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Algebra A - This course allows students to receive a comprehensive education in Algebra I with an integration of basic geometry, but extends the curriculum over a two year period to provide adequate time for the students to master the material. The main focus of this course is to provide students with the fundamentals of algebra and geometry that will enable them to have an in depth understanding of more advanced material as they progress through their academic careers.

The course begins with an intensive review of basic arithmetic principles such as multiplication, division, addition, and subtraction of whole numbers. The ultimate goal of this is to provide students with an understanding of basic mathematics in conjunction with the order of operations without a reliance on a calculator. The course will then extend these same concepts to integers and the number line. Students will also begin exploring open sentences as well as patterns and sequences.

Rational numbers will then be introduced. Students will focus on extending basic mathematic principles to fractions. Students will explore the concepts of least common multiples and greatest common factors in order to gain a complete understanding of rational number operations (reduction, equivalence, addition, subtraction).

Next, the course will extend the students’ understanding of integer and rational number operations by focusing on statistics and probability. Students will understand and apply the measures of central tendency. Graphical representations of data will also be covered including: stem-leaf plots, box-whisker plots, histograms, scatter plots, and pie charts. Probability is introduced next, with students discovering the probability of both single and compound events.

Afterwards, equations and basic algebraic concepts are introduced to the students. Students will understand the concepts of a variable and apply that understanding through open sentences. Students will be introduced to the rule of opposites and apply it through solving one-step equations through addition, subtraction, multiplication, and division. This understanding will then be extended to solve two-step equations.


Algebra B - Algebra B is the second part of a two year Algebra curriculum. The purpose of the two year course is to allow lower level math students more time to fully absorb all of the material in a typical Algebra I course, while at the same time giving them a sound foundation in geometry. The specific goal of Algebra B is to take the materials learned in Algebra A and to provide a deeper understanding by expanding upon previously learned topics by showing the interconnection between Algebra and Geometry.

The course will begin by reintroducing equations. Students will recall how to solve single and two-step equations by using the rule of opposites. Students will then recall how to solve more advanced equations, through simplification and the application of various algebraic properties.

Next, students will recall how to solve and plot inequalities using the rules of algebra. Techniques previously learned in Algebra A will be expanded on through the teaching of both compound and absolute value inequalities.

Students will be introduced to the coordinate plane, functions, and graphing linear equations. Students will learn to plot points on the coordinate plane. Linear equations and linear inequalities will be introduced, as well as the notion of slope, distance, midpoint and intercepts. This idea will connect into the study of the various forms of linear equations and the manipulation of said forms using the rules of solving equations. Students will integrate the notions of parallel and perpendicular lines into their study of linear equations.

Transformations will be studied next. Students will learn how to transform various geometric shapes using the coordinate plane. Students will learn to reflect, rotate, translate, and dilate the various shapes.

Algebra I - Students apply the concept of variables as they write and simplify algebraic expressions. Patterns and sequences are introduced to enhance problem-solving skills and stem-and leaf plots are integrated into the chapter to provide students with another tool for data representation. Students connect relevant number rules and properties to the organization and structure of algebra. The distributive property is emphasized because of its vital rule in performing algebraic operations.

The basic operations are applied to integers and rational numbers. The number line is used as a mathematical model to develop the rules for the addition of integers. Students apply their knowledge of the rules for addition and the additive inverse property to develop rules for the subtraction of integers. Then the connection is established between these rules for integers and the rules for rational numbers. Rules for multiplying and dividing rational numbers are also explored. Finally, students examine the information presented in verbal problems and translate that information into algebraic expressions, as well as reversing the process and writing descriptions of the problems from algebraic expressions.

Cups and counters are used as models to develop an understanding of equations, and then, in carefully sequence lessons, the addition, subtraction, multiplication, and division properties of equality are presented and applied to solving equations. Then students use their knowledge of equations to integrate geometry skills by studying properties of angles and triangles. They also learn to use more than one property to solve equations with the variable on either side or on both sides. The chapter concludes with students learning to find the mean, median, and mode.

Students apply the process of mathematical modeling to real-world problem situations, making the connection with the equation-solving skills and concepts that they mastered in the previous chapter. Students solve proportions in the first lesson. Then, they study relationships between similar triangles and use similarity properties to find the measures of corresponding parts of similar triangles. This background leads to the study of the sine, cosine, and tangent ratios associated with an acute angle in a right triangle. Next, students solve problems involving percent, simple interest, percent of increase or decrease, discount, and sales tax. Students learn to find the probability ad the odds of a simple event. The chapter concludes with lessons involving mixture problems, uniform motion problems, and direct and inverse variation problems.

