An MVCDS Education

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Mathematics

The mission of the Maumee Valley Math department is to provide our students with a solid base of mathematical knowledge based on a sound sense of mathematics developed in a cooperative atmosphere of active exploration and constructivist learning.  We will develop persistent and confident students who use multiple strategies to solve real-world problems, effectively communicate their logical solutions, and understand math’s global impact and importance.

  • Accelerated Precalculus

    This rigorous course will cover an in-depth study of various functions in rectangular and polar planes, in addition to other topics that are needed for Calculus. The course will combine trigonometric, geometric, and algebraic techniques to strengthen the students’ conceptual understanding of mathematics. Students will demonstrate their understanding for the material covered by working on the assigned challenging problems, proving identities and theorems, and deriving formulas. Classroom discussions will move from the concrete to abstract and theorems will be proven in more detail.
     
    Students will actively engage in problem solving, reasoning, connecting and communicating mathematically as they explore various families of functions. Special emphasis will be on Exponential functions, Logarithmic functions, Rational functions, Trigonometric functions, and the Inverse of Trigonometric functions from numerical, graphical, and algebraic approaches. Graphs in 3-Dimensional plane, conics, and polar equations of conics will be discussed, too. In order to prepare the students for AP Calculus, the emphasis of the course after Spring Break will shift to Calculus. 
     
    The instructional strategies will vary throughout the year. Investigative and collaborative group activities, questioning for understanding and metacognition, guided practice, addressing students’ learning style, scaffolding of classroom activities, and differentiation will be implemented in this course. 
     
    In class students are expected to work collaboratively on formative assessments including homework, mini quizzes, and chapter tests. In this course we will use WebAssign, an online course management system. Students will be assigned problems in WebAssign and can access hints, practice problems, and pdf copies of chapters. 
     
    Ti-83 or Ti-84 graphing calculator is required. By using technology to collect and model data, students will be able to make conjectures about the data and develop a robust understanding of the concepts discussed.
    This is the course you will need to take before the SAT II Exam.
     
  • Algebra I

    Algebra is the language through which most mathematics is communicated. Algebra I will begin to provide a means of operating with the concepts of variable, expressions, equations, inequalities, matrices, and relations. The skills taught in this course lay the foundation for upper level math and science courses and have practical uses. The concept of function is emphasized throughout the course. Some topics include: operations with real numbers, linear functions and inequalities, relations, solving systems of linear equations and inequalities, and quadratic functions, factoring and equations.

    Algebra I will provide students with the required depth of knowledge in the language of
    mathematics. A student who is familiar with the terms of mathematics in Algebra I will be well-positioned to succeed in subsequent years. Emphasis will be placed on knowledge of the language as well as computational skills.

    Students will use Ti­83 or Ti­84 calculators extensively to help them visualize functions and find solutions to problems. Students will be assessed through traditional quizzes and tests, as well as through projects and other individual and group work.
  • Algebra II

    This course is a transition course intended to revisit and shore up the knowledge learned in Algebra I while providing introductory looks at a variety of more advanced topics that will be necessary for engaging in the content of higher level class such as trigonometry, precalculus and calculus.  The first half of the course will review topics from Algebra I in greater depth and cover new material.  Topics include essential properties of numbers, as well as a discussion of common mathematical notation, then linear functions and equations, matrices, quadratic functions, and polynomials.

    The latter half of the course covers a variety of other kinds of functions: exponential, logarithmic, rational, and trigonometric. The concepts of inverse, symmetry and zero are integral in the class and will be discussed across all topics.  Students will develop strategies for writing equations to model a variety of mathematical relationships, both abstract and concrete.

    Connections to real life will be made when applicable.  The use of technology such as a TI-83/84 graphing calculator will allow for data analysis and creation of equations to model a variety of situations. In this course we will use Math XL, an online course management system. Students will be assigned problems in Math XL and can access hints, practice problems, and pdf copies of chapters.  They will have the opportunity to redo problems they get incorrect. 

    Students will be graded on homework, regular quizzes, projects, and periodic tests as well as midterm and final exams.
     
