Mathematics

Algebra IA Foundations I, II & III NCAA

1.5 Credits, Grade 9

Essential Question:

How can algebra be used to relate quantities and numbers and utilize concepts and skills to model and solve real world applications?

Placement based on guidelines set by K-12/District Math Committee. Algebra IA Foundations uses an investigative approach in learning algebra. Students will examine interesting questions and hands-on investigations that precede the introduction of formulas and symbolic representations. Students will also spend some time reinforcing the basic skills required to learn Algebra. A graphing calculator and graphing utilities are used to help students learn and understand concepts. Topics in this course include review of basic arithmetic, using proportional reasoning, solving linear equations and linear inequalities, fitting a line to data, working with direct and inverse variation, writing and graphing equations of lines, and solving systems of equations. In the third course students explore data by creating and interpreting measures of center, box and whisker plots, using function notation, finding the domain and range of relations.

Course Competencies:

Algebra IA - I Foundations

  1. Demonstrate an understanding of real numbers and their properties.

  2. Demonstrate an understanding of functions and relations.

Algebra IA - II Foundations

  1. Demonstrate the ability to solve equations and inequalities.

  2. Demonstrate the ability to solve system of equations.

  3. Demonstrate an understanding of direct and inverse functions.

Algebra IA - III Foundations

  1. Demonstrate the ability to write and plot linear equations.

  2. Demonstrate the ability to use rules of exponents and use exponential functions.


Algebra I - I, II & III NCAA

1.5 Credits, Grade 9

Essential Question:

How can algebra be used to relate quantities and numbers and utilize concepts and skills to model and solve real world applications?

Placement based on guidelines set by K-12/District Math Committee. The main goal of Algebra is to develop fluency in working with linear, quadratic, and radical functions. These topics are taught throughout the year and include the following units: solving equations and inequalities, identifying domain and range of relations and functions; solving absolute value equations and inequalities. The main focus of Algebra I-2 will be linear equations and inequalities and their graphs, systems of equations and inequalities, exponent rules, and polynomials. In Algebra I-3 students will work with polynomials, quadratics and their graphs, and radical expressions and equations.

Course Competencies:

Algebra I - I

  1. Demonstrate an understanding of real numbers and their properties.

  2. Demonstrate the ability to solve equations.

  3. Demonstrate the ability to solve inequalities, absolute value inequalities and equations, and work with sets.

Algebra I - II

  1. Demonstrate the ability to write and plot linear equations, solve inequalities, absolute value inequalities and equations, and work with sets.

  2. Demonstrate the ability to solve systems of equations and inequalities.

  3. Demonstrate the ability to understand exponent rules and solve exponential equations.

Algebra I - III

  1. Demonstrate the ability to work with polynomials and polynomial expressions.

  2. Demonstrate the ability to graph quadratic functions and work with quadratic equations.

  3. Demonstrate the ability to simplify radical expressions and solve radical equations.


Algebra I Honors I, II & III NCAA

1.5 Credits, Grade 9

Essential Question:

How can algebra be used to relate quantities and numbers and utilize concepts and skills to model and solve real world applications?

Placement based on guidelines set by K-12/District Math Committee. This course is designed for the student with good mathematical ability. The depth and pacing of this course is at an honors level. The algebraic component for this trimester consists of equation manipulation, solving equations, absolute value, linear equations and inequalities, and graphs. The main focus of Algebra I-2 will be systems of equations and inequalities, linear programming, exponent rules, arithmetic and geometric sequences, polynomials, quadratic and exponential functions and their graphs. In Algebra I-3 students will work with radical functions, rational functions, and graphing data. Students will also be introduced to graphing technology throughout the year.

Course Competencies:

Algebra I Honors - 1

  1. Demonstrate an understanding of real numbers and their properties.

  2. Demonstrate the ability to solve equations and inequalities, absolute value inequalities and equations, and work with sets.

  3. Demonstrate the ability to work with relations and functions. 

Algebra 1 Honors - II

  1. Demonstrate the ability to solve systems of equations and inequalities.

  2. Demonstrate the ability to understand exponents and solve exponential functions.

  3. Demonstrate the ability to use linear programming to solve real world applications.

  4. Demonstrate an understanding of polynomials and the ability to factor polynomials. 

Algebra I Honors - III

  1. Demonstrate the ability to graph and solve quadratics.

  2. Demonstrate the ability to simplify radical expressions and solve radical equations.

  3. Demonstrate and understanding of rational functions and the ability to solve them.


Algebra IB Foundations I & II

1 Credit, Grades 10-11 

Essential Question:

How can algebra be used to relate quantities and numbers and utilize concepts and skills to model and solve real world applications? 