Algebra II - The beginning of the course provides a review of essential skills and concepts in algebraic and statistical settings. Students survey evaluating expressions, the properties of real numbers the use of line and stem-and-leaf plots to represent data, and the use of measures of central tendency to interpret and describe sets of data. Then, the procedures for solving linear equations are presented and extended to solving inequalities. The number line is used as a mathematical model to review absolute value, and equations and inequalities involving absolute values are solved.

Students graph relations and identify those that are functions. Next, they graph linear equations from a table of ordered pairs, identify the slope and intercepts, and use these to group other linear equations. Graphing technology is applied to graph linear equations and to approximate solutions of equations in one variable. Then students determine if the lines are parallel, perpendicular, or neither. The strategy of identifying and using a pattern is integrated to help students solve problems. Next, students draw scatter plots and find prediction equations to solve problems. They conclude their study by graphing special functions and linear inequalities.

Students’ understanding of linear equations and inequalities extends by examining and solving systems of linear equations and inequalities. They use graphing techniques, graphing technology, and algebraic methods to solve systems of linear equations and inequalities. Then determinants are introduced and systems are solved by using Cramer’s rule. Finally, the students solve systems of three equations in three variables.

Next, the students are introduced to matrices through the concept of matrix logic. They organize known data into a table that enables them to eliminate possibilities and arrive at the only possible solution. Students learn to create a matrix, perform scalar multiplication on it, and then add matrices. Determinants are related to matrices, and students connect the content to a number of real-world applications, as well as to other areas of mathematics, such as transformational geometry. Students also solve systems of equations by using inverse matrices. Finally, students examine the statistical tool known as a box-and-whisker plot.

The knowledge of operations on monomials and polynomials is reviewed and extended. Addition, subtraction, and multiplication of polynomials are addressed. Methods for factoring polynomials are covered as well as methods for dividing polynomials, including synthetic division. Students also learn to simplify, add, subtract, multiply, and divide radicals. They make the connection between fractional exponents and radicals and then simplify expressions with fractional exponents. Complex numbers and operations on complex numbers are introduced, and students simplify expressions containing complex numbers.

Students learn to solve quadratic equations by using graphing technology, by factoring, by completing the square, and by using the quadratic formula. Students use the discriminant to determine the nature of the roots of a quadratic equation and learn how to write a quadratic equation when two roots are known.

Next chapters open with the development of the formulas for finding the distance between two points and finding the midpoint of a line segment. Students identify and graph parabolas, circles, ellipses, and hyperbolas. They also write the equations for these curves given certain properties or the graph of the curve. Conic sections are classified, and students learn to identify a conic section from its quadratic equations written in standard form. Modeling lessons provide students with hands-on activities relating to chapter concepts. Finally, students solve systems in which one or more of the equations are quadratic equations.

Students use graphing technology to graph power functions and exponential functions. They apply their knowledge of integers used as exponents to simplify simple expressions and solve equations where real numbers are used as exponents. Next, students learn to differentiate between exponential and logarithmic functions. They derive properties of logarithms from the properties of exponents. Then they solve simple exponential and logarithmic equations. Students are introduced to common and natural logarithms to solve equations and real world problems by using logarithms and their graphs.

Algebra-Geometry-Concepts - This course is designed for students who have passed Algebra A and B and are entering their third year of mathematics. The content of this course consists of material in Algebra I and II, as well as geometry. The focus of this course is to complete students’ education in geometry, while at the same time reinforcing and expanding on material learned in Algebra I and introducing material from Algebra II.

The course will begin with a review of equations and inequalities. Students will use the rules of algebra to solve multi-step equations and inequalities. Throughout the review, there will be a focus on solving equations in conjunction with previously learned geometric concepts such as area, volume, parallel lines, and transversals. Students will also explore compound and absolute value inequalities.

Next, students will explore polygons and their area. Initially, students will recall how to name various polygons. The course will then explore specific polygons such as triangles, parallelograms, rhombi, and trapezoids. Students will then learn about regular polygons. Students will explore the angle measures of regular polygons and their relationship to the polygons’ areas. Throughout this section there will be a strong focus on connecting algebraic concepts to the formulas presented.

Students will recall how to solve and write linear equations as well as the equations of parallel and perpendicular lines. They will also explore relations, functions, and special functions.

Students will then expand on their understanding of linear equations by beginning to solve systems of linear equations. They will initially solve systems of linear equations by graphing and finding the point of intersection for the two lines. Then, students will solve systems of linear equations algebraically through substitution and elimination.

Polynomials are examined next. This section begins by reviewing the laws of exponents and how to multiply and divide monomials. Students will then recall how to add, subtract, and multiply polynomials, as well as how to solve polynomials through factoring. Division of polynomials will then be explored, with an emphasis placed on synthetic division. The section will conclude with an exploration of radical expressions and rational exponents.

