Math 

Math Courses
 

Life Skills Math

Core Textbook: Life Skills Math, AGS Publishing

Curriculum Overview:
This course presents functional mathematic skills in their real-world applications, offering practical and relevant study of emergent numeracy skills.
This course is designed to enhance students’ knowledge of the foundational skills necessary in the study of mathematics.  Students will learn to become effective consumers with the necessary math skills for independent living.  This  course will draw from a variety of resources to ensure that students achieve mastery in all areas.

Life Skills Math Goals:

• To build confidence and competence in the area of math.
• To promote student responsibility and personal life skills.
• To develop the self-advocacy skills of each student.
• To apply basic mathematics skills to real world applications.

  Course Outline:

• Foundations review
• Spending and earning money
• Watching the clock
• Fractions at home
• Sports mathematics   

Algebra I

Core Textbooks:
Algebra 1 by Larson, Boswell, Kanold and Stiff (McDougal Littell 2007) OR
Algebra: Structure and Method, Book 1 by Brown, Dolciani, Sorgenfrey and Cole (McDougal Littell 2000)

Curriculum Overview:
This foundational introductory class initiates the development of algebraic skills through the study of linear, quadratic and polynomial functions.   Topics studied will include: problem solving, integers, fractions, decimals, percents, variable expressions, linear and quadratic equations, exponents, polynomials, rational expressions, square roots, factoring, and linear graphs.

Algebra I Goals:

• Students will be able to work with the real number line and simplify numerical expression involving decimals, fractions, positive and negative numbers through the use of one or more operations (multiplication, division, addition or subtraction).
• Students will be able to use the distributive property to simplify expressions.
• Students will be able to write equations representing relationships among integers.
• Students will be able to solve an equation for an unknown variable by using more than one transformation.
• Students will learn the laws of exponents and will be able to use them in simplifying algebraic expressions and equations.
• Students will be able to multiply and divide monomials.
• Students will be able to solve rate-distance-time problems.
• Students will be able to factor integers and find the greatest common factor of several integers.
• Students will be able to factor quadratic expressions and will be able to solve quadratic equations.
• Students will be able to multiply, divide, add and subtract rational functions.
• Students will be able to solve problems involving ratios.
• Students will be able to solve problems involving percents and decimals.
• Students will be able to graph ordered pairs and linear equations in two variables.
• Students will be able to find the slope of a line.
• Students will solve a system of two linear equations.   

Geometry

Core Textbook:  Geometry  by Larson, Boswell, Kanold and Stiff (McDougal Littell 2007)

Curriculum Overview:
This course will provide extensive analytical ability to students through the study of proofs, congruency, triangle relationships, and similarity. Topics studied in this course will include points, lines, planes, triangles, conditional statements, deductive reasoning, angle relationships, proportionality, matrices, vectors, symmetry, quadrilaterals, parallelograms, transformations, circles, and arc measures. 

Geometry Goals:
Students will understand the mathematical foundations of basic geometry.  Students will use problem solving skills combined with geometric drawings to explore this area of mathematics.  Specifically, we will work with the following concepts:

• Identification of points, lines and planes.
• Measurement and classification of angles.
• Geometric reasoning and proofs.
• Triangles, sine, cosine and tangent.
• Quadrilaterals and circles.
• Surface area and volume of solids. 

Algebra II

Core textbook:  Algebra II, by Larson, Boswell, Kanold and Stiff (McDougal Littell 2007)

Curriculum Overview:
This course is a continuation of a first year high school introductory course in algebra.  Students will study functions and their corresponding graphs in order to solidify algebraic skills.

Algebra II Goals:

• Students will be able to solve linear, quadratic, exponential, rational, and logarithmic functions and expressions.
• Students will be familiar with the graphs of polynomials, as well as exponential and logarithmic functions.
• Students will be able to work with inequalities.
• Students will gain an introduction to analytic geometry.
• Students will gain an introduction to basic probability and statistics.
   

PreCalculus

Core textbook:Precalculus 4th Edition by Robert Blitzer (Pearson Prentice Hall 2010)

Curriculum Overview:
In this course, students will gain the skills needed to be successful in a calculus course through the study of rational, polynomial, logarithmic, exponential and trigonometric functions.

PreCalculus Goals:

• Students will have a solid understanding of functions and their graphs.
• Students will understand what a linear function is and how to calculate its slope.
• Students will be able to graph a function and a given transformation of that function.
• Students will be able to find combinations of functions, as well as a composition of functions.
• Students will be able to find the inverse of a function.
• Students will be able to use the distance and midpoint formulas.
• Students will be familiar with polynomial functions and their graphs.
• Students will be familiar with rational functions and their graphs.
• Students will be able to solve polynomial and rational inequalities.
• Students will understand the properties and graphs of exponential and logarithmic functions, and will be able to use them in order to solve exponential and logarithmic equations.
• Students will be able to use exponential functions to model growth and decay problems.
• Students will be able to convert between degrees and radians.
• Students will be able to find values of trigonometric functions and their inverses.
• Students will use right triangle trigonometry to solve real world problems.
• Students will be familiar with the graphs of the sine, cosine, tangent, secant, cosecant and cotangent functions.
• Students will be able to solve problems using applications of trigonometric functions.
• Students will be able to verify trigonometric identities, including double-angle and half-angle formulas.
• Students will be familiar with the law of sines and the law of cosines and how to use them to solve problems.
• Students will be familiar with polar coordinates and graphs of polar equations.
• Students will be able to put complex numbers in polar form and will be familiar with DeMoivre’s theorem.
• Students will be familiar with vectors, and will be able to compute the dot product of two vectors.
• Students will be able to solve a system of linear (and nonlinear) equations in two and three variables.
• Students will be able to work with partial fractions.
• Students will be able to solve a system of inequalities.
• Students will gain an understanding of basic matrix operations and their applications.
• Students will be able to use multiplicative inverses of matrices to solve matrix equations.
• Students will be able to find determinants of matrices using Cramer’s Rule.
• Students will be able to use point plotting to graph plane curves described by parametric equations.
• Students will understand what a geometric sequence is.
• Students will understand the principle of mathematical induction and will use it to prove statements.

