Mathematics
Information on WHS Math Sequences and Pathways
| F/S = Semester Course | (+) = Honors Point | (*) = Possible Course |
Math Foundations
Term: Yearlong
This course is designed to support students through Math I. The course is intended to be concurrently enrolled with Math I by reviewing and supplementing critical Math I standards.
Skills and Assessment: Students will be able to…
- Make sense of problems and persevere in solving them – in individual work as well as collaborative work.
- Connect concepts to the real world by modeling with mathematics.
- Show that they can reason abstractly and quantitatively by explaining and justifying the processes they use in solving problems.
- Communicate mathematical understanding and problem solving through the use of multiple representations such as diagrams, models, tables, graphs and symbols.
- Develop and extend strategies to transition from knowledge of concepts and skills to theoretical reasoning and application of concepts.
- Demonstrate mastery of concepts and skills through various assessments in the form of homework, quizzes and tests.
- Use appropriate technology to enhance learning and understanding.
Prerequisite: Teacher or counselor recommendation.
Math Lab
Term: Yearlong
This course is designed to support students through Math II and Math III. The course is intended to be concurrently enrolled with Math II and Math III by reviewing and supplementing critical Math II and Math III standards.
Skills and Assessment: Students will be able to…
- Make sense of problems and persevere in solving them – in individual work as well as collaborative work.
- Connect concepts to the real world by modeling with mathematics.
- Show that they can reason abstractly and quantitatively by explaining and justifying the processes they use in solving problems.
- Communicate mathematical understanding and problem solving through the use of multiple representations such as diagrams, models, tables, graphs and symbols.
- Develop and extend strategies to transition from knowledge of concepts and skills to theoretical reasoning and application of concepts.
- Demonstrate mastery of concepts and skills through various assessments in the form of homework, quizzes and tests.
- Use appropriate technology to enhance learning and understanding.
Prerequisite: Teacher or counselor recommendation.
Math I
Term: Yearlong | Level: College Preparatory (CP) | UC/CSU "c" requirement
Math 1 is the first course in the college preparatory math sequence. It is a study of real numbers and their properties; linear, quadratic and exponential functions; equations and expressions; statistics and probability. This course is aligned with the Common Core state standards. Passing this course is a requirement for graduation.
Skills and Assessment: Students will be able to…
- Make sense of problems and persevere in solving them – in individual work as well as collaborative work.
- Connect concepts to the real world by modeling with mathematics.
- Show that they can reason abstractly and quantitatively by explaining and justifying the processes they use in solving problems.
- Communicate mathematical understanding and problem solving through the use of multiple representations such as diagrams, models, tables, graphs and symbols.
- Develop and extend strategies to transition from knowledge of concepts and skills to theoretical reasoning and application of concepts.
- Demonstrate mastery of concepts and skills through various assessments in the form of homework, quizzes and tests.
- Use appropriate technology to enhance learning and understanding.
Prerequisite: Teacher or counselor recommendation.
MATH II
Term: Yearlong | Level: College Preparatory (CP) | UC/CSU "c" requirement
Math II is the second course in the college preparatory math sequence. Instructional time will focus on five critical areas: extending the laws of exponents to rational exponents; comparing key features of quadratic functions with those of linear and exponential functions; creating and solving equations and inequalities involving linear, exponential, and quadratic expressions, including those with complex solutions; extending work with probability; and establishing criteria for similarity. This course is aligned with the Common Core State Standards.
Skills and Assessment: Students will be able to…
- Connect concepts to the real world using mathematical modeling.
- Reason quantitatively and use units to solve problems.
- Explain and justify the processes they use in solving problems.
- Communicate mathematical understanding and problem solving through the use of multiple representations such as diagrams, models, tables, graphs, and symbols.
- Develop and extend strategies to transition from knowledge of concepts and skills to theoretical reasoning and application of concepts.
- Demonstrate mastery of concepts and skills through various assessments in the form of homework, quizzes, tests, and performance tasks.
- Use appropriate technology to enhance learning and understanding.
Prerequisite: Grade of C or higher in Math I and teacher recommendation.
