Magnet Program Math Course Offerings

Mathematics

The Magnet Mathematics Curricula provide opportunities and experiences for students to learn at an accelerated pace, broadening and deepening their understanding of concepts, integrated themes, and connections among the various branches of mathematics and other disciplines. Students use calculators, computers, and other tools for learning and doing mathematics. There e is an emphasis on higher-level thinking and problem solving that requires students to question, explore, reconceptualize, transform, and apply knowledge in a variety of ways. Students learn to read, write, and speak in the language of mathematics. They gain an appreciation of the economy, power, and elegance of mathematical notation and terminology and its role in the development and application of mathematical ideas.

Major mathematical topics and the underlying properties and structures of various mathematical systems are introduced in Grade 6 and revisited with extensions and connections in all of the magnet mathematics courses. The program aims to present mathematics as a unified whole rather than a field with isolated strands.

Magnet Math 6

This course provides a motivating and challenging experience for those who have completed all or a substantial part of the K-8 ISM curriculum. It is designed to provide a strong foundation for future magnet mathematics courses. The development of the language of mathematics, properties, and structures is stressed through the extension of familiar and new topics. Emphasis is placed on analysis, application, communication, and problem solving. Interdisciplinary connections within topics link mathematics/science/computer science through data collection and simulation, data manipulation and display, and data analysis.

Set Theory and Number Theory

The basic concepts of set theory are introduced using mathematical notation for representing sets of numbers and for describing operations such as intersection, union, complement, and difference. Venn diagrams are explored as a problem solving strategy. The set of rational numbers and its subsets are studied, including natural number subsets of primes, composites, factors, and multiples. Special types of numbers related to primes and composites, as well as theorems involving primes and composites, are included. Operations with rational numbers include basic operations, absolute value, and laws of exponents.

Number Relationships

Students represent and use numbers in a variety of equivalent forms including fraction, decimal, percent, exponential, and scientific notation. Analysis and calculations involving ratio and proportion are used in a variety of applied situations such as dimensional analysis. Students represent various number relationships in tables as well as one or two-dimensional graphs.

Operational Systems

Mathematical structure is introduced through the study of basic number properties. Students compare and contrast various combinations of finite and infinite systems by examining properties of groups and Abelian groups. Concurrently, students operate within the real number system, studying rational and irrational numbers in exponential and radical form, as well as within finite mathematical systems.

The Language of Algebra

Students use algebraic notation to create models that describe relationships and patterns. Emphasis is placed on translating verbal expressions and sentences into symbolic notation for problem solving situations. Students evaluate algebraic expressions, use algebraic formulae, and simplify simple polynomial expressions. Students solve equations and inequalities and graphically display representations of their solution sets. Matrices and basic matrix operations are also introduced.

Mappings and Relations

The study of mappings lays the groundwork for later examination of sequences and series, geometric transformations, and algebraic functions. Students learn to identify an assignment procedure that is a mapping and to name the domain, codomain, and range of a mapping. They work with one-to-one and onto mappings, find pre-images and images, and determine rules for inverse mappings. A new binary operation, composition, that is basic in the study of higher level mathematics is introduced. Students become acquainted with linear functions and function notation.

Probability and Statistical Analysis

Students collect, organize, display, and interpret data using a variety of presentations including stem and leaf, box and whiskers, scatter plots, and glyphs. Students conduct experiments simulating real world events to make connections between theoretical probabilities and the use of data to make predictions. The Fundamental Counting Principal, permutations, and combinations are formally introduced. Students learn to differentiate between simple, compound, dependent, and independent events and computation of probability and odds.

Geometry

Students use geometry as a means of describing relationships in the physical world. They learn to identify, describe, and classify geometric figures in one, two, and three dimensions. Students study properties and relationships of polygons and solids such as symmetry, congruence, and similarity. Measurements of figures including length, perimeter, area, surface area, and volume are calculated using appropriate formulas. Activities include building models of polyhedra and studying their characteristics. Fundamental transformations (reflections, rotations, translations, glide reflections, and dilations) are studied from an algebraic viewpoint as well as geometrically. Projects involving art and spatial sense are included.

Magnet Algebra

All of the traditional topics with their corresponding objectives from MCPS Algebra are included in Magnet Algebra 1 as well as extensions and enrichment with nontraditional algebraic content. The language of algebra, unifying mathematical properties and structures, real world problem solving, and interdisciplinary connections are emphasized. Students explore and analyze patterns and functional relationships using technology when appropriate.

Sets, Operations, and Mathematical Systems

Formal development of the vocabulary and notation regarding sets, operations, and mathematical systems is continued throughout the course. Familiar topics of sets, operations, and properties are broadened as students are introduced to the fundamental algebraic structures of groups, rings, fields, and ordered fields. The definitions, axioms, and theorems of these structures are developed in coordination with algebra. Students also explore matrix operations, properties, and applications.