  • AP Calculus AB

    Prerequisites: Precalculus, 600 or higher on PSAT Math, and department approval.

    In this rigorous college level course, students will move from the finite to the infinite. In previous math courses students have studied functions and average rate of change, such as average velocity to approximate instantaneous rates of change. They have also studied behavior of functions and have found maximum and minimum values of a function by graphing. In AB Calculus we will study the behavior of functions as the x value gets “infinitely close to” a given x value to find exact values of instantaneous rates of change, derivatives. We will also find accumulated change in a function given its derivative, the idea of integration. AP Calculus AB is essentially one continuous topic, starting from an understanding of functions to limits, continuity, differentiation, integration, and applications in math, physics, and economics. Students will be able to, for example, find equations of tangent lines to approximate functions, find marginal cost and maximize profit, analyze motion along a line, find areas and volumes and finally learn where all the formulas they learned in fifth grade actually came from, such as the volume of a cone. We will take an active approach in learning Calculus. Through explorations, experimentation, and activities students will have a better intuitive understanding of calculus concepts, which we will then prove more formally. Students will use Ti­83 or Ti­84 calculators extensively to help them visualize functions and find solutions to problems they could not without a graphing calculator. Students will be assessed through traditional quizzes and tests, as well as through projects, take-home work, and other individual and group work. In this course we will use Math XL, an online course management system. Students will be assigned problems in Math XL and can access hints, practice problems, and PDF copies of chapters.  We will also use AP classroom for additional problems and past AP questions.   They will have the opportunity to redo problems they get incorrect. In the spring, students are
    required to take the Calculus Advanced Placement Exam. Those who take the AB exam and get a 4 or 5, and often a 3, could get a semester of college credit, at the discretion of the college. A Ti­83 or Ti­84 or equivalent graphing calculator is needed for this class. ​Estimated exam cost: $98
  • AP Calculus BC

    Advanced Placement Calculus BC covers all the topics of Calculus AB plus additional integrations techniques ( integration by parts, improper integrals, partial fraction decomposition); sequences and series (specifically MacLaurin and Taylor polynomials with error estimates, MacLaurin and Taylor series, convergence and interval of convergence of series); areas and arc length of functions given in polar and parametric form;  and vector Calculus. Students will be required to take the  BC exam, typically a 4 or a 5, and may get up to a year’s college credit.  A Ti­83 or Ti­84 or equivalent graphing calculator is needed for this class.​Estimated exam cost: $95
  • AP Statistics

    More and more programs in college now require a background in statistics, and virtually anyone pursuing a graduate degree must have a course in statistics. AP Statistics is an introductory, college ­level course that will help students understand the world around them and make predictions based on sampling and probability. The course deals with four main areas: Exploring data (describing and interpreting data and distributions), Sampling and Experimentation—how to collect data representative of the population and how to design and carry out experiments; Probability and Simulation—using mathematical models, probability and simulation,and Statistical Inference (making predictions of populations based on samples, making statistical arguments and testing claims using statistics). Taking a typical one­ semester college course in a year in high school gives students the opportunity to do more “hands-­on” statistics—experiments and simulations—than possible in college. In class we will often perform simulations, collect data, or do experiments to motivate and understand theorems and statistical procedures and results. Students’ previous algebra skills, and their concept of proof will help them understand these theorems and procedures. AP Statistics is very different from previous math courses. There is a strong reading and writing component. Students will be expected to read 800 pages of text and be able to communicate their knowledge through written explanations. They must demonstrate a high level of motivation, good study and language skills, and proven mathematical ability in order to be successful in this course. Students will demonstrate their knowledge through quizzes, tests, and individual or group projects and investigations.  We will also use AP classroom for additional problems and past AP questions.   Students are required to take the AP exam in May. Those who get a 4 or 5 on the AP exam could qualify for a semester’s college credit at the discretion of university.  A Ti­83 or Ti­84 graphing calculator is required. Estimated exam cost: $95
  • Business Math

    This course is designed to discuss various topics in business, including interest rates, job costing, merchandising, payroll, credit, loans, insurance, automobile and housing expenses, taxes, insurance, and global business. The ability to estimate and approximate answers in solving financial problems will be emphasized. In Business Math, you will be able to demonstrate using and developing mathematical skills, including whole numbers, fractions, decimals, percents, ratio and proportion, commercial discounts, simple and compound interest, basic statistics, and graphs that are required to function in today’s business world as well as to handle personal finances.
  • Calculus I

    Prerequisite: Precalculus and departmental approval.  

