*Updated: 12.2020*

Student placement in math courses will be based on teacher recommendations for individual students by way of the FRHS Registration Card. Parents/students that disagree with course placement recommendation(s) must follow the following steps:

**Math Placement Guidelines**Student placement in math courses will be based on teacher recommendations for individual students by way of the FRHS Registration Card. Parents/students that disagree with course placement recommendation(s) must follow the following steps:

*Parent/Student MUST contact the recommending Teacher FIRST regarding concerns**Teacher will help parent/student understand criteria for recommendations.**If an alternative placement selection is made, a waiver will be signed by parent and student to confirm the course decision was made outside of teacher recommendations.*

__6125 Pre-Algebra (Ramp-up to Algebra)__Credits: 10 (completed in a single semester)

Prerequisites: None

Meets requirement(s): Mathematics, Elective

Open to Grades: 9 (teacher recommendation only)

Pre-Algebra is a course designed to offer students the ability to be Algebra 1 ready by mastering middle school standards that are necessary to understand the Algebra 1 material.

**At FRHS:**

*Ramp-up to Algebra is a year-long mathematics course, designed to solidify a student’s understanding of arithmetic and to provide a foundation for the key concepts taught in Algebra I. Ramp-up to Algebra takes place daily according to a double-block period and uses a flexible Extended Workshop format to provide students with a higher level of concentration on the mathematics. The double-block format allows students to examine the concepts in greater depth, and have time to share, discuss, and explore strategies and solutions. Upon successful completion, students will progress to Algebra 1 through teacher recommendation.*

__6230 Algebra I__Credits: 10

Prerequisites: None

Meets requirement(s): Mathematics

Open to Grades: 9, 10, 11 & 12

The fundamental purpose of this course is to formalize and extend the mathematics that students learned in the middle grade. Because it is building on the middle grades standards, this is a more ambitious version of Algebra I than has generally been offered. The critical areas, called units, deepen and extend understanding of linear and exponential relationships by contrasting them with each other and by applying linear models to data that exhibit a linear trend, and students engage in methods for analyzing, solving, and using quadratic functions. The Mathematical Practice Standards apply throughout each course and, together with the content standards.

**Upon successful completion, students will progress to Geometry through teacher recommendation.**

__6240 Geometry__Credits: 10

Prerequisites: Successful completion of Algebra I

Meets requirement(s): Mathematics

Open to Grades: 9, 10, 11 & 12

The fundamental purpose of the course in Geometry is to formalize and extend students' geometric experiences from the middle grades. Students explore more complex geometric situations and deepen their explanations of geometric relationships, moving towards formal mathematical arguments. Important differences exist between this Geometry course and the historical approach taken in Geometry classes. For example, transformations are emphasized early in this course. Close attention should be paid to the introductory content for the Geometry conceptual category found in the high school CCSS. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations. The critical areas, organized into six units are as follows: Congruence, Proof, and Constructions; Similarity, Proof and Trigonometry; Connecting Algebra and Geometry through Coordinates; Circles With and Without Coordinates; Extending to Three Dimensions; Applications or Probability.

**Upon successful completion, students will progress to Algebra 2 through teacher recommendation.**

__6226 Algebraic Concepts__Credits: 5 (2nd semester only)

Prerequisites: Successful completion of Geometry and Algebra 1

Meets requirement(s): Mathematics

Open to Grades: 9, 10, 11 & 12

This course is designed as an introductory algebra course. Topics taught might include, but not be limited to signed numbers, writing and solving simple algebraic equations, learning algebraic terminology and application of algebraic concepts.

**At FRHS:**

*T**his course will help students needing extra support between Algebra 1 and Algebra 2.*

__6250 Algebra 2__Credits: 10

Prerequisites: Successful completion of Geometry

Meets requirement(s): Mathematics

Open to Grades: 9, 10, 11 & 12

Building on their work with linear, quadratic, and exponential functions, students extend their repertoire of functions to include polynomial, rational, and radical functions. Students work closely with the expressions that define the functions, and continue to expand and hone their abilities to model situations and to solve equations, including solving quadratic equations over the set of complex numbers and solving exponential equations using the properties of logarithms. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations. The critical areas for this course, organized into four units are as follows: Inferences and Conclusions from Data; Polynomial, Rational, and Radical Relationships; Trigonometric Functions; Modeling with Functions.

