MATHEMATICS
VISION STATEMENT
CNG inspires its student mathematicians at all levels through challenging, well aligned, and balanced curriculum. Students learn the true nature of mathematics through engaging and authentic tasks. CNG students are persistent, flexible thinkers, who clearly communicate their ideas and apply their knowledge to solve problems in a variety of contexts. Teachers at CNG encourage and model a growth mindset through a collaborative, safe environment where mistakes and risk taking are valued as learning opportunities. The instructional strategies and practices that we use spark curiosity, facilitate discourse, and encourage inquiry.
Essential Agreements: The curriculum will balance conceptual understanding and procedural fluency. The CNG math department offers math courses on three standard levels: on-level, Honors, or Accelerated Honors Placement. On-level and Honors classes are taught using the same curriculum and the depth of the material taught may differ. The math curriculum is designed so that every CNG math student has the optimal opportunity to be successful and complete an AP mathematics course before graduation.
The Accelerated Honors course levels mandate mastery of new concepts with a depth of understanding that extends topics beyond the normal course level while moving through the material at a more rapid pace. The Honors course level covers the topics as the Pre-AP level but with greater depth and self-directed learning. Students who complete AP Statistics, AP Calculus AB or AP Calculus BC math courses and pass the AP Exam with a 3 or higher may have the opportunity to earn college credit.
NOTE: Students who are not prepared to be placed in the standard levels of mathematics courses should have discussions with their counselor and/or Learning Center team about the sequencing of their high school math courses and what the mathematics requirements may be for their choice of university.
Pathways offered in Math Department for 2024-2025
These Pathways are for the Class of 2025, 2026, and 2027.
Course information for the Class of 2028 is below the table.
Please refer to the first column in the table below to see the available options for the 23-24 school year.
Class of 2028: Based on MAP scores and recommendations, you will be placed in either Pre-AP Math 1, Honors Pre-AP Math 1, or Accelerated Pre-AP Geometry and Statistics. All options will allow students the opportunity to take AP Statistics and/or AP Calculus before graduation without having to take two math classes in the same year.
_______________________________________________SUPPLIES______________________________________________
All math courses require the following materials:
__________________________________________COURSE DESCRIPTIONS______________________________________
Pre-AP MATH 1
MAT114/MAT115
0.5 credit each
The Pre-AP Math 1 course is designed to deepen student understanding of
Successful completion of grade 8 regular math course is a prerequisite
Pre-AP GEOMETRY & STATISTICS A & B
MAT102/MAT103
0.5 credit each
Geometry is a math course that allows students to develop their deductive and inductive thinking skills. Students of a formal Geometry course such as this one take enhanced problem solving skills with them into all areas of their lives. The curriculum, Discovering Geometry uses inductive and deductive reasoning to introduce Euclidean geometry studying all polygon properties with emphasis on triangles, the study of circles, area and volume, and the important Pythagorean Theorem.
Successful completion of Algebra I is a prerequisite
ACCELERATED HONORS Pre-AP GEOMETRY & STATISTICS A & B
MAT160/MAT161
0.5 credit each
Average Workload: 2-3 hours per week outside of class
This is a highly accelerated math course for students planning to finish with the BC Calculus course in their senior year. The year begins with the investigation of relationships using congruence and similarity of plane figures and three-dimensional geometric figures. Students will use inductive and deductive reasoning to prove conjectures. Geometric proofs are an important part of this course as they are one way of developing a student’s problem solving skills. During the second part of the year students will study logic and set theory, bases, conics, polar coordinates, statistical analysis and properties of trigonometric functions.
Successful completion of Honors Algebra I and teacher recommendation are prerequisites.
HONORS ALGEBRA II A & B
MAT254/MAT255
0.5 credit each
Average Workload: 2-3 hours per week outside of class
Students in this course will deepen their understanding of several families of functions such as linear, quadratic, rational and exponential functions. They will also work with conic sections, sequences, series, and exponential and logarithmic functions. Students will use combinatorial mathematics to develop the binomial distribution and find probabilities.
Prerequisite: Successful completion of Honors Geometry or successful completion of Pre-AP Geometry with teacher recommendation.
PRECALCULUS A & B
MAT300/MAT301
0.5 credit each
The main goal of Precalculus is for students to gain a deeper understanding of the fundamental concepts and relationships of functions. Students will expand their knowledge of quadratic, exponential and logarithmic functions to include power, polynomial, rational, piecewise and trigonometric functions. Students will investigate mathematical ideas and develop strategies for analyzing complex situations. At times, calculators will be used to build understanding, make connections between representations and provide support in solving problems. Students will communicate mathematics through writing and modeling, using precise mathematical language and symbolic notation. All units will attempt to make connections between mathematical ideas and other areas of study.