    In this introductory calculus course, students will move from the finite to the infinite. In previous math courses students have studied functions and average rate of change, such as average velocity to approximate instantaneous rates of change. They have also studied behavior of functions and have found maximum and minimum values of a function by graphing. In Calculus I we will study the behavior of functions as the x value gets “infinitely close to” a given x value to find exact values of instantaneous rates of change, derivatives. We will also find accumulated change in a function given its derivative, the idea of integration. We will start from a review of precalculus topics, without a calculator, to gain a better understanding of functions. We will then study  limits, continuity, differentiation, integration, and applications in math, physics, and economics. Students will be able to, for example, find equations of tangent lines to approximate functions, find marginal cost and maximize profit, analyze motion along a line, and find areas under curves. We will take an active approach in learning Calculus. Through explorations, experimentation, and activities students will have a better intuitive understanding of calculus concepts.  We will not be under the same time constraint as AP Calculus, so will focus on intuitive understanding, and students should be well prepared to take calculus in college. Students will use Ti¬83 or Ti¬84 calculators extensively to help them visualize functions and find solutions to problems they could not without a graphing calculator. Students will be assessed through traditional quizzes and tests, as well as through projects, take-home work, and other individual and group work. In this course we will use an online course management system. Students will be assigned problems and can access hints, practice problems, and pdf copies of chapters. 

    Calculus I will cover many of the same topics as AP Calculus, but will not be taught at the same conceptual level, and assessments will be more book-oriented rather than focused on AP style questions.  In short, Calculus I will provide a solid foundation for calculus in college, but is not meant to adequately prepare the student to take the AP Calculus exam.
     
  • Data Analysis

    This course is designed as an introduction to statistics and data analysis, and would offer a firm foundation for subsequent work in AP Statistics. . Its focus is on probability, statistics and data analysis. Through sampling, simulation, and experimentation, students will  model real world situations to approximate probability and to make predictions.  They will use graphing and regression features of their graphing calculators to display and analyze data. They will use sampling to make predictions about populations, through confidence intervals, and they will also use sampling to conduct hypothesis testing.  A Ti-83 or Ti-84 graphing calculator is required. We will make use of an online homework system where students can get hints and see examples and work out problems.
  • Geometry

    Prerequisites: Algebra I or departmental approval.

    In the first semester of Geometry, students will be introduced to the fundamental concepts of reasoning and logic, basic coordinate Geometry, and congruence. In doing this students will be exploring many relationships between points, lines, angles, etc. They will be called upon to explain their ideas and justify their answers in rigorous ways, utilizing definitions, postulates, and theorems. At times, they will use informal explanation methods and at other times, they will use the more formal two-column proof. Students will first learn basic terminology and relationships, as well as the basics of deductive reasoning and proofs. They will then explore relationships between lines and angles using parallel lines. Following this, students will explore the idea of congruence through transformations in the coordinate plane and considering what it takes for triangles to be congruent. The term will end with an in depth look at some of the relationships that exist within right triangles. Skills from Algebra I will be utilized regularly. The second rotation will begin with a study of similarity and trigonometry, with a continued focus on triangles. When we wrap up our study of triangles, we will study quadrilaterals and other polygons, followed by circles, and finally surface area and volume.
  • Intro to Probability and Statistics

    Prerequisites: Algebra I.