ENHANCED MATH II
Term: Yearlong | Level: College Preparatory (CP) | UC/CSU "c" requirement
Enhanced Math II is the first course in the rigorous accelerated sequence of high school math courses. Instructional time will focus on five critical areas: extending the laws of exponents to rational exponents; comparing key features of quadratic functions with those linear and exponential functions; creating and solving equations and inequalities involving linear, exponential, and quadratic expressions, including those with complex solutions; extending work with probability and statistics; and establishing criteria for similarity. In addition, students will deepen and extend their understanding in each of these areas, through study of advanced related topics and application to more complex problem solving situations, in order to prepare students for advanced mathematics at an accelerated pace. This course is aligned with the Common Core State Standards.
Skills and Assessment: Students will be able to…
- Connect concepts to the real world using mathematical modeling.
- Reason quantitatively and use units to solve problems.
- Explain and justify the processes they use in solving problems.
- Communicate mathematical understanding and problem solving through the use of multiple representations such as diagrams, models, tables, graphs, and symbols.
- Develop and extend strategies to transition from knowledge of concepts and skills to theoretical reasoning and application of concepts.
- Demonstrate mastery of concepts and skills through various assessments in the form of homework, quizzes, tests, and performance tasks.
- Use appropriate technology to enhance learning and understanding.
Prerequisite: Placement criteria (must meet 2 of 3): grades of A in all marking periods of prerequisite courses (8th grade Enhanced Math I or 9th grade Math I); 85% or higher on an end of course exam (Enhanced Math I/Math I); teacher appraisal.
MATH III
Term: Yearlong | Level: College Preparatory (CP) | UC/CSU "c" requirement
Math III is the third course in the college preparatory math sequence. Instructional time will focus on four critical areas: applying methods from probability and statistics to draw inferences and conclusions from data; expanding understanding of functions to include polynomial, rational, and radical functions; expanding right triangle trigonometry to include general triangles and trigonometric functions; and consolidate functions and geometry to create models and solve contextual problems. This course is aligned with the California Common Core State Standards.
Skills and Assessment: Students will be able to…
- Connect concepts to the real world using mathematical modeling.
- Reason quantitatively and use units to solve problems.
- Explain and justify the processes they use in solving problems.
- Communicate mathematical understanding and problem solving through the use of multiple representations such as diagrams, models, tables, graphs and symbols.
- Develop and extend strategies to transition from knowledge of concepts and skills to theoretical reasoning and application of concepts.
- Demonstrate mastery of concepts and skills through various assessments in the form of homework, quizzes, tests, and performance tasks.
- Use appropriate technology to enhance learning and understanding.
Prerequisite: Grade of “C” or higher in Math II and teacher appraisal.
ENHANCED MATH III
Term: Yearlong | Level: College Preparatory (CP) + | UC/CSU "c" requirement
Enhanced Math III is the second course in the rigorous accelerated sequence of high school math courses. Instructional time will focus on five critical areas: expanding understanding of functions to include polynomial, rational, and radical functions; extending their work with complex numbers; extending trigonometry to general triangles, trigonometric functions, reciprocal functions, and inverse functions; working with parametric and polar curves; and consolidating functions and geometry to create models and solve contextual problems. In addition, students will deepen and extend their understanding in each of these areas through study of advanced related topics and application to more complex problem solving situations, in order to prepare students for advanced mathematics at an accelerated pace. This course is aligned with the California Common Core State Standards.
Skills and Assessment: Students will be able to…
- Connect concepts to the real world using mathematical modeling.
- Reason quantitatively and use units to solve problems.
- Explain and justify the processes they use in solving problems.
- Communicate mathematical understanding and problem solving through the use of multiple representations such as diagrams, models, tables, graphs and symbols.
- Develop and extend strategies to transition from knowledge of concepts and skills to theoretical reasoning and application of concepts.
- Demonstrate mastery of concepts and skills through various assessments in the form of homework, quizzes, tests, and performance tasks.
- Use appropriate technology to enhance learning and understanding.
Prerequisite: Placement criteria (must meet two of three): grades of B or better in all marking periods of prerequisite course (Enhanced Math II or HS Summer Bridge); 85% or better on End of Course Assessment for Enhanced Math II; teacher appraisal of work habits and mathematical practices.
