Curriculum

# Mathematics

The Mathematics Department works to give students the tools necessary to succeed at the college level. Each course helps the student to develop logical thinking and problem solving skills.
The Department is committed to the integration of technology into the learning process. Graphing calculators are used as a tool to enhance the curriculum in all classes at all levels. Problems are solved algebraically, graphically, and numerically to give each student the opportunity to find his or her best learning style. Graphing calculators are required for all courses, with the Ti-84 plus series preferred.

## Essential Outcomes

### List of 5 items.

• #### Functions and Formulas

Students will be able to Manipulate mathematical functions and formulas. (Grad at Grad: Concern for Poor and Social Justice, Excellence in Education, Respect for All People)
Students will:
1. Determine when and how a mathematical formula can be applied
2. Identify the characteristics of a variety of mathematical functions
3. Understand how to use mathematical functions to model real world situations
• #### Mathematical Properties

Students will be able to Apply numeric, algebraic, and geometric properties. (Grad at Grad: Faith in Presence of God, Excellence in Education)
Students will:
1. Simplify mathematical expressions
2. Use numeric, algebraic, and geometric properties to justify and prove mathematical truths
• #### Patterns and Data

Students will be able to Recognize mathematical patterns, and analyze data. (Grad at Grad: Concern for Poor and Social Justice, Excellence in Education)
Students will:
1. Analyze patterns and trends in data to make future predictions
2. Recognize patterns that occur in the solving process of many types of equations
• #### Solution Methods

Students will be able to Recognize and use appropriate solution methods. (Grad at Grad: Excellence in Education, Participation within Inclusive Community)
Students will:
1. Use commonly accepted practices to solve a variety of equations
2. Analyze an equation’s solution for accuracy
• #### Technology

Students will be able to Use current technology as a tool for solving and graphing. (Grad at Grad: Excellence in Education)
Students will:
1. Understand the capabilities of their graphing calculators and other available technology
2. Use their graphing calculators to solve and graph a variety of functions

## Faculty

### List of 9 items.

• #### George Dinwiddie

Department Chair
george.dinwiddie@mullenhigh.com
BS Mathematics, Metropolitan State University
MA Ed- Use of technology in education, Lesley College

• #### Tomi Ahearn

tomi.ahearn@mullenhigh.com
BA in Mathematics Minor in Honors, University of Montana

• BS Secondary Math, Minor Biology, Louisiana Tech University
MA in Art and Science of Teaching, Grand Canyon University
• #### Heidi Capek

heidi.capek@mullenhigh.com
BS in Mathematics, Doane College
MA in Curriculum and Instruction, Doane College
• #### Lorraine Capra

lorraine.capra@mullenhigh.com
BA in Education minor in Mathematics, Metro State University
• #### Carolyn Heaney

carolyn.heaney@mullenhigh.com
BA Mathematics, Gonzaga University
MA in Curriculum and Instruction, University of Denver
• #### Leah Leddin '00

leah.leddin@mullenhigh.com
BS in Mathematics, Metro State University

• #### Pam Paulus

pam.paulus@mullenhigh.com
Clemson University
BS in Industrial Engineering
DePaul University
MA in Mathematics Education
• #### Annemarie Roberts

annemarie.roberts@mullenhigh.com
BS Mathematics minor is Business &
MEd, University of Notre Dame

## Course Offerings

### List of 30 items.

• #### Algebra I

This is a full year course that combines the content from Algebra I A CP and Algebra I B CP. This course includes the following topics: simplifying variable expressions, order of operations, properties of algebra, solving linear equations, solving proportions, graphing and writing linear equations, solving linear inequalities, solving absolute value equations and inequalities, solving systems of equations and inequalities, exponential properties and functions, polynomials and factoring, solving and graphing quadratic functions, solving rational functions, and solving radical functions. Math courses at Mullen build conceptual understanding, procedural fluency of skills, and application of concepts in real-world situations at a level appropriate for the course content. A graphing calculator is required. (NCAA Course)
• #### Algebra I A College Prep

This course includes the following topics: simplifying variable expressions, properties of algebra, solving linear equations, solving proportions, graphing and writing linear equations, solving linear functions and linear inequalities, and solving systems of equations. Math courses at Mullen build conceptual understanding, procedural fluency of skills, and application of concepts in real-world situations at a level appropriate for the course content. A graphing calculator is required. (NCAA course)
• #### Algebra I B College Prep