**Upon successful completion, students can progress to either College Algebra**

**, Pre-Calculus, or AP Statistics through teacher recommendation.**

__6275 College Algebra__

__6275CEFR College Algebra__**(may be taken for concurrent enrollment credit through FRCC)**

Credits: 10

Prerequisite: Successful completion of Algebra II

Meets requirement(s): Mathematics

Open to Grades: 9, 10, 11 & 12

College Algebra is designed to allow deeper analysis and extension of advanced algebra topics. College Algebra is the first half of a post-Algebra II class that begins to bridge students to Calculus topics. Students are encouraged to represent problems algebraically, pictorially, verbally, and graphically. Critical thinking problems are provided to stretch their reasoning and communication skills. College Algebra extends learning in simplifying expressions and solving equations; solving systems of equations and optimization problems; and modeling with functions (polynomial, rational, exponential, and logarithmic).

**Upon successful completion, students will progress to College Trigonometry & Analytic Geometry.**

**College Algebra may be taken for concurrent enrollment credit through FRCC.**

__6276 College Trigonometry & Analytic Geometry__

__6276CEFR College Trigonometry & Analytic Geometry__**(may be taken for concurrent enrollment credit through FRCC)**

Credits: 10

Prerequisites: Successful completion of College Algebra

Meets requirement(s): Mathematics

Open to Grades: 9, 10, 11 & 12

College Trigonometry & Analytic Geometry is the second half of a post-Algebra 2 class to bridge students to Calculus topics. Students are encouraged to represent problems algebraically, pictorially, verbally and graphically. Critical thinking problems are provided to stretch their reasoning and communication skills. College Trigonometry & Analytic Geometry explores numerical and analytical trigonometry; application of trigonometric functions; vectors; polar coordinates; analytic geometry; sequences and series; and mathematical induction. Upon successful completion, students may progress to Calculus through teacher recommendation

**. Upon successful completion, students can progress to Calculus I through teacher recommendation. College Trigonometry and Analytic Geometry**

**may be taken for concurrent enrollment credit through FRCC.**

__6280 Pre-Calculus__

__6280CEFR Pre-Calculus__**(may be taken for concurrent enrollment credit through FRCC)**

Credits: 10

Prerequisites: Successful completion of Algebra II

Meets requirement(s): Mathematics

Open to Grades: 9, 10, 11 & 12

Pre-Calculus is the post-Algebra 2 class to bridge students to Calculus topics. Students are encouraged to represent problems algebraically, pictorially, verbally, and graphically. Critical thinking problems are provided to stretch their reasoning and communication skills. Pre-Calculus explores advanced algebra topics such as polynomial, rational, exponential, and logarithmic functions; numerical and analytical trigonometry; vectors; polar coordinates; analytic geometry; sequences and series; and mathematical induction. Upon successful completion, students may progress to Calculus through teacher recommendation.

**Upon successful completion, students can progress to Calculus I through teacher recommendation.**

**Pre-Calculus**

**may be taken for concurrent enrollment credit through FRCC.**

__6290 AP Calculus AB__

__6290CECU AP Calculus Ab (Calculus I)__(may be taken for concurrent enrollment credit through CU Denver)Credits: 10

Prerequisites: Pre-Calculus or College Trigonometry and Analytic Geometry

Meets requirement(s): Mathematics

Open to Grades: 9, 10, 11 & 12

Calculus is a study of all topics traditionally offered in a college Calculus I course. Topics covered are limits derivatives of algebraic functions applications of the derivatives applications of the definite integral transcendental functions and methods of integration. This course will help prepare the student to take the AP-BC Calculus test.

**AP Calculus AB may be taken for concurrent enrollment credit through C.U. Denver.**

__6291 AP Calculus BC__

__6291CECU AP Calculus Bc (Calculus II)__(may be taken for concurrent enrollment credit through CU Denver)Credits: 10

Prerequisites: AP Calculus AB

Meets requirement(s): Mathematics

Open to Grades: 9, 10, 11 & 12

Calculus is a study of all topics traditionally offered in a freshman college calculus course. Topics covered are limits, derivatives of algebraic functions, applications of the derivatives, applications of the definite integral transcendental functions and methods of integration in function, parametric vector and polar modes. This course will help prepare the student to take the AP Calculus test.