FUNCTIONS, STATISTICS, AND TRIGONOMETRY
Term: Yearlong | Level: College Preparatory (CP) | UC/CSU "c" requirement
This course is a college-preparatory mathematics elective. It is designed to follow Math III with extended mathematical concepts that enhance critical thinking skills. This course satisfies the California State Content Standards for Trigonometry and Math Analysis. The course focuses on the development of reasoning and problem solving skills. Topics that students will study include trigonometric functions using the concepts of circular functions, logarithmic functions, series and sequences, probability and statistics, and function transformations.
Skills and Assessment: Students will be able to…
- Communicate mathematical understanding and problem solving through the use of multiple representations, written and verbal explanations
- Investigate connections and relationships with appropriate use of technology
- Develop proficiency by analyzing characteristics of models, graphs and properties of function families - linear, polynomial, rational, exponential, logarithmic and trigonometric
- Extending understanding of statistics: graphical representations of data, normal approximation, binomial probabilities
- Investigating transformation of graphs
- Exploring trigonometric functions, identities, graphs and applications
- Analyze sequences and series
- Progress as Complex thinkers by strengthening their ability to investigate, analyze, interpret, and apply information to formulate conclusions and solve problems
- Progress as effective communicators by fostering understanding and forging connections with applications beyond the classroom.
Prerequisite: Successful completion of Math III
R.O.P. ACCOUNTING
Grade Level: 11-12 | Term: Yearlong | Level: High School Credit
Accounting is an ROP course, embedded in the Woodbridge High School bell schedule, which grants math credits toward graduation. The Accounting course introduces students to basic accounting principles and practices along with general business concepts. This study is based on the objectives outlined in the California Career Technical Education Standards. The course focuses on the complete eight-step accounting cycle, the use of financial reports for ethical decision making, cash management and payroll functions as well as personal finance topics such as banking, credit and career planning. This course is part of the business and finance industry sector.
Skills and Assessment: Students will be able to…
- Demonstrate proficiency in the creation of General Journal entries, General Ledger postings, Worksheets, Balance Sheets, Income Statements, and period-closing entries and reports.
- Practice and be proficient applying basic math skills (addition, subtraction, multiplication, division) and concepts (percentages, fractions) to accounting and personal finance topics.
- Be able to use technology (calculators, online working papers, internet searches) to facilitate their completion of accounting problems and projects.
- Gain life and career-readiness skills by using computerized accounting simulation software, and participating in personal finance simulation activities and mock job skills/interview exercises.
- Demonstrate proficiency via class work/homework, online problem sets, concept quizzes, unit tests, final exams and tasks and projects.
Prerequisite: Open to 11th and 12th grade students.
PRE-CALCULUS
Term: Yearlong | Level: College Preparatory (CP) | UC/CSU "c" requirement
This course is intended to prepare students for Calculus and other higher level mathematics. In this course students will use and expand their knowledge and understanding of topics learned in Math 3, such as real and complex numbers, functions, equations and expressions, modeling polynomial and rational functions, exponential and logarithmic functions, and analytic geometry. In addition, students will study trigonometric functions, vector theory, and sequences & series. Students may take AP Statistics concurrently with this course.
Skills and Assessment: Students will be able to…
- Make sense of problems and persevere in solving them – in individual work as well as collaborative work.
- Connect concepts to the real world by modeling with mathematics.
- Show that they can reason abstractly and quantitatively by explaining and justifying the processes they use in solving problems.
- Communicate mathematical understanding and problem solving through the use of multiple representations such as diagrams, models, tables, graphs and symbols.
- Develop and extend strategies to transition from knowledge of concepts and skills to theoretical reasoning and application of concepts.
- Demonstrate mastery of concepts and skills through various assessments in the form of homework, quizzes and tests.Use appropriate technology to enhance learning and understanding.
- Use appropriate technology to enhance learning and understanding.
Prerequisite: Grades of B or better in all marking periods of Math III.
HONORS PRE-CALCULUS
Term: Yearlong | Level: College Preparatory (CP) + | UC/CSU "c" requirement
This course is intended to prepare students for AP calculus BC and other higher level mathematics. In this course students will use and expand their knowledge and understanding of topics learned in honors Algebra 2, such as real and complex numbers, functions, equations and expressions, modeling polynomial and rational functions, exponential and logarithmic functions, analytic geometry, and sequences & series. In addition, students will study trigonometric topics. These topics include graphing and solving equations involving trigonometric, inverse trigonometric functions; trigonometric identities and their proofs; mathematical induction; basic vector theory and polar coordinates; and an analytic treatment of the conic sections.
