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MAA401: Algebra II (2010-2011)

CALENDAR YEAR: 2010-2011

Major Concepts/Content: This course engages students in advanced algebraic concepts through the study of functions of functions, polynomials, complex matrices, and sequences and series. Students will make connections by integrating algebra into geometry, data analysis, and into other curricular areas. Student reasoning will involve linear equations and inequalities, systems of linear equations, matrices and determinants, quadratic equations and relations, functions and graphs, powers, roots, and radicals, exponential and logarithmic functions, polynomials and polynomial functions, rational expressions and functions, sequences and series, probability and statistics, and circular trigonometric functions.

Major Instructional Activities: Students will be involved in communicating ideas trough conjecture and validation of thinking involving linear and quadratic equations, and polynomial and rational functions. Included will be the use of technology and calculators to explore mathematical patterns and graphs as well as many methods of solving equations. Students will use properties, models, and transformations in interesting, authentic real-life applications. Students will be engaged in cooperative groups, whole-class settings, or individually to reinforce concepts in algebra, geometry, sequences, series, probability, and statistics. Students should have access to calculators at all times.

Major Evaluative Techniques: Many evaluative processes should be used to assess students’ written and oral work. These include multiple-choice, short-answer, discussion, or open-ended interview; homework; projects; journals; essays; dramatization; and class presentations. Testing formats will include restricted-time written tests, two staged tests, take-home tests, oral tests and student produced tests. Assessment methods can be supplemented by student-produced analysis of problem situations, solutions to problems, reports on investigations and journal entries. Students will be provided the opportunity to do chapter projects that capture the concepts and skills presented throughout the chapter unit that emphasizes real world situations.

Course Objectives:

Essential Expectations: Upon successful completion of Algebra II course, the student should be able to:

  • Carry out counting procedures such as those involving sets (unions and intersections) and arrangements (permutations and combinations)
  • Use appropriate technology effectively and efficiently in carrying out complex calculations
  • Define, use and manipulate expressions involving variables, parameters, constants, and unknowns in work with formulas, functions, equations, and inequalities
  • Represent geometric curves and graphs of functions in standard coordinate systems
  • Describe, generalize, and use basic types of functionsar, exponential, power, rational, square and square root, and cube and cube root
  • Use arithmetic sequences and geometric sequences and their sums, and sees these as the discrete forms of linear and exponential functions, respectively
  • Solve equations symbolically, graphically, and numerically and knows how to use the quadratic formula for solving quadratic equations
  • Use equations to represent curves such as lines, circles, and parabolas
  • Use functions to analyze patterns and represent their structure
  • Identify conic sections and their properties to include parabolas, ellipses, and hyperbolas
  • Interpret representations of data, compares distribution of data, and critiques conclusions and uses of statistics, both in school materials and public documents
  • Explore questions of experimental design, use of control groups, and reliability
  • Use relative frequencies based on empirical data to arrive at an experimental probability for a chance event
  • Design simulations to estimate probabilities
  • Works with the normal distribution in some of its basic applications
  • Use matrix theory with graphics calculators to solve systems of equations, transformations, and finite functions
  • Use technology to create graphs or spreadsheets that contribute to the understanding of a problem
  • Evaluate and analyze formulas and functions of many kinds, using both pencil and paper and more advanced technology

This course can be used to partially satisfy the requirements for an endorsement in the following pathways.

Cluster | Pathway | Required/Recommended/Related
Information Technology | Programming/Software Engineering | Recommended