This course includes the following topics: solving systems of equations and inequalities, exponential properties and functions, polynomials and factoring, solving and graphing quadratic functions, solving rational and radical functions. Math courses at Mullen build conceptual understanding, procedural fluency of skills, and application of concepts in real-world situations at a level appropriate for the course content. A graphing calculator is required. (NCAA course)
• #### Algebra I A Honors

This course includes the following topics: a brief review of solving linear equations and
linear inequalities, followed by graphing linear functions, writing equations for linear
functions, writing and graphing arithmetic sequences as functions, solving and graphing
linear inequalities, solving and graphing absolute value functions and inequalities, and
solving systems of linear equations and inequalities. Math courses at Mullen build
conceptual understanding, procedural fluency of skills, and application of concepts in
real-world situations at a level appropriate for the course content. A graphing calculator
is required. (NCAA course)
• #### Algebra I B Honors

This course includes the following topics: exponential properties and functions, solving
exponential equations, writing and graphing geometric sequences as functions,
operations with polynomials, factoring and solving polynomial equations, solving and
applications of square root functions, solving radical equations, and inverse of a
function. Math courses at Mullen build conceptual understanding, procedural fluency of
skills, and application of concepts in real-world situations at a level appropriate for the
course content. A graphing calculator is required. (NCAA course)
• #### Algebra II A College Prep

This course is an in-depth review of important Algebra I concepts. It covers problem solving, linear equations and inequalities, solving absolute value equations and inequalities, graphing and writing linear equations and functions, graphing and solving systems of equations and inequalities, solving systems of equations using matrices, solving and graphing quadratic equations using several methods, complex numbers, simplifying polynomial expressions, properties of exponents, solving and graphing polynomial equations. In depth regression analysis of all functions is included. Math courses at Mullen build conceptual understanding, procedural fluency of skills, and application of concepts in real-world situations at a level appropriate for the course content. A graphing calculator is required. (NCAA Course)
• #### Algebra II B College Prep

This course studies rational exponents, power functions, solving radical equations, finding inverse relations, solving and graphing exponential functions and logarithmic functions, inverse and inverse and direct variation, simplifying rational expressions, solving and graphing rational equations, solving quadratic systems. In depth regression analysis of all functions is included. Math courses at Mullen build conceptual understanding, procedural fluency of skills, and application of concepts in real-world situations at a level appropriate for the course content. A graphing calculator is required. (NCAA Course)
• #### Algebra I B/ Geometry Honors

This is a full year course. Topics include writing equations for linear functions, solving systems of linear equations, exponential properties and functions, solving exponential equations, writing and graphing geometric sequences as functions, operations with polynomials, factoring and solving polynomial equations, solving and graphing quadratic functions, applications of quadratic functions, graphing and applications of square root functions, solving radical equations, and inverse of a function. The geometry portion begins with integrating logical reasoning and spatial visualization skills, deductive reasoning, theorems, and proofs are used to study relationships of points, lines, planes, angles and congruent triangles. The inequality relationships that exist between these figures will also be studied. In addition, quadrilaterals, similar polygons, right triangles, introduction to trigonometry, circles, areas of plane figures, and areas and volumes of solids will be covered. There will be continued use of algebraic equations and graphing calculators with respect to geometry. Math courses at Mullen build conceptual understanding, procedural fluency of skills, and application of concepts in real-world situations at a level appropriate for the course content. (NCAA Course)

• #### Algebra II A Honors

This course is an in-depth review of important Algebra I concepts. It covers problem solving, linear equations and inequalities, solving absolute value equations and inequalities, graphing and writing linear equations and functions, graphing and solving systems of equations and inequalities, solving systems of equations using matrices, solving and graphing quadratic equations using several methods, complex numbers, simplifying polynomial expressions, properties of exponents, solving and graphing polynomial equations. In depth regression analysis of all functions is included. Math courses at Mullen build conceptual understanding, procedural fluency of skills, and application of concepts in real-world situations at a level appropriate for the course content. A graphing calculator is required. (NCAA Course)
• #### Algebra II B Honors

This course studies rational exponents, power functions, solving radical equations, finding inverse relations, solving and graphing exponential functions and logarithmic functions, inverse and inverse and direct variation, simplifying rational expressions, solving and graphing rational equations, solving quadratic systems. In depth regression analysis of all functions is included. Math courses at Mullen build conceptual understanding, procedural fluency of skills, and application of concepts in real-world situations at a level appropriate for the course content. A graphing calculator is required. (NCAA Course)

