Bishop Ready High School

Algebra III 243- section 1

2008-2009

Instructor: Mrs. Armstrong

Room 130

Course Syllabus

Prerequisite:

                Successful completion of Algebra II Trignonmetry-226 and/or Algebra II-220.  Permission of the Department Chairperson and/or instructor required. Signature required.

Textbook:  Angel, Abbott, Rundle.  A Survey of Mathematics with Applications.  Boston, Massachusetts:     

                Pearson/Addison Wesley.  2005.

Course Description:

                This course is a review and an extension of the material covered in Algebra II-220 including some trigonometry topics.  It is a general preparatory course for students who do not intend to pursue a career that requires an extensive mathematical, scientific or technical background but need further preparation with the transition to college algebra.  The topics to be studied center around applications of and problem solving with polynomials, functions and inverses, exponential and logarithmic equations, and basic trigonometry.  Students will be evaluated and assessed on individual performance in the following areas: daily homework, weekly quizzes, and tests.  Students will be using a TI-83 plus or a TI-84 plus graphing calculator.

Format:

                Class meetings will include lectures, class work, homework, and special projects.

Lectures:

                Lectures are designed to provide a critical, current perspective on select topics of importance in understanding and applying the subject area.

Readings:

                The text contains examples and information which supplements the lectures, class work, homework, and special projects.  It is strongly encouraged to read the section before the lecture.

Evaluation and Assessment:

                Grades are computed based on the following ratio:

Points earned / Total points possible

• Students are expected to review material daily.
• Students are expected to complete homework but it will not be collected.
• Students are expected to do their assignments by themselves unless otherwise indicated by Mrs. Armstrong.
• Students are expected to participate either through volunteering or being called upon by Mrs. Armstrong.
• Quizzes may or may not be announced.
• Assessment will be any of the following formats: short answer, multiple choices, essays, true/false, matching, and/or problem solving.
• Students are expected to show their work.  Without showing proper work, full credit will not be given.
• Students may be asked to orally present a problem, a topic or a chapter.
• Class work will be collected and graded for accuracy.

 

Number and Number Sense Standard

Benchmarks 8-10

·         Identify subsets of the real number system.

·         Use scientific notaiton to express larger numbers and numbers less than one.

·         Apply properties of operations and the real number system, and justify when they hold for a set of numbers.

·         Connect physical, verbal and symbolic representations of integers, rational numbers and irrational numbers.

·         Compare, order and determine equivalent forms of real numbers.

·         Explain the effects of operations on the magnitude of quantities.

·         Estimate, compute and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions.

 

·         Find the square root of  perfect squares, and approximate the square root of non-perfect squares.

·         Estimate, compute and solve problems involving scientific notation, square roots and numbers with integer exponents.

·         Demonstrate that vectors and matrices are systems having some of the same properties of the real number system.

·         Develop an understanding of properties of and representations for addition and multiplication of vectors and matrices.

·         Apply factorials and exponents, including fractional exponents, to solve practical problems.

·         Demonstrate fluency in operations with real numbers, vectors and matrices, using mental computation or paper and pencil calculations for simple cases and technology for more complicated cases.

·         Represent and compute with complex numbers.

Benchmarks 11-12

·         Demonstrate that vectors and matrices are systems having some of the same properties of the real number system.

·         Develop an understanding of properties and representations for addition and mutilplication of vectors and martices.

·         Apply factorials and exponents including fractinal exponents to sokve practical problems.

·         Demonstrate fluency in operations with real numbers, vectors and matrices using mental computaion or paper and pencil calculations for simple cases and technology for more complicated cases.

·         Represent and compute with complex numbers.

 

Measurement Standard

 

Benchmarks 8-10

·         Solve increasingly complex non-routine measurement problems and check for reasonableness of results.

·         Use proportional reasoning and apply indirect measurement techniques, including right triangle trigonometry and properties of similar triangles, to solve problems involving measurements and rates.

