course provides one of the elective credits required for a Standard, Standard Technical,

Advanced Technical, or Advanced Studies Diploma. Students may receive college credit for

successful achievement on the AP Computer Science Exam.

SY 2010 - 2011

COURSE TITLE: Advanced Functions and Modeling

PREREQUISITE: Algebra II

DESCRIPTION: Advanced Functions and Modeling provides opportunities for students to deepen understanding

and knowledge of functions-based mathematics. Problem solving and critical thinking will

provide the structure in which functions (polynomial, exponential, logarithmic, transcendental,

and rational) are studied. Experimental design will provide the foundation for data gathering,

curve sketching, and curve fitting in order to provide a graphical interpretation of real world

situations. Graphing calculators and other emerging technologies along with the precepts of

transformational graphing will be incorporated into instruction to enhance teaching and learning.

Mathematical communication, reasoning, problem solving, critical thinking, and multiple

representations will be emphasized throughout the course.

.




Identify, graph, and write linear, quadratic, polynomial functions, radical, rational, exponential,

and logarithmic functions and to apply the concepts of those

functions to real world models.

Find the domain, range, zeros, and inverse of a function, the value of a function for a given

element in its domain, and the composition of multiple functions.

Identify and use trigonometric ratios, inverses, and formulas.

Solve application problems using Trigonometry.

Graph the six trigonometric functions and their inverses.

Understand and apply circular functions.

Prove trigonometric identities.

Solve trigonometric equations.

included.

CREDIT INFO: This course may provide a standard unit of credit for Standard, Standard Technical, Advanced


SY 2010 - 2011

COURSE TITLE: Advanced Algebra/Precalculus


DESCRIPTION: This course is an elective beyond the Algebra II level which prepares the student for college

mathematics. Advanced Algebra/Precalculus students receive a bridge from Algebra to analysis

by being introduced to the notion of a limit. Advanced Algebra/Precalculus is a course for very

capable mathematics students who have successfully completed the academic program through

Algebra II. The objective is to provide a thorough preparation for college mathematics, especially

Calculus, by including a study of Trigonometry and other advanced mathematics topics.





Understand the subsets of the complex number system.

Review complex numbers, polynomial expressions, radicals, and exponents.

Find compositions and inverses of functions. Investigate the continuity of functions.

Solve and graph polynomial functions and inequalities.

Solve problems involving arithmetic and geometric sequences and series.

Find the limit of an algebraic function.

Solve and graph rational, logarithmic, and exponential functions.


Solve application problems using Trigonometry.

Graph the six trigonometric functions and their inverses.

Understand and apply circular functions.

Prove trigonometric identities.

Solve trigonometric equations.


Technical, or Advanced Studies Diploma. Students who have successfully completed Advanced

Algebra may not take this course for credit.

SY 2010 - 2011

COURSE TITLE: Statistics and Probability


DESCRIPTION: Statistics and Probability is a one-semester elective course which is designed to introduce students

to the fundamental concepts of collecting, describing, displaying, and interpreting data, as well as

making decisions and predictions on the basis of that information. This course is an elective

beyond the Algebra II level which prepares the student for college mathematics. In Statistics and

Probability, students learn sampling, distributions, and statistical testing.

MAIN TOPICS: Incorporate the use of technology when appropriate.

Analyze graphical displays of data and numerical characteristics of univariate data sets.

Compare distributions of two or more univariate data sets.

Analyze scatterplots to identify and describe the relationship between two variables.

Find and interpret linear correlation.

Analyze categorical data.

Describe methods of data collection in given surveys and experiments. Plan and conduct a survey

and experiment.

Compute and identify permutations and combinations.

Find probabilities. Describe events as complementary, dependent, independent, and/or mutually

exclusive.

Identify and apply normal distribution.

Apply hypothesis-testing procedures.

CREDIT INFO: This course provides 0.5 of the elective credits required for a Standard or Advanced Studies

Diploma. This course may provide a standard unit of credit for a Standard, Standard Technical,

Advanced Technical, or Advanced Studies Diploma.

SY 2010 - 2011

COURSE TITLE: Discrete Mathematics



mathematics. Discrete Mathematics students are introduced to logic and the finite processes used

to solve applied problems.


Model problems using vertex angle graphs, investigating valence, connectedness, paths, planarity,

and directed graphs. Solve problems using adjacency matrices and matrix operations.

Solve problems by investigating and applying circuits, cycles, Euler Paths, Euler Circuits,

Hamilton Paths, and Hamilton Circuits.

Apply graphs to conflict-resolution problems.

Apply algorithms relating to trees, networks, and paths and use them to schedule tasks.

Solve linear programming problems. Analyze, investigate, and describe fair division, weighted

voting, results of various elections, and salary caps.

Use recursive process and difference equations to generate compound interest, sequences and

series, fractals, population growth models, and the Fibonacci sequence.

Select, justify, and apply an appropriate technique to solve a logic problem.

Apply the formulas of combinatorics.

CREDIT INFO: This course provides 0.5 elective credits required for a Standard or Advanced Studies Diploma.

This course may provide a standard unit of credit for a Standard, Standard Technical, Advanced


SY 2010 - 2011

COURSE TITLE: Advanced Placement Calculus AB

PREREQUISITE: Pre-Calculus


mathematics. In AP Calculus pupils learn the concepts of differential and integral Calculus.


Discuss and graph elementary functions and their properties.

Find one-sided, infinite, and non-existent limits.

Determine the continuity of a function.