• #### Calculus AB AP

This is a three-trimester course leading to the Advanced Placement Examination. Students will study limits and continuity, derivatives, applications of derivatives, integration, applications of the definite integral, transcendental functions, and techniques of integration. Math courses at Mullen build conceptual understanding, procedural fluency of skills, and application of concepts in real-world situations at a level appropriate for the course content. A graphing calculator is required. All students will take the Advanced Placement exam at the end of the year. (NCAA Course
• #### Calculus BC AP

This is a three-trimester course leading to the Advanced Placement BC examination. Students will do an in-depth study of limits and continuity, derivatives, applications of derivatives, integration, applications of the definite integral, transcendental functions, techniques of integration, improper integration, parametric, polar, and vector functions, convergence and divergence of series, Taylor and Maclaurin series. Math courses at Mullen build conceptual understanding, procedural fluency of skills, and application of concepts in real-world situations at a level appropriate for the course content. A graphing calculator is required. A graphing calculator is required. All students will take the Advanced Placement examination at the end of the year. (NCAA Course)
• #### Calculus A Honors

This is the first trimester course of a two-trimester series. The second trimester is called Calculus B Honors. In this first trimester, students will study limits and continuity, derivatives, related rates and applications of derivatives. Math courses at Mullen build conceptual understanding, procedural fluency of skills, and application of concepts in real-world situations at a level appropriate for the course content. A graphing calculator is required. (NCAA Course)
• #### Calculus B Honors

This course is a continuation of the concepts studied in Calculus A H. Additionally; students will study integration, applications of the definite integral, and integration techniques. Math courses at Mullen build conceptual understanding, procedural fluency of skills, and application of concepts in real-world situations at a level appropriate for the course content. A graphing calculator is required. (NCAA Course)
• #### Differential Equations Honors

This course includes first and second order differential equations, linear algebra, Laplace transforms and systems of equations. Emphasis will be on modeling and applications. Math courses at Mullen build conceptual understanding, procedural fluency of skills, and application of concepts in real-world situations at a level appropriate for the course content. A graphing calculator is required. (NCAA course)
• #### Geometry A

This course emphasizes the integration of logical reasoning and spatial visualization skills. Deductive reasoning, theorems and proofs are used to study relationships of points, lines, planes, angles, congruent triangles, and quadrilaterals. The inequality relationships that exist between these figures will also be studied. There will continued use of algebraic equations and graphing calculators with respect to geometry. Math courses at Mullen build conceptual understanding, procedural fluency of skills, and application of concepts in real-world situations at a level appropriate for the course content. (NCAA Course)
• #### Geometry B

This course emphasizes the integration of logical reasoning and spatial visualization skills. Deductive reasoning is used in the approach to similar polygons, right triangles, introduction to trigonometry, circles, areas of plane figures, and areas and volumes of solids. There will be continued use of algebraic equations and graphing calculators with respect to geometry. Math courses at Mullen build conceptual understanding, procedural fluency of skills, and application of concepts in real-world situations at a level appropriate for the course content. (NCAA Course)
• #### Geometry A College Prep

This is a course enhanced by emphasizing and integrating logical reasoning and spatial visualization skills. Deductive reasoning, theorems, and proofs are used to study relationships of points, lines, planes, angles, congruent triangles, and quadrilaterals. The inequality relationships that exist between these figures will also be studied. There will continued use of algebraic equations and graphing calculators with respect to geometry. Math courses at Mullen build conceptual understanding, procedural fluency of skills, and application of concepts in real-world situations at a level appropriate for the course content. (NCAA Course)
• #### Geometry B College Prep

This course emphasizes the integration of logical reasoning and spatial visualization skills. Deductive reasoning is used in the approach to similar polygons, right triangles, introduction to trigonometry, circles, areas of plane figures, and areas and volumes of solids. There will be continued use of algebraic equations and graphing calculators with respect to geometry. Math courses at Mullen build conceptual understanding, procedural fluency of skills, and application of concepts in real-world situations at a level appropriate for the course content. (NCAA Course)
• #### Geometry A Honors

This is a course enhanced by emphasizing and integrating logical reasoning and spatial visualization skills, deductive reasoning, theorems, and proofs are used to study relationships of points, lines, planes, angles and congruent triangles. The inequality relationships that exist between these figures will also be studied. There will continued use of algebraic equations and graphing calculators with respect to geometry. Math courses at Mullen build conceptual understanding, procedural fluency of skills, and application of concepts in real-world situations at a level appropriate for the course content. (NCAA Course)
• #### Geometry B Honors