Mappings, Relations, and Functions

Students examine the fundamental concepts of mappings, relations, and functions in conjunction with operations, properties, and basic structures. The concepts of sets and subsets lead to work with mappings and binary relations with an emphasis on functions. The study of functions includes discontinuous, continuous, step, and piece-wise functions. Students identify functions and one-to-one functions from algebraic rules and graphs.

Real World Data Analysis

The construction of graphical representations of real world data is an extension of the analysis begun in Magnet Math 6. Best fit lines and trend curves are used to describe relationships and make predictions. Students evaluate the validity of models produced with and without the aid of technology.

Linear, Quadratic, and Exponential Functions

Linear, quadratic, and exponential functions are studied in depth. Students compute the slope of a line, study various forms of linear functions, determine the equation of a line from given information, identify intercepts from equations and graphs, and find inverses of one-to-one functions. Students work with quadratic functions written in general and standard forms, and find the vertex, line of symmetry, and intercepts of quadratic functions. After operating with linear and quadratic functions, students explore exponential functions. They graph, study transformations of, identify properties relating to, and engage in problem solving applications involving all three types of functions.

Polynomial, Rational, and Irrational Expressions

The laws of exponents, including fractional and negative exponents, as well as theorems about radicals are used to simplify monomials and more complex expressions. Students simplify polynomials, factor binomials and trinomials, and operate with polynomials. They also perform operations with rational and irrational expressions.

Solving Open Sentences

Students begin by solving various types of equations and inequalities of the first degree. In addition, polynomial equations of degree three or more that can be solved by factoring are examined. Then quadratics are solved by factoring, completing the square, and using the quadratic formula. Open sentences involving absolute value, rational, exponential, and radical expressions are studied. Integrated strategies and algebraic modeling are used to solve systems of equations (linear/linear, linear/quadratic, and quadratic/quadratic) by the graphing, substitution, and elimination methods. Subsequently, students are introduced to systems of three equations with three variables.

Magnet Geometry

This course provides an in-depth study of geometry to students who have strong mathematical backgrounds and seek a rigorous, thoughtful approach to the subject. Geometry is studied in several forms: affine, coordinate, and the standard Euclidean geometry. Areas of emphasis include logic, reasoning, proper use of mathematical language and symbols, and problem-solving applications. In certain units, interdisciplinary activities link concepts studied in geometry class to applications in science and computer science.

Mathematical Reasoning

Throughout the course, students apply inductive and deductive reasoning skills to discover patterns, develop conjectures, and prove or disprove those conjectures. Beyond acquiring a broad knowledge of the content, students consider the "why's" and "how's" of geometry, e.g. “How can we prove this property holds in all cases? Why are certain axioms accepted as true and what happens if we do not accept them?” In class, discussion and debate of mathematical ideas are encouraged.

Proof

The study of proof begins with a unit on logic, an exploration of the laws fundamental to mathematical proof. Students then apply these laws of logic to writing direct and indirect proofs in several forms: paragraph, two-column, and flowchart. They also examine different ways of proving theorems; a theorem from coordinate geometry may reappear later in a unit on polygons, and other methods of proving it are explored. Students should be able to write rigorous proofs, a necessary skill for success in higher-level math courses, by the end of Magnet Geometry.

Mathematical Systems

Introduced in previous courses, the components of a mathematical system – axioms, undefined and defined terms, theorems, laws of logic – are revisited. Students begin at square one, with a set of axioms and undefined terms, and study how the components interact to build up the system. By defining new terms and proving theorems, students gain an understanding of how a mathematical system develops and can view mathematics as a process, not just a body of knowledge.

Geometric Figures in 2 and 3 Dimensions

The study of traditional Euclidean geometry begins with an examination of the properties of lines, angles, planes, triangles, and quadrilaterals. Students are familiar with some geometric properties from previous mathematics classes but now have the tools to prove them true. The study is extended to other polygons and circles as well as 3-D figures. In the spirit of classical geometry, students create constructions and discuss why the constructions work. Students also derive, verify, and apply formulas for angle measure, length, area, and volume of regular and irregular figures.

Similarity and Congruence

Relationships between geometric figures are a major theme of the geometry course. Students study methods of proving the similarity or congruence of triangles and other polygons. This topic is particularly rich in applications, giving students opportunities to apply their knowledge of similarity and congruence to solve word problems and determine heights, lengths, areas, and angles. Trigonometry is a natural outgrowth of the study of similar triangles where students learn the definitions of the trigonometric ratios, find values for special angles, and engage in problem-solving applications.

Algebra Connections

Throughout Magnet Geometry, students revisit and build upon concepts from Magnet Algebra 1. While studying affine geometry, students apply properties of mappings and relations to prove theorems about points, lines, and planes. The ability to solve equations and determine terms in a proportion is crucial for solving problems in the similarity unit. While studying coordinate geometry, students apply their knowledge of graphing to prove theorems about geometric figures. Overall, students should discover connections to algebra during every unit in Magnet Geometry.