Prerequisite: Algebra IA Foundations. This course is the second half of the two-year Algebra I Foundations course and uses an investigative approach in learning algebra. Students will examine interesting questions and hands-on investigations that precede the introduction of formulas and symbolic representations. Students will also spend some time reinforcing the basic skills required to learn Algebra. A graphing calculator is used to help students learn and understand concepts. Topics include: working with data, probability, and statistics, examining exponential models and where they are seen in the real world, determining the area and volume of geometric figures, examining the transformations of functions, including quadratics, and using right triangle in real world applications. 

Course Expectations:

Algebra IB-1 Foundations

  1. Demonstrate the ability to interpret data and use probability.

  2. Demonstrate the ability to calculate area geometric figures and volume of solids.

  3. Demonstrate the ability to use translations while graphing functions and relations.

Algebra IB-II Foundations

  1. Demonstrate the ability to use translations while graphing functions and relations.

  2. Demonstrate an understanding of properties of quadratics and their real world applications.

  3. Demonstrate the ability to use right triangle trigonometry to solve problems.


Algebra II - I & II NCAA

1 Credit, Grades 10 - 12 

Essential Question:

How can Algebra 2 be used to relate quantities and numbers and utilize concepts and skills to model and solve real world applications? 

Prerequisite: Algebra I and Geometry. This course is designed for the student with good mathematical ability and motivation. The intent of this course is to augment knowledge and methods garnered in Algebra I and Geometry while simultaneously preparing the students for the rigors of more advanced mathematics. Students will explore patterns of relations and functions. Emphasis will be on linear functions, systems of equations and quadratic functions. In addition, students will be asked to communicate their comprehension through multi-representations. The second half of the course will build upon concepts studied previously, including function composition; inverse functions; exponential, logarithmic, and rational functions; and rational exponents. 

Course Competencies:

Algebra II - I

  1. Demonstrate ability to find solutions to systems of equations and inequalities.

  2. Demonstrate understanding of quadratic and parabolic functions.

  3. Demonstrate the ability to graph and identify roots of higher degree polynomial functions.

Algebra II - II

  1. Understand nth roots of real numbers and inverse functions.

  2. Demonstrate the ability to solve and simplify exponential and logarithmic functions.

  3. Demonstrate the ability to solve and graph rational functions.


Algebra II Honors I & II NCAA

1 Credit, Grades 10 - 12 

Essential Question:

How can Algebra 2 be used to relate quantities and numbers and utilize concepts and skills to model and solve real world applications? 

Recommended: Grade of "B-" or better in Geometry Honors; grade of "B-" or better in Algebra I Honors or Algebra II Honors Prep.

This course is designed for the student with exceptional mathematical ability and interest. The intent of this course is to augment knowledge and methods garnered in Algebra I Honors and Geometry while simultaneously preparing the students for the rigors of more advanced mathematics. The course will build upon concepts studied previously. It will explore the relationships of quadratic functions, higher order polynomial functions, exponential functions, logarithmic functions and rational functions. Students will also be introduced to the concepts of conic sections and trigonometry. 

Course Competences:

Algebra II - 1 Honors

  1. Demonstrate understanding of quadratic and parabolic functions.

  2. Demonstrate the ability to determine the graph and roots of polynomial functions.

  3. Understanding nth roots of real numbers and inverse functions. 

Algebra II - 2 Honors

  1. Demonstrate the ability to graph and solve exponential and logarithmic functions.

  2. Demonstrate the ability to graph and solve rational functions.

  3. Demonstrate the ability to identify and graph Conic sections / Basic Unit Circle Trigonometry.


Algebra II H Prep NCAA

1/2 Credit, Grade 9 

Essential Question:

How can algebra be used to relate quantities and numbers and utilize concepts and skills to model and solve real world applications? 

Prerequisite: Geometry Honors.

