Math
MATHEMATICS
The Mathematics Department of MMRHS believes a strong mathematics program emphasizes problem solving, communicating, reasoning and making connections to real life problems. The curriculum offers students opportunities to learn important mathematical concepts and procedures with understanding. Our teachers help students make, refine, and explore conjectures on the basis of evidence and use of a variety of reasoning techniques to confirm or disprove those conjectures. Students are expected to work productively and reflectively, whether alone or in groups, with the guidance of their teachers.
Sequence leading to post-secondary options including the work force, certificate programs, technical schools and associate degrees:
Fundamentals of Algebra I
Fundamentals of Geometry
Fundamentals of Algebra II
Applied Math
Sequence leading toward a 4-year college program:
Algebra I
Geometry
Algebra II
Precalculus
Sequence leading toward Math and Science related careers:
Algebra I (8th grade)
Honors Geometry (9th grade)
Honors Algebra II
Advanced Mathematics
Advanced Placement Calculus or Calculus
Electives:
Probability
Statistics
Honors Math Elective
ALGEBRA I Credit: 1
Grades 9-12 Prerequisite: None
The first mathematics course for college-bound students, Algebra is taught through systematic instruction emphasizing skills and reasoning and provides a strong background for all future mathematics.
GEOMETRY Credit: 1
Grades 10-12 Prerequisite: Algebra I
This course is designed to give students a background in informal geometry and right triangle trigonometry. Students will explore geometric concepts and relationships with hands on activities and with the use of technology. This course will reinforce basic algebra concepts.
ALGEBRA 2 Credit: 1
Grades 11-12 Prerequisite: Algebra I
This course is designed to review and delve more deeply into topics from algebra. The course explores systems of linear equations, quadratic, polynomial, rational and exponential functions. Possible topics include conic sections and probability and statistics.
PRECALCULUS Credit: 1
Grade 12 Prerequisite: Algebra II
The fourth year of the CP sequence is designed to prepare students for college mathematics, including calculus. The concepts explored are functions, trigonometry, exponents and logs, sequences and limit.
FUNDAMENTALS OF ALGEBRA I Credit: 1
Grades 9-12 Prerequisite: None
Fundamentals of Algebra I will cover four major content strands:
- Number sense and operations
• Patterns, relations and algebra
• Measurement
• Data analysis, statistics and probability
Fundamentals of Algebra I teaches the basic concepts of algebra in a step-by step approach and meets the standards set by the National Council of Teachers of mathematics.
FUNDAMENTALS OF GEOMETRY Credit: 1
Grades 10-12 Prerequisite: Algebra I
Fundamentals of Geometry is designed to teach students informal geometry. Students will explore geometric concepts and relationships with hands on activities and the use of technology.
FUNDAMENTALS OF ALGEBRA II Credit: 1
Grades 11-12 Prerequisite: Fund. of Algebra I, Algebra I
The topics explored in the third year of the Fundamentals sequence are quadratic functions, systems of equations, exponents, radicals, inequalities, and trigonometry. The course is designed to improve students’ computational skills and to enhance their understanding of the algebraic process.
APPLIED MATHEMATICS Credit: 1
Grades 10-12 Prerequisite: One credit in mathematics
This course consists of a series of activities which will emphasize the application of mathematical principles in the context of work-related situations. These activities are designed for students who learn best by applying skills in concrete and visual situations that are relevant to their lives. This course is to be taken after at least one year of math other than Fundamentals of Algebra I.
HONORS GEOMETRY Credit: 1
Grades 9-12 Prerequisite: Honors Algebra I
This full year course will help the student make the transition from concrete to conceptual mathematics. Comprehensive in scope, this course thoroughly develops mathematical proof techniques. Problem-solving strategies develop vital reasoning skills and help students prepare for college entrance exams.
HONORS ALGEBRA II Credit: 1
Grades 10-12 Prerequisite: Algebra I in 8th Grade or Department Recommendation
Algebra I skills are further developed to explore the concepts involved in more advanced mathematics studies. After a thorough review of Algebra I principles in greater complexity, the concepts of function and functional notation are applied to quadratic, exponential and logarithmic relations. Additional topics include an introduction to conic sections, sequences and series and probability and statistics.