Successful completion of Algebra 2/Trigonometry is a prerequisite.
HONORS PRE-CALCULUS A & B
MAT356/MAT357
0.5 credit each
Average Workload: 1-3 hours per week outside of class
Students extend their depth of study of previous topics and introduce the fundamental geometric transformations in two dimensions. Students study trigonometry, vectors, analytic trigonometry including law of sines and cosines, probability, and analytic geometry (conic sections). They also explore exponential, polynomial, rational, logarithmic, and periodic families of functions along with partial fractions. They combine functions using arithmetic operations and composition and also explore the inverse function. This is an essential course for students planning on taking AP Calculus.
Prerequisite: Successful completion of Honors Algebra II.
AP PRE-CALCULUS A & B
MAT408/MAT409
0.5 credit each
Average Workload: 3-5 hours per week outside of class
In AP Precalculus, students explore everyday situations using mathematical tools and lenses. Through regular practice, students build deep mastery of modeling and functions, and they examine scenarios through multiple representations. They will learn how to observe, explore, and build mathematical meaning from dynamic systems, an important practice for thriving in an ever-changing world.
AP Precalculus prepares students for other college level mathematics and science courses. The framework delineates content and skills common to college precalculus courses that are foundational for careers in mathematics, physics, biology, health science, social science, and data science.
Prerequisite: Successful completion of Honors Algebra II or successful completion of Algebra II with a teacher recommendation.
CALCULUS A & B
MAT400/MAT401
0.5 credit each
Students will study the concepts of limit, continuity, the basic rules for differentiation, the derivative as the slope of a curve and as a rate of change, curve sketching, indefinite integrals, area and definite integrals, the Fundamental Theorem of Calculus, and some applications. Emphasis will be placed on applying previous skills and concepts to develop the Calculus concepts. This fulfills the requirement for a fourth credit in math. This course can count as a capstone concentration course taken along with another senior level math class.
Successful completion of a PreCalculus course is a prerequisite
AP CALCULUS AB A & B
MAT450/MAT451
0.5 credit each
Average Workload: 5-7 hours per week outside of class
Summer work: A summer packet of Algebra and Pre-Calculus Review
This course is intended for students who are interested in STEM careers like engineering, software development, economics, statistics, mathematics, and science and want/need to receive the credit for those paths. Students will understand the concept of a limit of a function, learn different techniques for finding limits and understand the concept of continuity. They will learn different methods for finding derivatives and they will be able to apply this concept to curve sketching, solving optimization and related rate problems, finding lines tangent and normal to a curve and solving motion problems.
Students will be able to approximate areas with Riemann sums, understand the concept of integral, be able to find integrals by substitution and apply this concept to finding areas between curves, volumes of solids of revolution and solids of known cross-sections as well as to solve simple differential equations. This fulfills the requirement for a fourth credit in math. This course can count as a capstone concentration course taken along with another senior level math class.
Prerequisite: Successful completion of Honors Pre- Calculus or successful completion of Accelerated Honors Algebra.
HONORS Pre-AP MATH 1
MAT116/MAT117
0.5 credit each
Average Workload: 2-3 hours per week outside of class
The Pre-AP Math 1 course is designed to deepen student understanding of
In the Honors-level course, students will dive deeper into linear concepts with real world data collection and other project-based applications of the core content.
Successful completion of math 8 class.
HONORS Pre-AP GEOMETRY & STATISTICS A & B
MAT158/MAT159
0.5 credit each
Average Workload: 2 hours per week outside of class
Students in this course explore relationships (including congruence and similarity) among classes of twoand three-dimensional geometric objects, make and test conjectures about them, and use inductive and deductive reasoning to solve problems and prove geometric relationships and trigonometry. Geometric proofs are taught as one way of developing a student’s problem solving skills. They also deepen their understanding of Algebra 1 concepts (Linear equations, transformations, distance and midpoint formulas) and use it to solve geometric problems on the coordinate plane (Coordinate Geometry). This advanced class will also introduce trigonometric concepts such as trigonometric ratios, the Law of Sines, The Law of Cosines, the unit circle, trigonometric functions and basic trigonometric identities. Students will also expand their understanding of statistical analysis. Students should take this course if they enjoy a challenging fast paced math course.
Successful completion of Honors PreAP Algebra 1 in high school or successful completion of PreAP Algebra 1 with teacher recommendation..