**AP Calculus BC may be taken for concurrent enrollment credit through C.U. Denver.**

__6297 Calculus 3__

__6297CECU Calculus III__(may be taken for concurrent enrollment credit through CU Denver)Credits: 10

Prerequisites: Calculus BC

Meets requirement(s): Mathematics

Open to Grades: 9, 10, 11 & 12

This is the third course of a three-semester sequence in Calculus. Vector algebra and analytic geometry in two and three dimensions; multivariable differential Calculus and tangent planes; multivariable integral Calculus; optimization and Lagrange multipliers; vector Calculus including Green’s and Stokes’s theorems.

**Calculus III may be taken for concurrent enrollment credit through C.U. Denver.**

__6296 Differential Equations__

__6296CECU Differential Equations__**(may be taken for concurrent enrollment credit through CU Denver)**

Credits: 10

Prerequisites: Calculus III

Meets requirement(s): Mathematics

Open to Grades: 9, 10, 11 & 12

This course meets the district goal of having students be given opportunities to earn credit beyond high school. It offers students who have completed math through Multivariable Calculus an opportunity to continue in the math progression.

**At FRHS:**

*The course would satisfy the next level of math, especially for our gifted and talented students in mathematics. The construction of mathematical models to address real-world problems has been one of the most important aspects of each of the branches of science. It is often the case that these mathematical models are formulated in terms of equations involving functions as well as their derivatives. Such equations are called differential equations. If only one independent variable is involved, often time, the equations are called ordinary differential equations. The course will demonstrate the usefulness of ordinary differential equations for modeling physical and other phenomena. Complementary mathematical approaches for their solution will be presented, including analytical methods, graphical analysis, and numerical techniques.*

*First and second order differential equations, Laplace transforms, systems of equations, with an emphasis on modeling and applications.*Differential Equations**may be taken for concurrent enrollment credit through C.U. Denver.**

__6142 Introduction to Statistics__Credits: 10

Prerequisites: Successful completion of Algebra II

Meets requirement(s): Mathematics

Open to Grades: 10, 11, 12

Introduction to Statistics is a semester long course centered on state standards related to statistics and probability. The course is designed as a semester alternative to AP Statistics. Introduction to Statistics explores data by describing patterns and departures from patterns; sampling and experimentation by planning and conducting a study; probability by analyzing random phenomena using probability and simulation; and statistical inference by estimating population parameters and testing hypotheses.

__6295 AP Statistics__Credits: 10

Prerequisites: Successful completion of Algebra II

Meets requirement(s): Mathematics

Open to Grades: 9, 10, 11 & 12

AP Statistics is a year-long mathematics course centered on four main topics: exploring data; planning a study; probability as it relates to distributions of data; and inferential reasoning. Students will be expected to propose and carry out a statistical study. This course is designed to help prepare students for the Advanced Placement exam.

__6146 Data Analysis & Probability__Credits: 5

Prerequisite: Successful completion of Geometry

Meets requirement(s): Mathematics

Open to Grades: Teacher recommendation only

Data Analysis & Probability is a semester long course centered on state standards related to statistics and probability. The course is designed for students with an interest in this area that are not planning on taking the AP Statistics course. Data Analysis & Probability explores data by describing patterns and departures from patterns; sampling and experimentation by planning and conducting a study; probability by analyzing random phenomena using probability and simulation; and statistical inference by estimating population parameters and testing hypotheses.

__6246 Discrete Mathematics__Credits: 5

Prerequisites: Successful completion of Geometry

Meets requirement(s): Mathematics

Open to Grades: Teacher recommendation only

Discrete Mathematics explores countable systems to make conclusions, decisions, or predictions. In contrast to continuous mathematics (calculus), discrete mathematics concentrates on the study of distinct objects and finite systems. Topics explored in Discrete Mathematics fall into four main categories: counting techniques, graph theory, iteration and recursion, and algorithmic problem solving and decision making.

__1831CEFRHS Fundamentals of Accounting__Credits: 5

Prerequisites: Accounting 1

Meets requirement(s): Mathematics

Open to Grades: 9, 10, 11, 12

This second-level accounting class goes beyond what is learned in Accounting 1 by introducing students to special journals, preparing payroll and payroll taxes, corporate accounting, and accounting for a merchandising business. QuickBooks Pro automated accounting will supplement every chapter in the textbook. Students completing this class will be prepared to be an entry-level bookkeeper or data entry clerk.

**At FRHS: S**

*tudents will have the opportunity to earn a National Bookkeeper Certification.*