Skills and Assessment: Students will be able to…
- Communicate mathematical understanding and problem solving through the use of multiple representations such as diagrams, models, tables, graphs and symbols.
- Apply verbal, analytical, graphical, and numerical approaches to problem solving in authentic settings.
- Make sense of problems and persevere in solving them – in individual work as well as collaborative work.
- Connect concepts to the real world by modeling with mathematics.
- Show that they can reason abstractly and quantitatively by explaining and justifying the processes they use in solving problems.
- Use appropriate technology to enhance learning and understanding.
Prerequisite: Must meet 2 of 3: grades of A or better in all marking periods of Math III; 85% or better on end of course assessment; teacher appraisal.
A.P. CALCULUS AB
Term: Yearlong | Level: Advanced Placement (AP) + | UC/CSU "c" requirement
In this college-level course, students will study major topics of mathematics outlined by College Board including: limits and continuity, derivatives, integrals, differential equations, and applications. The A.P. exam for this course requires students to use a graphing calculator, the calculator suggested for use is the TI-84+. This course qualifies for the extra honors grade point credit.
Skills and Assessment: Students will be able to…
- Make sense of problems and persevere in solving them – in individual work as well as collaborative work.
- Connect concepts to the real world by modeling with mathematics.
- Show that they can reason abstractly and quantitatively by explaining and justifying the processes they use in solving problems.
- Communicate mathematical understanding and problem solving through the use of multiple representations such as diagrams, models, tables, graphs and symbols.
- Develop and extend strategies to transition from knowledge of concepts and skills to theoretical reasoning and application of concepts.
- Demonstrate mastery of concepts and skills through various assessments in the form of homework, quizzes and tests.Use appropriate technology to enhance learning and understanding.
- Use appropriate technology to enhance learning and understanding.
Prerequisite: Must meet 2 of 3: grades of C or better in all marking periods of Enhanced Math III; 80% or better on end of course assessment; teacher appraisal. OR grades of C or better in all marking periods of Pre-Calculus.
A.P. CALCULUS BC
Term: Yearlong | Level: Advanced Placement (AP) + | UC/CSU "c" requirement
In this college-level course, students will study major topics of mathematics outlined by College Board including: limits and continuity, derivatives, integrals, differential equations, Taylor series, parametric/polar/vector functions, and applications. The A.P. exam for this course requires students to use a graphing calculator, the calculator suggested for use is the TI-84+. This course qualifies for the extra honors grade point credit.
Skills and Assessment: Students will be able to…
- Make sense of problems and persevere in solving them – in individual work as well as collaborative work.
- Connect concepts to the real world by modeling with mathematics.
- Show that they can reason abstractly and quantitatively by explaining and justifying the processes they use in solving problems.
- Communicate mathematical understanding and problem solving through the use of multiple representations such as diagrams, models, tables, graphs and symbols.
- Develop and extend strategies to transition from knowledge of concepts and skills to theoretical reasoning and application of concepts.
- Demonstrate mastery of concepts and skills through various assessments in the form of homework, quizzes and tests.Use appropriate technology to enhance learning and understanding.
- Use appropriate technology to enhance learning and understanding.
Prerequisite: Must meet 2 of 3: grades of B or better in all marking periods of Enhanced Math III; 80% or better on end of course assessment; teacher appraisal. OR grades of A in all marking periods of Pre-Calculus.
A.P. STATISTICS
Term: Yearlong | Level: Advanced Placement (AP) + | UC/CSU "c" requirement
In this college-level course, students will study major topics of mathematics outlined by College Board. The purpose of the AP course in statistics is to introduce students to the major concepts and tools for collecting, analyzing and drawing conclusions from data. Students are exposed to four broad conceptual themes: 1. Exploring Data: Describing patterns and departures from patterns; 2. Sampling and Experimentation: Planning and conducting a study; 3. Anticipating Patterns: Exploring random phenomena using probability and simulation; 4. Statistical Inference: Estimating population parameters and testing hypotheses.