INTENSIVE GEOMETRY/ALGEBRA II
MAT106/MAT107
0.5 credit each
Average Workload: 2 hours per week outside of class
This course is for students who were in the PreAP Algebra 1 or Honors PreAP Algebra 1 in 9th grade and would like to move or continue to the honors track, upon approval. This course will cover the standards required for success in PreCalculus and AP Calculus AB.
Students in this course:
Successful completion of PreAP Algebra I is a prerequisite.
ACCELERATED HONORS ALGEBRA II A & B
MAT256/MAT257
0.5 credit each
Average Workload: 2 hours per week outside of class
Students in this course are on the BC Calculus track and will deepen their understanding of all topics presented in Accelerated Pre-AP Geometry including higher degree polynomials, transformation of several parent functions along with rational and trigonometric functions. They will extend the basic concepts of Conic Sections by performing translations, dilations and rotations of the four Conic Sections. They will be introduced to basic Calculus concepts such as limits and derivative rules such as the constant, power, product, and quotient rules as well the chain rule. They will also use the limit process to find instantaneous rates of change.
Successful completion of Accelerated Honors Geometry is a prerequisite.
ALGEBRA II / TRIGONOMETRY A & B
MAT200/MAT201
0.5 credit each
Algebra II builds on skills and concepts students learned in Algebra I and in Geometry and extends them in order to prepare students for success in AP PreCalculus, Probability & Statistics, and AP Statistics class. We continue our work with linear equations, including systems of equations. The study of functions is deepened with attention to some transformations and basic input/output notation. An emphasis is placed on understanding domain, range, and graphing of several families of functions. We develop an understanding of quadratic, exponential, and logarithmic equations, solution processes and their graphs. This course will also cover basic, and analytic trigonometry.
Successful completion of Pre-AP Geometry is a prerequisite
AP CALCULUS BC A & B
MAT452/MAT453
0.5 credit each
Average Workload: 5-7 hours per week outside of class
This course is intended for students who are interested in a full year’s course of Calculus. It is also for students who believe they would pursue a degree in a math related field. This is an advanced course at the high school level with the expectation that students are dedicated to maintaining a rigorous pace.
This is the final course for students who have completed the Accelerated Pre-AP courses. Students will be able to approximate areas with Riemann sums, understand the concept of the integral, be able to find integrals by substitution and apply this concept to finding areas between curves, volumes of solids of revolution and solids of known cross-section. The course also includes Taylor approximations and series including Maclaurin and harmonic series. All through the course the student will use technology to help solve problems and interpret results. This fulfills the requirement for a fourth credit in math. This course can count as a capstone concentration course taken along with another senior level math class.
Prerequisites: Successful completion of AP Calculus AB is a prerequisite.
PROBABILITY AND STATISTICS A & B
MAT460/MAT461
0.5 credit each
This is an introduction to Probability and Statistics. Students will 1) Explore data: looking at various distributions and relationships. 2) Make inferences based on explorations: looking at data in samples and experiments; probability and sampling distributions. 3) Make inferences about variables 4) Make inferences about relationships. This class is great for students going into fields such as, communication, business, health fields, psychology, social sciences, law, and journalism. This course is taught at the same level or rigor as AP Statistics but covers fewer topics.
Successful completion of Algebra 2/Trigonometry is a prerequisite
AP STATISTICS A & B
MAT470/MAT471
0.5 credit each
Average Workload: 5-8 hours per week outside of class
This course is intended for students who are interested in studying a different branch of mathematics that is not as heavy on math but more on logic and data analysis. Students will be expected to communicate well and show a capacity for critical thinking skills. This course will reflect that of an introductory statistics course in a university. In this course students will learn about the major concepts of statistics. Students are exposed to four main themes: Exploring Data: Students will write summaries based on describing patterns and interpreting information. Sampling and Experimentation: Students will make conclusions and generalizations based on studies. Anticipating Patterns: Students will learn; binomial distribution, standard deviation, normal distribution, Central Limit Theorem, sampling distributions, t-distribution, and the Chi-Square distribution. Statistical Inference: Students will explore margin of error, confidence intervals, and significance testing which includes null hypothesis, alternative hypothesis, and p-values. The AP course will focus on the curriculum laid out from the College Board. Students will work towards taking the AP Statistics Exam in May. This class is great for students going into fields such as, communication, business, health fields, psychology, science, social sciences, law, math, engineering, and journalism.
Successful completion of Algebra II or higher is a prerequisite.