COURSE OUTCOMES ALGEBRA (SECONDARY) (July 2013) Algebra may be entered by any student who has mastered Mathematics 12/13 or its equivalent. The course assumes familiarity with basic equations and fluency in the order of operations and in performing operations with real numbers. The course expands into solving, graphing, and writing linear equations, systems, inequalities, and quadratic equations. Wherever possible, real-life activities are integrated into the curriculum. Mastery of Algebra is the normal prerequisite for enrollment in Geometry. The course is divided into ten Essential Units and several Selective Units. Each unit is sub-divided into Essential Outcomes (TSWs) that must be assessed for mastery. In addition to the Essential Outcomes, some units include Introduced and Practiced Outcomes which are taught but not assessed for mastery. The normal pace for this course leads to mastery of the ten Essential Units in one school year. However, time is used as a resource to complete these units, rather than as a boundary condition to control the beginning and ending of the course. Thus, some students will progress in Algebra according to their needs, taking either a longer or shorter amount of time to attain mastery. A number of Selective Units are available for the student wishing to pursue additional topics and to gain additional secondary credits. This course is aligned with the Common Core State Standards (CCSS) for Mathematics. The fundamental principles guiding this approach are included in the CCSS Mathematical Practices. UNIT COMPOSITION: It is intended that this course be taught during minimum of five 45-minute periods each week. The normal pace for this course leads to mastery of ten Essential Units during the school year. Additional Selective Units are included for highly motivated students who are able to achieve beyond the essential course content. Mastery is based on demonstrable and measurable achievement of all the Essential Outcomes (TSWs) in each unit. Real-life Activities: Some Essential Units require the student to use the skills and concepts in the unit in a reallife activity. More than story problems, these are actual hands-on experiences in which the student applies mathematics to practical situations relevant to his/her existence, e.g. the student will make measurements, generate data, draw conclusions, etc. Real-life activities may be limited, short-term experiences, or long-term experiences lasting several days, weeks, or months. They may be cross-cultural and/or cross-disciplinary. At the end of each unit there is a brief list of possible activities (denoted by an asterisk *), although teachers and students are encouraged to generate their own activities that have relevance to the local situation. Additional ideas and links can be obtained from the QSI website, the publisher s website, as well as from resources such as: http://www.educationworld.com/a_curr/curr148.shtml 1
Note: Even though a hands-on activity is identified in the last TSW, the activity does not have to take place at the end of the unit. It can be engaged at any time during the unit. This course is related to all the Success Orientations, Competencies, and Knowledge noted in the Mathematics Program Outcomes. RESOURCES: The teacher has a number of resources to provide differentiated instruction to ensure success for all types of learners. The textbook identified for use in this course is: Holt McDougal ALGEBRA 1 by Burger, Chard, Kennedy, Leinwand, Renfro, Roby, and Waits, 2012 ISBN: 978-0-547-64703-6 Various Holt McDougal Algebra 1 workbooks and resources identified for use in this course include: Interactive Answers and Solutions CD-ROM Lesson Tutorial Videos DVD-ROM On Core Mathematics Deluxe Examview Grades 6-12 CD-ROM On Core Mathematics High School Activity Generator CD-ROM Teacher One Stop DVD: Alternate Openers: Exploration with Answers Are You Ready? Intervention and Enrichment with Answers Chapter Resources with Answers Volumes 1 & 2 Classroom Manipulatives KitCollege Entrance Exam Practice for Mathematics I.D.E.A. Works! Modified Worksheets and Tests Lab Activities with Answers Multi-Language Visual Glossary Problem Solving Workbook Teacher s Guide Ready to go ON? Intervention and Enrichment with Answers Solutions Key Technology resources that support the course include: CD-ROMs: Teacher One Stop, Interactive Answers and Solutions Web: Online Resources at (http://my.hrw.com/tabnav/controller.jsp?isbn=9780547708508) Calculator: A scientific calculator with y x function is essential for this course. Additionally, all students are required to use a graphing calculator or emulator. TECHNOLOGY LINKS: Follett Destiny WebPath Express (found on school s automated library system) Tenmarks www.tenmarks.com/ Khan Academy https://www.khanacademy.org/ PhET Simulations http://phet.colorado.edu/en/simulations/category/math ASSESSMENT: A suggested rubric is provided with each unit to help determine if a student has reached A level mastery or B level mastery. B denotes the student has mastered the material 2