This course is held during the first trimester and is intended for students who are taking Geometry Honors in the ninth grade or for sophomores who are planning to move from College Prep to Honors. Topics in this course include a quick review of linear equations and their graphs, absolute value functions, systems of equations, quadratics, radical functions, operations with radicals, solving radical equations, graphing radical functions and rational expressions. 

Course Competencies:

  1. Demonstrate the ability to solve equations, inequalities, absolute value equations, absolute value inequalities, and work with linear equations and systems of equations.

  2. Demonstrate the ability to work with exponential and quadratic functions.

  3. Demonstrate the ability to simplify radical expressions, solve radical equations; simplify rational expressions, and solve and graph rational functions.

  4. Demonstrate the ability to determine measures of central tendency, create and interpret graphs related to data, apply counting techniques using permutations and combinations, determine theoretical and experimental probability, and determine probability of compound events.


Geometry Foundations I & II

1 Credit, Grades 11 - 12 

Essential Question:

How would I use my prior mathematical knowledge to explore, examine, analyze, and utilize new geometrical concepts and their applications in my world? 

Prerequisite: Algebra IB Foundations. This course is intended for students that have a basic understanding of algebra. Students will perform geometry investigations that help discover geometric properties. Topics for part 1 and 2 of this course include an introduction to the language of geometry, using inductive and deductive reasoning to develop a logical argument in various forms and solve for missing measures, triangle properties, polygon properties, congruent figures, area and volume, properties of quadrilaterals, the Pythagorean Theorem, and similar triangles, polygons, and probability and data. The algebra component of this course will reinforce algebraic topics taught in Algebra Foundations, including working with radicals, solving multi-step equations, and applications of linear equations. 

Course Competencies:

Geometry I Foundations

  1. Students will be able to use the language of geometry and basic deductive reasoning skills to develop solutions to various real world problems.

  2. Students will be able to use properties of polygons to analyze problems, develop ideas, and create solutions.

  3. Students will be able to use properties of triangles to solve problems and using special segments in triangles, triangle congruence, and the Triangle Inequality Theorem.

  4. Students will be able to use similar figures and the Pythagorean Theorem, Special Right Triangles and Trigonometry to find missing measures. 

Geometry II Foundations

  1. Students will be able to formulate ideas that allow them to solve problems involving properties, surface area and volume of 2 and 3-dimensional objects.

  2. Students will be able to use properties of circles to solve problems involving arcs and angles within circles.

  3. Students will be able to use probability to accurately assess the possible outcomes of real world problems.

  4. Students will be able to use statistical reasoning to analyze data.


Geometry I & II NCAA

1 Credit, Grades 10-12 

Essential Question:

How would I use my prior mathematical knowledge to explore, examine, analyze, and utilize new geometrical concepts and their applications in my world? 

Prerequisite: Algebra I. This course uses a variety of approaches to expose students to the world of geometry. Students will apply prior topics from algebra including solving multi-step equations, working with radicals and using properties of linear equations to solve problems in this course. The focus of Geometry I is to learn how to apply geometric terms along with deductive reasoning to solve problems involving angle and segment measurements and parallel lines. These skills are then combined with knowledge of properties of polygons to solve problems involving various polygons. The focus of these problems is mostly congruent triangles, regular polygons, quadrilaterals, similarity and right triangles. The focus of Geometry II includes similarity and right triangles, area and volume, and properties of circles. Different reasoning strategies will continue to be used to solve application problems involving these topics. 

Course Competencies:

Geometry I

  1. Students will be able to use the language of geometry and basic deductive reasoning skills to develop solutions to various real world problems.

  2. Students will be able to use properties of polygons to analyze problems, develop ideas, and create solutions. 

Geometry II

  1. Students will be able to formulate ideas that allow them to solve problems involving properties, surface area and volume of 2 and 3-dimensional objects.

  2. Students will be able to use properties of circles to solve problems involving arcs and angles within circles.

  3. Students will be able to use probability to accurately assess the possible outcomes of real world problems.

  4. Students will be able to use statistical reasoning to analyze data.


Geometry H I & II NCAA

1 Credit, Grade 10-12 

Essential Question:

How would I use my prior mathematical knowledge to explore, examine, analyze, and utilize new geometrical concepts and their applications in my world? 