The A.P. exam for this course requires students to use a graphing calculator, the calculator suggested for use is the TI-84+. This course qualifies for the extra honors grade point credit.
Skills and Assessment: Students will be able to…
- Engage in real world problem solving through analyzing the statistics of actual data from complex problems in or society.
- Clearly articulate the meaning of their solutions in ways that would be understandable to those who are not well versed in statistics.
- Use technology (mainly graphing calculators and computers) to help break down larger data sets into manageable and understandable summary statistics.
- We will test after every chapter and have two summative tests. One at the end of the first semester and one before the actual AP test. This second test is cumulative for the entire year’s worth of information.
Prerequisite: Grade of B or higher in Math III or a grade of C or better in Enhanced Math III, Pre-Calculus, or any class higher than these. Student must also have the ability and desire to complete short, meaningful assignments every night. Good, clear communication skills are a major asset.
COLLEGE MATH PREP (FALL)
Term: Yearlong | Level: Irvine Valley College (IVC)
Math 353 (Fall Semester) is a college-level course designed for students who desire would like to get an early start on their post high school mathematics. This course is similar to Math I and Math II. There will be a variety of topics covered in the class with an emphasis on beginning algebra skills. From the Irvine Valley College catalog:
“This is the first course in algebra. The course introduces signed numbers, equations and inequalities, graphs, linear equations, functions, and polynomials. Students perform arithmetic operations with a real numbers and algebraic expressions; graph and solve linear equations and inequalities; and perform algebraic operations with polynomials, rational expressions, and equations.”
Prerequisite: Successful completion of Math I.
COLLEGE MATH PREP (SPRING)
Term: Yearlong | Level: Irvine Valley College (IVC)
Math 253 (Spring Semester) This course is the continuation of elementary algebra and is intended to prepare students for subsequent math classes. This course is similar to Math II and Math III. From the Irvine Valley College catalog:
“This course includes the study of the real number system, open sentences in one variable, polynomials, factoring, systems of linear equations, rational numbers, and functions. The course also covers irrational and complex numbers, quadratic equations and functions, exponential and logarithmic functions, and quadratic relations and systems.”
***The approach to Math 353/253 is through the mymathlab.com computer program. Students are expected to work to the best of their ability in completing problems online during class time. Not all work will be able to be completed during class time so homework must be done on your own time (outside of class) to be successful. Calculator use is encouraged and any scientific calculator, such as the TI-34IIX is highly recommended. The rigor of the class is not to be underestimated, yet it is designed to be an enjoyable experience.
Prerequisite: Successful completion of Math I.
Practical MATH IAB
Term: Yearlong | Level: Directed/Not College Preparatory
Pratical Mathematics 1AB is a special education class, consisting of specialized academic instruction designed to meet the California State Framework and Irvine Unified School District Guidelines for graduation. The course is focused on developing both the procedural skills and conceptual understanding leading to the application of mathematical concepts. Course topics include solving equations for a variable, modeling quantities for equations, inequalities, and compound inequalities, graphing relationships, functions, and lines, using arithmetic sequences, linear functions, statistics and data modeling, solving and modeling linear systems. Enrollment in this class is based on a student’s IEP team decision that this class is appropriate. The curricular focus is based on the student’s individual needs (accommodations/modifications and identified goals) agreed to by the IEP team.
Prerequisite: Placement based on consultation with the student’s IEP team.
Practical MATH ICD
Term: Yearlong | Level: Directed/Not College Preparatory
Directed Mathematics 1CD is a special education class, consisting of specialized academic instruction, focused on developing both the procedural skills and conceptual understanding leading to the application of mathematical concepts. Course topics include linear and exponential functions, solving equations, expressions, inequalities, graphing, sequences, Statistics, transformations, and Systems. Students develop mathematical understanding and connect Algebra to the world we live in through real-life applications. Enrollment in this class is based on a student’s IEP team decision that this class is appropriate. The curricular focus is based on the student’s individual needs (accommodations/modifications and identified goals) agreed to by the IEP team.
Prerequisite: Placement based on consultation with the student’s IEP team. Successful completion of Directed Math I AB.