·         Estimate and compute various attributes, including length, angle measure, area, surface area and volume, to a specified level of precision.

·         Write and solve real-world, multi-step problems involving money, elapsed time and temperature, and verify reasonableness of solutions.

·         Explain differences among accuracy, precision and error, and describe how each of those can affect solutions in measurement situations.

·         Apply various measurement scales to describe phenomena and solve problems.

Benchmarks 11-12

·         Estimate and compute areas and volume in increasingly complex problem situations

·         Solve problem situations involving derived measurements

 

Geometry and Spatial Sense Standard

Benchmarks 11-12

·         Use trigonometric relationships to verify and determine solutions in problem situations.

·         Formally define geometric figures.

·         Represent transformations within a coordinate plane and describe the results.

 

               

Patterns Functions and Algebra Standard

Benchmarks 8-10

·         Identify and classify functions as linear or nonlinear, and contrast their properties using tables, graphs or equations.

·         Generalize and explain patterns and sequences in order to find the next term and the nth term

·         Translate information from one representation (words, table, graph or equation) to another representation of a relation or function.

·         Use algebraic representations, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations.

·         Analyze and compare functions and their graphs using attributes, such as rates of change, intercepts and zeros.

·         Solve and graph linear equations and inequalities.

·         Solve quadratic equations with real roots by graphing, formula and factoring.

·         Solve systems of linear equations involving two variables graphically and symbolically.

·         Describe and interpret rates of change from graphical and numerical data.

Benchmarks 11-12

·         Analyze functions by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior.

·         Use the quadratic formula to solve quadratic equations that have complex roots.

·         Use recursive functions to model and solve problems; e.g., home mortgages, annuities

Data Analysis and Probability

   Benchmarks 8-10

• Construct convincing arguments based on analysis of data and interpretation of graphs.
• Describe sampling methods and analyze the effects of method chosen on how well the resulting sample represents the population.
• Use counting techniques such as permutations and combinations to determine the total number of options and possible outcomes.
• Compute probabilities of compound events, independent events and simple dependent events.
• Make predictions based on theoretical probabilities and experimental results.

Benchmarks 11-12

·         Create and analyze tabular and graphical displays of data using appropriate tools, including spreadsheets and graphing calculators.

·         Use descriptive statistics to analyze and summarize data including measures of center, dispersion, correlation and variability.

·         Design and perform a statistical experiment, simulation or study; collect data and interpret data and use descriptive statistics to communicate and support predications and conclusions.

  

Mathematical Processes Standard

Benchmarks 8-10

·         Formulate a problem or mathematical model in response to a specific need or situation, determine information required to solve the problem, choose method for obtaining this information, and set limits for acceptable solution.

·         Apply mathematical knowledge and skills routinely in other content areas and practical situations.

·         Recognize and use connections between equivalent representations and related procedures for a mathematical concept; e.g., zero of a function and the x-intercept of the graph of the function, apply proportional thinking when measuring, describing functions, and comparing probabilities.

·         Write clearly and coherently about mathematical thinking and ideas

Benchmarks 11-12

·         Construct algorithms for multi-step and non-routine problems.

·         Assess the adequacy and reliability of information available to solve a problem.

·         Evaluate a mathematical argument and use reasoning and logic to judge its validity.

·         Understand the difference between a statement that is verified by mathematical proof, such as a theorem, and one that is verified emperically using examples and data.

·         Use formal mathematical language and notation to represent ideas, to demonstate relationships within and amoung reprentation systems and to formulate generalizations.

·         Communicate mathematical ideas orally and in writing with a clear purpose and appropriate for a specific audience.

·         Apply mathematical modeling to workplace and consumer situations including problem formulation, identification of mathematical model, interpretation of solution within the model and validation to original problem situation

 

The following topics will be covered but not limited to the following:

Please note that this schedule is tentative.