Liberal Arts Math

Core Textbook: Thinking Mathematically by Robert Blitzer (Pearson Prentice Hall 2008)

Curriculum Overview:
This course will provide students with a general survey of topics and ideas in mathematics that are useful in our contemporary world.  Topics studied will include set theory, logic, number representation and calculation, measurement, geometry and algebra, basic financial math, basic probability theory and statistics, mathematical systems, and voting and apportionment.  This class is intended to develop analytical and critical thinking skills by studying mathematics found in everyday life.  Moreover, students will gain a fundamental understanding of the importance and relevance of mathematics.

Liberal Arts Math Goals:

• Students will understand basic set concepts, Venn Diagrams, set operations and will be able to apply them to survey problems.
• Students will understand quantified statements and negations and will be able to express them into logic symbols.
• Students will express compound logic statements in symbolic form.
• Students will be familiar with truth tables for negation, conjunction and disjunction.
• Students will use and apply DeMorgan’s Laws.
• Students will be able to solve problems involving percents, sales tax, and income tax.
• Students will be solve problems involving simple and compound interest formulas.
• Students will be familiar with the equation to find the future value of an annuity.
• Students will gain a basic understanding of stocks and bonds as investments.
• Students will use the Fundamental Counting Principle to determine the number of possible outcomes in a given situation.
• Students will understand the difference between a combination and a permutation and will be able to use these formulas to find a desired quantity or probability.
• Students will compute theoretical, empirical and conditional probabilities.
• Students will be able to compute the probabilities of multiple events.
• Students will understand and use odds and will be able to find expected values of events.
• Students will be familiar with sampling, frequency distributions, and graphs.
• Students will be able to determine measures of central tendency given a set of data.
• Students will be able to determine a measure of dispersion given a set of data.
• Students will gain an understanding of the voting methods used today and their flaws.
• Students will gain an understanding of apportionment methods and their flaws.
• Students will understand early numerical positional systems.
• Students will be able to change base ten numerals to numerals in other bases, and compute operations in these bases.
• Students will be familiar with the Fundamental Theorem of Arithmetic.
• Students will be familiar with geometric and arithmetic sequences.
• Students will understand the real number system and properties of real numbers.
• Students will be familiar with exponents and scientific notation.
• Students will have a solid understanding of all concepts in algebra, including equations, inequalities graphs, functions and linear systems.
• Students will be able to measure lengths, areas, volumes, weight and temperature using the metric system.
• Students will be familiar with the definitions of points, lines, planes, angles, triangles, polygons, perimeter and tessellations.
• Students will be able to compute volumes, circumferences, and areas of geometric objects and figures.

Fundamentals of Higher Math

Core textbook: Thinking Mathematically by Robert Blitzer (Pearson Prentice Hall 2008)

Curriculum Overview:
This course will provide students with a general survey of topics and ideas in higher mathematics that are useful in our contemporary world.  Topics studied will include set theory, logic, number representation and calculation, consumer mathematics and financial management, counting methods and probability theory, statistics, mathematical systems, voting and apportionment, and graph theory.  Students will develop analytical and problem-solving skills by studying mathematics they encounter in everyday life.

Fundamentals of Higher Math Goals:

• Students will understand basic set concepts, Venn Diagrams, set operations and will be able to apply them to survey problems.
• Students will understand quantified statements and negations and will be able to express the into logic symbols.
• Students will express compound logic statements in symbolic form.
• Students will be familiar with truth tables for negation, conjunction and disjunction.
• Students will use and apply DeMorgan’s Laws.
• Students will be able to solve problems involving percents, sales tax, and income tax.
• Students will be solve problems involving simple and compound interest formulas.
• Students will be familiar with the equation to find the future value of an annuity.
• Students will understand stocks and bonds as investments.
• Students will use the Fundamental Counting Principle to determine the number of possible outcomes in a given situation.
• Students will understand the difference between a combination and a permutation and will be able to use these formulas to find a desired quantity or probability.
• Students will compute theoretical, empirical and conditional probabilities.
• Students will be able to compute the probabilities of multiple events.
• Students will understand and use odds and will be able to find expected values of events.
• Students will be familiar with sampling, frequency distributions, and graphs.
• Students will be able to determine measures of central tendency given a set of data.
• Students will be able to determine a measure of dispersion given a set of data.
• Students will recognize characteristics of the normal distribution and will understand the rules associated with it as well as percentiles and quartiles.
• Students will be able to find z-scores.
• Students will be able to make a scatter plot and interpret a correlation coefficient to find the equation of a regression line.
• Students will understand what is meant by a mathematical system and will be able to interpret one.
• Students will gain an understanding of the voting methods used today and their flaws.
• Students will gain an understanding of apportionment methods and their flaws.
• Students will understand early numerical positional systems.
• Students will be able to change base ten numerals to numerals in other bases, and compute operations in these bases.
• Students will be familiar with the Fundamental Theorem of Arithmetic.
• Students will be familiar with geometric and arithmetic sequences.
• Students will be familiar with graphs, paths, circuits, including both Euler and Hamilton paths and circuits, and trees.
• Students will be introduced to rotational symmetries, groups and clock arithmetic.