    This course in introductory statistics and probability will introduce the student to descriptive statistics, uses and abuses of statistics, simulations, probability, and uses of statistics in the real world. Students will have the opportunity to do hands-on probability experiments and simulations. They will learn the basics of probability including the use of tree diagrams, rules of probability, combinations, permutations, and the binomial theorem; binomial and normal distributions; using the Ti-84 to perform simulations and find probabilities; displaying and analyzing data; and making predictions. The course will culminate in a project involving probability and statistics.  Required materials: Ti-84 graphing calculator.  
  • Numerical Analysis

    Prerequisites: Successful completion of Algebra II or higher and departmental approval.

    This semester course is intended to focus on the study of algorithms that use basic techniques for efficient numerical solutions of problems using inductive and deductive reasoning, problem-solving skills, infinite sets and their cardinalities, conversion between Number Bases, real numbers, and complex numbers. Topics include the essential art of problem solving, the basic concepts of set theory, logic, numeration systems, number theory, graph theory, and real numbers and their representations. The instructional strategies will vary throughout the year. Investigative and collaborative group activities, questioning for understanding and metacognition, guided practice, addressing students’ learning style, scaffolding of classroom activities, and differentiation will be implemented in this course.
     
    In class, students are expected to work collaboratively on formative assessments including homework, mini quizzes, and chapter tests. In this course we will use MathXL, an online course management system. Students will be assigned problems in MathXL and can access hints, practice problems, and pdf copies of chapters.
     
    Ti-83 or Ti-84 graphing calculator is required. By using technology to collect and model data, students will be able to make conjectures about the data and develop a robust understanding of the concepts discussed.
     
    Students will be graded on homework, regular quizzes, projects, and periodic tests as well as midterm and final exams.
     
  • Precalculus

    This advanced algebra course will concentrate on a variety of functions. Primary emphasis will be on understanding operations, general properties, and behavior of classes of functions, including a complete development of the trigonometric functions. Students will be able to represent and analyze relationships using tables, verbal rules, equations and graphs; and to translate among tabular, symbolic and graphical representations of functions. Important concepts of calculus will be foreshadowed through an emphasis on graphs. This informal exploration will lay the foundation for future study by providing students with rich intuitions about functions and graphs. 

    Students will be graded on homework, regular quizzes, and periodic tests as well as midterm and final exams. In this course we will use Math XL, an online course management system. Students will be assigned problems in Math XL and can access hints, practice problems, and pdf copies of chapters.

    *Ti-83 or Ti-84 graphing calculator is required. Calculators will be extensively used to help students visualize functions and find solutions to problems they could not without a graphing calculator.
     
  • Statistics in Athletics

    Students will calculate and analyze various statistics from both team and spectator’s point of view. Recently, there have been various trends and analysis throughout the world of sports, and students in this course will not only algebraically solve problems, but will have in-depth discussion as to their legitimacy. The class will look at some of the statistics they may see on television or the internet and we will discuss what they mean and how to calculate. Students will look at what coaches particularly look at in high school, college and pro level, including some Maumee Valley athletics. We will tie in some of the probability, statistics, and graphs that students will see on the SAT and ACT. TI 83 or TI 84 graphing calculator is highly recommended.
  • Trigonometry

    Trigonometry is the combination of Algebra and Geometry. Concepts from both courses combine to provide us with the tools for modeling and analyzing the real world in ways that were not possible previously. Trigonometric functions, like numerous events in the real world hold hidden patterns and are cyclical.  In this course, the students will use their Algebraic skills to develop an understanding of trigonometric functions, their identities, and their applications.  The skills developed in this course will help prepare the students for precalculus and the study of calculus and other mathematics courses that require the knowledge of trigonometry at the college level.  Students will be exposed to ample real world problems, and a practical mathematical symbolic approach to solving them.  The critical thinking skills developed in this course will be transferable to other discipline areas like physics and environmental science.  Students will be given daily homework assignments and assessed with quizzes and tests as well as a cumulative exam.  Students will be required to have a TI-83/84 Calculator.
Maumee Valley Country Day School is the only age 3 - 12th grade accredited, co-educational, independent school in Northwest Ohio and Southeast Michigan.