Prerequisite: Algebra I-Honors. Ninth grade placement based on guidelines set by K-12/District Math Committee. This course is designed for the student with exceptional mathematical ability and interest. The scope of this course builds on the topics introduced in Algebra I including linear and quadratic equations, functions, and systems of linear equations. The focus of Geometry I is to learn how to apply geometric terms along with deductive reasoning to solve problems involving angle and segment measurements and parallel lines. These skills are then combined with knowledge of properties of polygons to solve in depth problems and answer questions involving various polygons. The focus of these problems and questions is mostly congruent triangles, regular polygons, quadrilaterals, similarity and right triangles. The focus of Geometry II includes area and volume, properties of circles and probability and data analysis. Different reasoning strategies will continue to be used to solve in depth application problems involving these topics. 

Course Competencies:

Geometry I Honors

  1. Students will be able to use the language of geometry and basic deductive reasoning skills to develop solutions to various real world problems.

  2. Students will be able to use properties of polygons to analyze problems, develop ideas, and create solutions.

  3. Students will understand and be able to apply properties of right triangles to solve problems using trigonometry, Pythagorean Theorem and special right triangles. 

Geometry II Honors

  1. Students will be able to formulate ideas that allow them to solve problems involving surface area and volume of 3-dimensional objects.

  2. Students will be able to use properties of circles to solve problems involving arcs and angles within circles.

  3. Students will be able to use probability to accurately assess the possible outcomes of real world problems.

  4. Students will be able to use statistical reasoning to analyze data.


Pre-Calculus I: Advanced Math NCAA

1/2 Credit, Grades 11 - 12 

Essential Question:

How can Advanced Math/Pre-Calculus be used to explore and analyze various types of functions and the role they play in building an understanding for the foundations of Calculus? 

Prerequisite: Algebra II (C or Better). The purpose of this class is to prepare students for introductory post-secondary mathematics programs. Many of these mathematical ideas will be put to practical use in the applied sciences, the natural sciences, and the social sciences. Topics to be studied include: higher order polynomials, rational functions and inequalities, exponential and logarithmic functions, conic sections, systems of equations, and matrices. 

Course Competencies:

  1. Students will demonstrate an understanding of properties of functions and their inverses.

  2. Students will demonstrate and understanding of graphing, solving and properties (including notation) of the polynomial systems and rational functions.

  3. Students will demonstrate their understanding of exponential and logarithmic functions, transformations, and solving expressions with exponential and logarithmic components.

  4. Students will demonstrate their understanding of conic sections, systems of equations, and matrices.


Senior Math

1/2 Credit, Grade 12 

Essential Question:

How can algebra be used to relate quantities and numbers and utilize concepts and skills to model and solve real world applications? 

Prerequisite: Algebra IB (B or Better) or Algebra II or permission of instructor. This is a survey course, focusing primarily on the algebra skills needed to enter the workforce or community colleges. Students will develop facility in simplifying and evaluating polynomial and rational expressions, as well as solve linear equations and inequalities, quadratic equations, and systems of linear equations. Emphasis will be placed on applying these skills in solving real world problems. 

Course Competencies:

  1. The student will demonstrate the ability to simplify expressions and solve equations.

  2. The student will demonstrate the ability to graph linear equations and inequalities and find solutions for systems of equations and inequalities.

  3. The student will demonstrate the ability to use exponent rule and simplify and factor polynomials.

  4. The student will demonstrate the ability to simplify radicals and solve quadratic equations. 


Statistics NCAA Running Start

1/2 Credit, Grade 12 

Essential Question:

How can statistics be used to explore mathematical concepts, analyze and understand data, and solve real world problems? 

Prerequisite: Algebra II (C or better). This course is an application-based course in which statistical analysis of experiments will be explored. Data will be collected, analyzed and projections of future occurrences will be predicted. This trimester course will focus on categorical and quantitative data, descriptive statistics, probability, random variables, probability models, confidence intervals, hypothesis testing, correlation and linear regression. This course can be taken for Running Start Credit. 

Course Competencies:

  1. Students will collect, categorize and make inferences from data using appropriate statistical analysis methods.

  2.  Students will calculate probabilities using probability rules, sample spaces, and Venn Diagrams.

  3. Students will demonstrate an understanding of random variables and probability models.

  4. Students will demonstrate an understanding of confidence intervals, hypothesis testing, and relationships between variables. 