and knows it well. The grade of A not only indicates that the student has mastered the material well, but is able to consistently demonstrate higher order thinking and performance skills such as problem solving, analysis, creativity, etc. Suggested Assessment Tools and Strategies: Teacher-created evaluations and/or sections of publisher s text are used to assess mastery of the essential outcomes (TSWs). Mastery intends that the student has mastered the facts and/or concepts to such an extent that they are usable tools in future endeavors. Forms of assessments may include: 1. Teacher Interview; 2. Quizzes, Mid-Chapter Tests, Chapter Tests, Standardized Test Practice; 3. Performance Assessment where hands-on activities help determine how well the skills and concepts have been mastered. Informal assessments give day-to-day, formative feedback. In conjunction with more formal assessments, they give a complete picture of conceptual development. Formal assessment can occur before and after the chapter, as well as at natural breaking points in the chapter. Pretests and Baseline Assessments help to determine prior knowledge. This enables the instructor to determine what skills need to be taught and which may be skipped. Assessment options for all units: Formal Assessment Masters: Chapter Tests (Forms A, B, C) Section Quizzes Cumulative Tests Performance Assessment Standardized Test Prep Exam View Assessment Suite 7.5 An outline of Essential and Selective units is as follows: Essential Units: E01 - Rules and Tools of Algebra This unit is intended as a reinforcement of essential skills necessary for success in Algebra. Algebra, Chapter 1 Sections 1-9. E02 - Inequalities Students solve simple and compound inequalities and work with real number lines to explore solutions. Algebra, Chapter 2 Sections 1-7. E03 - Graphing Linear Functions Students solve linear functions using a variety of mathematical operations. Algebra, Chapter 3 Sections 1-6. 3
E04 - Writing Linear Functions Students identify solutions of linear functions in two variables as ordered number pairs. Algebra, Chapter 4 Sections 1-9. E05 - Linear Systems Students work with linear systems that consist of two or more linear equations or inequalities. Algebra 1, Chapter 5 Sections 1-6 E06 Exponents and Polynomials Students work with rational exponents. Students also move towards more complex ideas involving polynomials performing addition, subtraction, multiplication, and division problems with differing degrees and terms Algebra, Chapter 6 Sections 1-6. E07 - Polynomials and Factoring Students apply the Fundamental Theorem of Arithmetic (that any number greater than one is either prime or the unique product of prime numbers) in order to factorize polynomials. Algebra, Chapter 7 Sections 1-6. E08 - Quadratic Equations Part 1 Students identify quadratic functions and write them in standard form using real numbers. Algebra, Chapter 8 Sections 1-4. E09 - Quadratic Equations Part 2 Students explore additional techniques for solving quadratic functions in this unit include completing the square and the quadratic formula. Algebra, Chapter 8 Sections 5-10. E10 Exponential Growth and Decay Students learn about the connection between geometric sequences and exponential functions. Algebra, Chapter 9 Sections 1-5. The following Selective Units are available for accelerated students: Selective Units: S01 Data Analysis and Probability Students collect, display, and interpret data using various calculations and graphs. Students connect algebra to data analysis and use measures of central tendency to describe variability of data sets. Algebra, Chapter10 Sections 1-7. 4
S02 Algebraic Concepts Students have the opportunity to review the key elements of the ten essential units covered in Algebra. Algebra Course Book Chapters 1-9. S03 Project 1 Students engage in an algebra concept-based project. Teacher and/or student-generated materials specific to the project. S04 Project 2 Students engage in an algebra concept-based project. Teacher and/or student-generated materials specific to the project. S05 Peer Tutoring Students act as mentors to other students of same or younger age. See selective unit appendices. 5