Geometry - By beginning with a review of the coordinate plane, the development uses this plane to make a logical transition from algebra to geometry. The undefined terms, point, line, and plane are then used to define other geometric terms such as angles; segment, and rays.

The exploration of inductive and deductive reasoning strategies leads into a study of if-then statements and their logic. Conditional statements, and their converses, prepare students for the more formal sections.

The relationship between points, lines, angles, planes, and spheres is examined. Parallel lines and their transversals are studied, as well as the angle measures formed when these lines intersect. In addition to angle measurements, slopes of parallel and perpendicular lines are found. Many postulates and theorems are introduced to related lines and angles. The theorems are used to enhance the learning of geometric proofs. The distance formula is used to find the distance between points and lines.

Next chapter provides an intensive study of triangles. It begins by classifying triangles according to angles and sides. Interior and exterior angles and their measures are explored. This leads to the coverage of triangle congruence including SSS, SAS, and ASA postulates as well as the MS Theorem. The chapter concludes with a study of isosceles and equilateral triangles. Compass and straightedge are used for constructions.

The congruence is applied to different types and parts of triangles. Students identify and use medians, altitudes, angle bisectors, and perpendicular bisectors. Tests for congruence of right triangles are used. Indirect reasoning and indirect proofs are used to reach conclusions and solve problems. Properties of inequalities are applied to the measures of segments and angles. Relationships between sides and angles in a triangle are modeled and investigated using a graphing calculator and/or Cabri Geometry software. The Triangle Inequality Theorem, SAS Inequality, and SSS Inequality are applied to different triangles.

Students are introduced to parallelograms, rhombi, rectangles, squares, and trapezoids. They use technology to investigate these quadrilaterals. Problems are solved by identifying sub goals. Students use the properties of parallelograms, rhombi, rectangles, squares, and trapezoids to solve problems. Students also apply these quadrilaterals to real examples such as kites.

Next, students use algebra skills to solve proportions. Then they identify similar figures and solve problems using proportions. They apply this practice to similar triangles. The proportional parts of similar triangles are used to solve problems and to divide segments into congruent parts. The proportional relationship between perimeters, altitudes, angle bisectors, and medians of similar triangles are investigated. Similar figure relationships are extended to fractals.

Students investigate and use the Pythagorean Theorem. They use paper to model the Pythagorean Theorem. Students find geometric means. They use geometric means to solve triangles using the altitude to the hypotenuse. They use the properties of special right triangles. Students extend their skills to trigonometry and use ratios to solve for specific sides or angles. Trigonometry is applied to the angles of elevation and depression through word problems.

The study of circles begins with definitions for radius, diameters, and circumference. Major and minor arcs and their relationships to central angles are explored. Chords, secants, and tangents and their properties are used to develop theorems involving inscribed angles and intercepted arc. Emphasis on measurement of angles and arcs provides problem-solving experiences throughout. Cabri Geometry constructions are used occasionally to verify theorems.

Students learn to identify and name polygons. They investigate interior and exterior angle measures of convex and regular polygons. Students use paper and pencil to create tessellations by translating and rotating polygons. They learn to identify types of tessellations and create specific tessellations. They also learn to solve problems by using guess and check. Students use a graphing calculator to compare the areas of parallelograms and rectangles. Then they use area formulas for parallelograms, triangles, rhombi, trapezoids, regular polygons, and circles. Students use area to investigate geometric probability.

The models of three-dimensional figures and their cross sections and slices are explored. Students learn to recognize many three-dimensional figures and learn to draw three-dimensional figures. They apply their learning to make tetrahedron kits. Students flatten three-dimensional figures and look at nets and surface area and learn how to determine surface area and volume for prisms, cylinders, pyramids, cones, and spheres

In the last chapter, students use two methods to graph linear equations. Then determine the equation of a line given information about its graph and solve problems by using equations.