Pre-Calculus II: Trigonometry NCAA

1/2 Credit, Grades 11 - 12
 

Essential Question:

How can Pre-Calculus:Trigonometry be used to explore and analyze various types of functions and the role they play in building an understanding for the foundations of Calculus? 

Prerequisite:Pre-Calculus I: Advanced Math. The purpose of this class is to prepare students for introductory post-secondary mathematics programs, including Calculus. Topics to be studied include: the unit circle, triangle trigonometry, trigonometric equations, graphing trigonometric functions and trigonometric applications. 

Course Competencies: 

Pre-Calculus II: Trigonometry

  1. Students will demonstrate their understanding of angles and radian measure, trigonometric ratios, functions, right triangle trigonometric applications, and oblique triangle applications.

  1. Students will demonstrate their understanding of graphing trigonometric functions and polar coordinates.

  2. Students will demonstrate their understanding of verifying trigonometric identities including sum and difference, double-angle, half-angle, product-to-sum and sum-to-product formulas as well as solve trigonometric equations. 


Quantitative Reasoning Running Start

1/2 Credit, Grade 12 

Essential Question:

How can algebra and geometry be used to relate quantities and numbers and utilize concepts and skills to model and solve real world applications? 

Running Start Course 4 college credits

Prerequisite: Senior Math (C or better), Algebra II (with permission of instructor)

This course is designed to expose the student to a wide range of general mathematics. Problem- solving and critical thinking skills, along with the use of technology, will be emphasized and reinforced throughout the course as the student becomes actively involved solving applied problems. Topics to be covered include: Number Theory and Systems, Functions and Modeling, Finance, Geometry and Measurement, Probability and Statistics, and selected subtopics related to the student's major field of study. 

Course Competencies:

  1. The student will demonstrate the use of number theory and number systems to solve real-world problems.

  2. The student will demonstrate the ability to use mathematical modeling to interpret data.

  3. The student will demonstrate the ability to use geometry and measurement to solve real-world problems.

  4. The student will demonstrate the ability to interpret data through statistics and probability. 


AP Calculus I, II & III NCAA

1.5 Credits, Grade 12 

Essential Question:

How would I use my prior mathematical knowledge to explore, examine, and analyze the change that occurs in quantities involved in various real world applications? 

Recommended: Grade of "A-" or better in Pre-Calculus Honors or by Mathematics Department approval. The course covers the standard topics of elementary calculus: limits; continuity; derivatives of functions and their applications to graphing; finding extreme values, and relating rates; and integrals and their applications to determining areas, volumes, and length of curves. Related topics include indefinite integrals, techniques of integration, numerical approximations. This course will prepare the student for the Advanced Placement Calculus Exam in Mathematics to be taken in the spring. 

Course Competencies:

AP Calculus I

  1. Students will demonstrate their understanding that the meaning of limits includes the difference quotient, bounded and unbounded behavior, the connection of limits to continuity, limits involving infinity, and continuity of functions and relation to limits.

  1. Students will demonstrate their understanding that derivatives can be represented in terms of rate of change, slopes of tangent lines, and local linear approximations.

  1. Students will demonstrate their understanding of the definition of the derivative by applying the rules of differentiation--fundamental, product, quotient, chain, implicit, and trigonometric differentiation.

AP Calculus II

  1. Students will demonstrate their understanding of the the definition of the derivative by applying the rules of differentiation--inverse trigonometric functions, exponential and logarithmic functions.

  2. Students will demonstrate their understanding by applying the derivative to: related rates, local or relative extrema, absolute extrema, first and second derivative tests and concavity, and applications of the above.

  3. Students will demonstrate their understanding that the definite integral is a limit of Riemann Sums and the net accumulation of change. Students will compare and contrast Riemann Sums, Trapezoidal Rule, and Simpson's Rule.

AP Calculus III

  1. Students will demonstrate their understanding that the relationship between derivatives and the definite integral as expressed in the Fundamental Theorem of Calculus.

  1. Students will demonstrate their understanding of the antiderivative and slope fields derived from differential equations. Students will demonstrate their understanding area in a plane and volume plus the length of curves.

  1. Students will demonstrate their understanding of both the derivative and integral by constructing dynamic models that represents a concept in both field which will support their mathematic within 2 percent of their experiment. The students will present their findings and run the experiments to an audience of students that will take AP Calculus next year.

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