This course emphasizes the integration of logical reasoning and spatial visualization skills. Deductive reasoning is used in the approach to quadrilaterals, similar polygons, right triangles, introduction to trigonometry, circles, areas of plane figures, and areas and volumes of solids. There will be continued use of algebraic equations and graphing calculators with respect to geometry. Math courses at Mullen build conceptual understanding, procedural fluency of skills, and application of concepts in real-world situations at a level appropriate for the course content. (NCAA Course)
• #### Math Analysis A

This course is designed to provide students a strong foundation of pre-calculus concepts, techniques, and applications that will prepare students for more advanced work in mathematics. The course will include study of the following types of functions: polynomial, exponential, and logarithmic. Conic sections and imaginary numbers will also be studied. Math courses at Mullen build conceptual understanding, procedural fluency of skills, and application of concepts in real-world situations at a level appropriate for the course content. A graphing calculator is required. (NCAA Course)
• #### Math Analysis B

This course is designed to provide students a strong foundation of pre-calculus concepts, techniques, and applications that will prepare students for more advanced work in mathematics. The course will include the study of trigonometry. Students will develop the unit circle, graphs of the six trigonometric functions, applications of the law of sines and cosines, and trigonometric identities. Math courses at Mullen build conceptual understanding, procedural fluency of skills, and application of concepts in real-world situations at a level appropriate for the course content. A graphing calculator is required. (NCAA Course)
• #### Multivariable Calculus Honors

In Multivariable Calculus, students extend their study of calculus from the xy-plane into 3-dimensional space. After an initial examination of geometry and algebra of 3D-space, students will use differential and integral calculus to study the nature of curves and surfaces in 3D-space. Topics include linear approximations of curves and surfaces in 3D-space, optimization of functions in several variables, use of integral calculus to study area, volume, and other applications, and an examination of the calculus of vector fields. Math courses at Mullen build conceptual understanding, procedural fluency of skills, and application of concepts in real-world situations at a level appropriate for the course content.
• #### Pre-Calculus College Prep

This course is the study of functions and the nature of their graphs, matrices, solving equations, systems of equations, logarithms, and limits. Math courses at Mullen build conceptual understanding, procedural fluency of skills, and application of concepts in real-world situations at a level appropriate for the course content. A graphing calculator is required. (NCAA Course)
• #### Pre-Calculus Honors

This course is an in-depth study of functions leading to AP Calculus. Students will fine tune and expand their problem solving skills through the study of the nature of graphs of functions. Students will solve problems involving exponential and rational functions, logarithms, limits, and conic sections. Students will be introduced to the derivative and integral functions from calculus. Math courses at Mullen build conceptual understanding, procedural fluency of skills, and application of concepts in real-world situations at a level appropriate for the course content. A graphing calculator is required. (NCAA Course)
• #### Statistics A College Prep

This course is an introduction into statistics and probability. Students will conduct simulations to better understand the complex world of data analysis. Students will then use a critical eye to create a multitude of summary statistics. Students will also look at applicable probabilities that they will see in their everyday life and into college. This is an interactive class, great for students looking into business or analysis in the future. Math courses at Mullen build conceptual understanding, procedural fluency of skills, and application of concepts in real-world situations at a level appropriate for the course content. Graphing calculator required. (NCAA Course)
• #### Statistics B College Prep

This course is a continuation of the concepts studied in Statistics A CP. Additionally, students will study inferential statistics, hypothesis testing, and regressions analysis. Math courses at Mullen build conceptual understanding, procedural fluency of skills, and application of concepts in real-world situations at a level appropriate for the course content. A graphing calculator is required. (NCAA Course)
• #### Trigonometry College Prep

This course is the study of trigonometry with emphasis on applications. Students will develop the unit circle, graphs of the six trigonometric functions, applications of the law of sines and cosines, and trigonometric identities. Math courses at Mullen build conceptual understanding, procedural fluency of skills, and application of concepts in real-world situations at a level appropriate for the course content. A graphing calculator is required. (NCAA Course)
• #### Trigonometry Honors

This course is an in-depth study of trigonometry. Students will develop the unit circle, graphs of the six trigonometric functions, applications of the law of sines and cosines, and trigonometric identities. Students will also study parametric and polar equations. Math courses at Mullen build conceptual understanding, procedural fluency of skills, and application of concepts in real-world situations at a level appropriate for the course content. A graphing calculator is required. (NCAA Course)

## Mullen High School

3601 South Lowell Blvd.
Denver, CO 80236

info@mullenhigh.com
(t) 303.761.1764
(f) 303.761.0502