ADVANCED MATHEMATICS Credit: 1
Grades 11-12 Prerequisite: Honors Algebra II
This is a full year course in introductory analysis for the mathematically-inclined and a preparation for Calculus. The course content includes elementary functions and their limits, trigonometry, sequences, series, data analysis and probability. Graphing calculators are used extensively in this course.
CALCULUS Credit: 1
Grade 12 Prerequisite: Advanced Mathematics or Precalculus (88 average or above)
This course is designed for the above average mathematics student in their senior year. Students will learn to use derivatives and integrals to solve a wide variety of problems. This course will cover many of the topics in A .P . Calculus but will be done on a less rigorous basis. No advanced placement credit will be given for this course.
ADVANCED PLACEMENT CALCULUS Credit: 1
Grade 12 Prerequisite: Advanced Mathematics
AP Calculus is an advanced placement course offering the mathematically talented student opportunity for a college level course. It consists of an academic year of work in calculus and related topics comparable to courses on the college level. Most colleges grant college level credit for this course, providing the advanced placement scores are adequate.
PROBABILITY Credit: .5
Grade 11-12 Prerequisite: Algebra I
Probability is a one-semester course that covers basic introduction to probability. Students will:
- Explore, summarize, and display data
• Design experiments
• Use probability to understand random behavior
• Make inferences about populations by looking at samples from those populations.
Students will use graphing calculators or statistical software for data analysis. This course is strongly recommended for students who will pursue studies in the social sciences, psychology, sociology, education, business, economics, the humanities, the physical sciences and communication.
STATISTICS Credit: .5
Grade 11-12 Prerequisite: Algebra I
Statistics is a one-semester course which builds on the experiences of Probability. The students will pursue more advanced statistics topics such as, inferences from two samples, correlation and regression, analysis of variance and non-parametric statistics. The course takes a hands-on approach rather than a theory based approach.
HONORS MATH ELECTIVE Credit: .5
Grades 9-12 Prerequisite: Algebra I and
recommendation of math teacher
This course is designed for students who have an interest in and an aptitude for mathematics. The course can be taken as a second math course in a student’s schedule or as the only math course. Students may take the course more than once because the topics will vary from semester to semester. Course content will be determined by the teacher and interests of the students. Possible areas of study include, but are not limited to: Discrete Math, Number Theory, Chaos Theory, Non-Euclidian Geometry and the math of Numb3rs. Material from math leagues will also be used.
BioMath Credit: .5
Grade 9-12 Prerequisite: CP or Honors Biology,
Honors Discussion with BioMath teachers
College Prep
The BioMath program is a multiple year initiative developed by the Discrete Mathematics program at Rutgers University and funded by the National Science Foundation. Its purpose is to create high school level units that simultaneously teach biology and math concepts. Approximately 25 units have been completed and field tested in high schools across the nation, including Monument Mountain. Four of Monument Mountain’s math and science teachers have been involved in writing and field testing these units. The individual units have been rewritten into a book that will serve as a text for the BioMath course. BioMath will run for the first time anywhere at Monument Mountain next fall.
The Monument Mountain course will likely choose from these modules – the Computational Molecular Biology series: Evolution by Substitution, Genetic Inversions, Spider Silk (DNA alignment), Microarrays; the Computational Epidemiology series: Competition in Disease Evolution, Modeling Disease Outbreaks, Imperfect Testing, Genetic Epidemiology; the Ecology series: Food Webs, Habitat-Squirrels, Ecological Footprint, Home Range; Additional Modules: Forensics, Evolutionary Game Theory, Tomography
At Monument Mountain this course will be aimed at all college bound students who are interested in biology and in learning the underlying math, particularly how the math is being used and applied. This means that the course is appropriate for both CP and Honors students and will be presented at the CP level, with an option to take it at the Honors level. One of the prerequisites is passing CP or Honors Biology. The primary prerequisite is a discussion with the course teacher(s) to make sure the student understands how the course material will be presented and where the student convinces the teacher(s) that the student is interested in the planned material and in doing the type of work required.