Pre-Calculus - Students begin with a review of the algebraic concepts that provide the foundation for further study in pre-calculus. They include the properties of the real-number system, manipulations of algebraic expressions, the solution of equations and inequalities, and the solution of applied problems. Graphing technology (i.e., the Texas Instruments TI-83 Plus Graphing Calculator) is used to enhance the understanding and visualization of these topics.
Students next focus attention on functions and equations with graphs that can be used to model real-life situations mathematically. Data that exhibits arithmetic growth can be modeled using a linear function. Such models are invaluable when doing analyses and making predictions in fields ranging from astronomy to zoology.
A polynomial function is a function that can be defined by a polynomial expression. A rational function is a function that can be defined as a quotient of two polynomials. Students study both kinds of functions and examine zeros of polynomials in greater depth. They also model real data with quadratic, cubic, and quartic polynomial functions and use these functions to make predictions. In addition, they study the graphs of rational functions and use the graphs of both polynomial and rational functions to solve related inequalities.
Students then consider two kinds of closely related functions. The first, called exponential functions are those that have a variable in the exponent. Such functions have many applications to the growth of populations, commodities, and investments. The opposite – or inverse – of an exponential function is called a logarithmic function Such functions are important in many applications like earthquake magnitude, sound level, and chemical pH.
Students are then introduced to an important class of functions called trigonometric, or circular, functions. Historically, these functions arose from a study of triangles; hence the name trigonometric. We will begin our study with right triangles and degree measure and solve applications involving right triangles. Then we will consider trigonometric functions of angles or rotations of any size with both degree and radian measure. A circle of radius 1 (a unit circle) is then used to define the six basic trigonometric functions; hence the name circular functions. The domains and ranges of these functions consist of real numbers.
There are a number of relationships among trigonometric functions, given by identities that are important in algebraic and trigonometric manipulations. Students will be introduced to those identities and their use in solving trigonometric equations. They are also shown a detailed examination of inverses of the trigonometric functions and provided not only a basis for applications but also a foundation for further work in mathematics.
Triangle trigonometry is important in applications such as large-scale construction, navigation, and surveying. In this chapter, the triangle trigonometry that students studied previously is continued and used to solve triangles that are not right triangles. Complex numbers are also studied further, with applications for electronics and engineering. Two new topics include the polar coordinate system and the idea of a vector. A vector is a quantity that has direction and magnitude; vectors have many practical applications in the physical sciences. Students conclude with partial fractions, a necessary skill used in calculus.
Students study the four curves that are formed by the intersection of a cone with a plane – the parabola, the circle, the ellipse, and the hyperbola. Conic sections and their properties were first studied by the Greeks. But today they have many applications, especially in calculus Students are introduced to parametric equations, an alternative to rectangular equations involving only two variables, x and y.
The course concludes with an introduction to sequence and series. For example, when the world bicycle production for various years is listed, a sequence is being formed. There are two basic types of sequences – arithmetic and geometric. Both are used to model rates of growth commonly found in the real world and encountered in calculus applications routinely. When the members of a sequence are numbers, they can be added. Such a sum is called a series.

Calculus - The calculus course has two parts- differential and integral calculus. The differential calculus begins with review of some elementary math concepts- functions, graphs of functions and the most widely used functions linear and quadratic, trigonometric, exponential and logarithmic.
Students begin with a prelude to the study of calculus by reviewing the real number system, functions, coordinate geometry, and graphing. The basics of trigonometry are also covered. Finally, we investigate what calculus is and how it is used.
Students are then introduced to the concept of finding the slope of a straight line tangent to the graph of a simple function at a specific point on the graph. Next, an intuitive understanding of the limit concept is explored, including: the realization that f(a) is not necessarily the limit of f(x) as x approaches a; the non-existence of some limits; knowledge of trigonometric limits. The use of factoring and of the conjugate to evaluate less obvious limits is also explored. Finally, continuity, composition, and the intermediate value property of continuous functions
Students then explore the derivative, beginning with an understanding of the derivative as the instantaneous rate of change. The mechanics of derivatives are presented, including algebraic and trigonometric functions. Problems involving maxima and minima of functions on closed intervals are touched upon, and then the investigation closes on implicit differentiation and related rates.
Students then extend the skills learned in the previously on derivatives. They start with the mean value theorem and its corollaries. Then they launch into max-min problems of the first derivative test. An increased proficiency with word problems is required, as well as the nature of extrema. Next, a move from critical points to inflection points in second derivatives is made. Finally, vertical and horizontal asymptotes are examined as limits that do not exist and as x approaches ±.
Students then study antiderivatives and solutions to initial value problems, particularly those having to do with vertical motion with constant gravitational acceleration. It then discusses area as a limit of improving approximations to it, leading to exact values of area. Summation and integration notation are introduced as logical extensions, and using antiderivatives to evaluate definite integrals follows. Then, the average value theorem and the fundamental theorem of calculus (continuity implies integrability) are discussed. Finally, the method of integration by substitution is practiced and areas of plane regions are found.
There are many different applications for using integrals. Students begin by showing how to set up integral formulas by first setting up Riemann sums. Next, volumes by the method of cross sections is covered, with volumes of revolution (disks and washers) as a special case, followed by finding volume by the method of cylindrical shells. Students will also learn how to find arc length and surface area of revolution.
Students then focus on the exponential and logarithmic functions, their inverse relationship to each other. The derivatives of these functions are introduced, and a clear understanding of such functions as ln x are presented.
The course concludes with a study of various techniques for integration, starting with substitution and use of integral tables. Integration of trigonometric functions, integration by parts, and partial fractions – when and how to use them, are studied.