Recognize and state the definition of a derivative.

Find the derivative of polynomial, algebraic, rational, and transcendental functions.

Apply the derivative to find rates of change, velocity, optimization, and curve analysis.

Find the anti-derivative and definite integral by using appropriate integration techniques.

Find the area between curves and the volumes of solids.

Approximate areas by using various techniques.

State and use the Fundamental Theorem of Calculus.

Interpret differential equations graphically through slope fields.


Technical, or Advanced Studies Diploma. Students may receive college credit for successful

achievement on the AP Calculus Exam.

SY 2010 - 2011

COURSE TITLE: Advanced Placement Calculus BC

PREREQUISITE: Mathematical Analysis or AP Calculus AB

DESCRIPTION: This course follows the course description of The College Board’s AP Calculus BC program. BC

Calculus applies the concepts of differential and integral Calculus.


Discuss and graph elementary functions and their properties.




Find the derivative of polynomial, algebraic, rational, transcendental, parametric, polar, and vector

functions.


Find numerical solutions to differential equations by various methods.

Explore connections to slope fields, graphs, and solutions to differential equations.

Find the anti-derivative and definite integral by using appropriate integration techniques.

Find the area between curves and the volumes of solids.

Approximate areas by using various techniques.

State and use the Fundamental Theorem of Calculus.

Investigative applications of parametric curves, polar graphs, and vector functions.

Explore sequences and series and test for convergence.

Explore improper integrals and methods of integration including partial fractions, trigonometric

substitution.




SY 2010 - 2011

COURSE TITLE: Advanced Placement Statistics


DESCRIPTION: This course follows the course description of The College Board’s AP Statistics program. AP

Statistics is a year long elective course which is designed to introduce students to the fundamental

concepts of collecting, describing, displaying, and interpreting data, as well as making decisions

and predictions on the basis of that information. This course is an elective beyond the Algebra II

level which prepares the student for college mathematics. In AP Statistics, students explore data

by observing patterns and departures from patterns, plan a study by deciding what and how to

measure data, anticipate patterns by producing models using probability theory and simulations,

and study statistical inference by confirming models.


Define and compare types of statistical distributions and sampling techniques for gathering data.

Univariate and bivariate data will be explored.

Study graphical displays including dotplot, stemplot, histogram, and cumulative frequency plots.

Collect, organize, tabulate, and display data using methods appropriate to the distribution.

Explore mean, median, range, interquartile range, quartiles, percentiles, and z-scores.

Interpret results and draw conclusions about specific data sets. Study outliers, clusters, gaps,

centers, and influential points.

Predict the likelihood of occurrence for given scenarios. Study probability as relative frequency

using the “Law of large numbers” and other rules. Investigate combining independent random

variables, normal distribution, and sampling distributions.

Select and perform tests of significance for given scenarios. Discuss large sample tests for a

proportion, for a mean, for a difference between two proportions, and others.

Describe population estimations with respect to confidence intervals, t-distributions, and chi-

square statistics.




SY 2010 - 2011

COURSE TITLE: Mathematical Analysis

PREREQUISITE: Algebra II and Trigonometry

DESCRIPTION: This course is part of a sequence of advanced mathematical studies beginning with Algebra II &

Trigonometry and including AP Calculus BC. The course combines concepts from Pre-Calculus

and Calculus AB. The course is designed for advanced students who are capable of a more

rigorous course at an accelerated pace.


Review complex numbers, polynomial expressions, radicals and exponents.

Solve and graph polynomial functions and inequalities, rational, logarithmic, and exponential

functions.


Solve application problems using trigonometry.

Graph the six trigonometric functions and their inverses. Prove trigonometric identities.

Apply vectors to solve problems.

Convert between rectangular equations and parametric equations. Graph polar equations and

identify polar graphs.

Identify and use permutations and combinations.




Find the derivative of polynomial, algebraic, rational, and transcendental functions.



Technical, or Advanced Studies Diploma. Students who have successfully completed Pre-

Calculus may not take this course for credit.

SY 2010 - 2011

COURSE TITLE: Functions, Algebra, and Data Analysis

PREREQUISITE: Algebra I

DESCRIPTION: Students will study functions and their behaviors, systems of inequalities, probability,

experimental design and implementation, and analysis of data within the context of mathematical

modeling and data analysis,. Students will solve problems that require the formulation of linear,

quadratic, exponential, or logarithmic equations or a system of equations. Through the

investigation of mathematical models and interpretation/analysis of data from real life situations,

students will strengthen conceptual understandings in mathematics and further develop

connections between algebra and statistics. Students should use the language and symbols of

mathematics in representations and communication throughout the course.

MAIN TOPICS: Investigate and analyze function (linear, quadratic, exponential, and logarithmic) families and their

characteristics.

\ Use knowledge of transformations to write an equation given the graph of a function

Design and conduct experiments using the concepts of sample size, sampling technique, and

controlling sources of bias and experimental error.

Using experimental data, generate an equation for the curve of best fit to model real-world

problems or applications.

Use the best fit equation to interpolate function values, make decisions, and justify conclusions

with algebraic and/or graphical models.

Analyze multiple representations of functions including algebraic formulae, graphs, tables, and

words. Sand use appropriate representations for analysis, interpretation, and prediction.

Determine optimal values in problem situations by identifying constraints and using linear

programming techniques.

Calculate probabilities.

Analyze the normal distribution. Key concepts include the characteristics of normally distributed

data, percentiles, normalizing data using z-scores, the area under the standard normal curve and

probability



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