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.
  • Algebra I

    Algebra I is the language through which most mathematics are communicated. Algebra I will begin to provide a means of operating with the concepts of variables, 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, 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 TI-83 or TI-84 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, linear functions and equations, matrices, quadratic functions, and polynomials. The latter half of the course covers a variety of other kinds of functions, including 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/TI-84 graphing calculator will allow for data analysis and creation of equations to model a variety of situations. In this course, students 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 BC

    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 AP Calculus, they 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. They also will find accumulated change in a function given its derivative: the idea of integration. AP Calculus is essentially one continuous topic, starting from an understanding of functions to limits, continuity, differentiation, integration, and applications in math, physics, and economics. For example, students will be able to find equations of tangent lines to approximate functions; find marginal cost and maximize profit; analyze motion along a line; find areas and volumes; and learn where all the formulas they learned in 5th Grade actually came from, such as the volume of a cone. The course takes an active approach in learning Calculus.

    Through explorations, experimentation, and activities, students will have a better intuitive understanding of calculus concepts, which they will then prove more formally. Students will use TI-83 or TI-84 calculators extensively to help them visualize functions and find solutions to problems that 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. This course uses 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. Students also will use AP classroom for additional problems and past AP questions. In the spring, students are required to take the Calculus Advanced Placement Exam.
  • 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. Students will often perform simulations, collect data, or do experiments to motivate and understand theorems, statistical procedures, and results. Students’ previous algebra skills and their concept of proofs 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 to be successful in this course. Students will demonstrate their knowledge through quizzes, tests, and individual or group projects and investigations. Students also will use AP classroom for additional problems and past AP questions. Students are required to take the AP Exam in the spring. A TI-83 or TI-84 graphing calculator is required.
  • Calculus I

    In this introductory 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, students 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. Students also will find accumulated change in a function given its derivative: the idea of integration. They will start from a review of precalculus topics without a calculator to gain a better understanding of functions. They will then study limits, continuity, differentiation, integration, and applications in math, physics, and economics. For example, students will be able to find equations of tangent lines to approximate functions, find marginal cost and maximize profit, analyze motion along a line, and find areas under curves. They will take an active approach in learning calculus.

    Through explorations, experimentation, and activities, students will have a better intuitive understanding of calculus concepts. They will not be under the same time constraint as AP Calculus, so they will focus instead on intuitive understanding and 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 that 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. This course uses Math XL, an online course management system. Students will be assigned problems and can access hints, practice problems, and PDF copies of chapters. 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.
  • College Algebra

    College Algebra is a course designed to examine the applied, real-world, and theoretical mathematical implications of the mathematical concept of any given function in detail. The symbolic, numerical, graphical, and narrative representations of the mathematical concept of a function introduced in previous math courses will be expanded and explored. In this class, students will learn about the building blocks of Calculus and Precalculus (called functions) and their properties, with a special focus on linear, quadratic, exponential, logarithmic, and trigonometric functions. The instructional strategies will vary throughout the year. Investigative and collaborative group activities, questioning for understanding and metacognition, guided practice, addressing students’ learning styles, scaffolding of classroom activities, and differentiation will be implemented in this course. In class, students are expected to work collaboratively on formative assessments, homework assignments, and quizzes. 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.
  • Geometry

    In the first semester, 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, and angles. They will be called upon to explain their ideas and justify their answers in rigorous ways using definitions, postulates, and theorems. At times, they will use informal explanation methods and at other times, 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 by 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 used regularly.
  • History of Math

    This intensive will focus on interesting historical topics in math. The whole history of math cannot be covered in three weeks, but we will explore interesting theories and the thought that went into them. Students will explore topics such as the history of numbers, constructions, Pythagoras' theorem, Zeno’s paradoxes, Pascal’s triangle and binomial expansions, number theory, conic sections, Platonic solids, inductive proofs, combinatorics, and series. We will spend time each day on problem-solving and on AMC (American Math Competition) problems as well as more advanced talent search questions. Near the end of the intensive, students will choose a topic we’ve touched on to explore in more detail or pick a new topic from the text or other sources to explore and report on.
  • Introduction to Probability and Statistics

    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.
  • Multivariable Calculus

    This course will extend students' knowledge of algebra and calculus to multi-dimensions. They will extend their knowledge of lines and vectors in two dimensions to equations of lines and planes in space. Their notation of derivative and integral will be extended to partial derivatives, tangent planes, and multiple integrals. Their previous work in 2 dimensions will be extended to n-dimensional space. They will also study vector calculus, including line and surface integrals. Students will use their graphing calculators as well as programs such as Wolfram Alpha to aid them in visualizing in 3 dimensions. 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 Web Assign, an online course management system. Students will be assigned problems in Web Assign and can access hints, practice problems, video explanations, and pdf copies of chapters. On Web Assign they will have the opportunity to redo problems they get incorrect. This course is equivalent to taking Calculus 3 in college.
  • Precalculus

    This advanced algebra course will concentrate on a variety of functions. The primary emphasis of the course 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, students 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.
Maumee Valley Country Day School is the only PreK-12th grade accredited, co-educational, and independent school in Northwest Ohio and Southeast Michigan.