Academics

2008-2009 IB GROUP 5: MATHEMATICS

The mathematics department of Verde Valley School believes that not only should a high school mathematics curriculum prepare students for further mathematical studies, the material learned should also be applicable to everyday situations.  The department realizes that every student learns material in different ways; as a result, the rule of four is the cornerstone to instruction.  Students will be exposed to and demonstrate understanding of the material graphically, numerically, analytically, and verbally.  The use of various technology has greatly enhanced the ability of the classroom teacher to effectively demonstrate or allow students to explore concepts graphically and numerically, which allows students to make their own generalizations.  While the mathematics department covers all of the core material that is required for a rigorous college preparatory math curriculum, it also endeavors to create a spirit of exploration and discovery of concepts that are beyond the traditional curriculum and are perhaps more personal, thereby creating a more lasting impression on the student.

2008-2009 IB GROUP 5: MATHEMATICS COURSES

9th and 10th Grade Courses:

Integrated Math I – Full-year course – graduation requirement

Integrated Math I, the first of a standards-based mathematics curriculum, integrates topics from number sense, geometry and algebra. This course provides numerous opportunities for real world applications. Throughout, students will continue to develop their language of mathematics which is so important for IB success. The TI-nspire graphing calculator is required.

For those familiar with the standard American high school math courses, Integrated Math I may be considered a hybrid Algebra I/Geometry course which focuses on pre-requisite skills necessary for success in IB math courses.

Number sense topics include determining reasonable solutions, converting standard and scientific notation, and unit measurement conversions.

Geometric topics include area and volume models, congruence, similarity, and transformations. Students will connect and analyze shapes and representations in the physical world. Geometric properties will be used to analyze the attributes and properties of two and three-dimensional shapes and to develop mathematical arguments about their relationships. Students will specify and describe spatial relationships using coordinate geometry, theorems and other representational systems.

Algebra topics include functions, domain and range, factoring, linear and quadratic graphing, distance and midpoint formulas, monomials, radical and rational expressions. Students will use variables to create, manipulate and solve algebraic equations. Algebraic thinking is encouraged through numerical, graphical, symbolic, and verbal means. Students will use tables and graphs to analyze patterns, and interpret linear equations and inequalities. Students will study polynomial equations and their graphs, if time permits.

Integrated Math II – Full-year course – graduation requirement
Integrated Math II is the second year of a standards-based mathematics curriculum. This course integrates topics from number sense, probability, statistics, algebraic functions, geometry, algebra, geometry, logic and discrete math to provide for a continual development in the language of mathematics. Students will be introduced to trigonometry. This varied curriculum provides numerous opportunities for real world applications. The TI-nspire or the TI-84 graphing calculator is required.

For those familiar with the standard American high school math courses, Integrated Math II may be considered a hybrid Algebra II/Geometry course which focuses on pre-requisite skills necessary for success in IB math courses.

Number sense topics include the concept of understanding and applying numbers, ways of representing numbers, the relationships among numbers and different number systems, and the concept of using estimation strategies reasonably and fluently.

Probability focuses on recording data from a probability experiment to compare the outcome with predictions made prior to performing the experiment, i.e. real vs. experimental probability. Other probability topics include permutations, combinations, combined events, tree diagrams, sampling with and without replacement, and conditional probability.

Statistics focuses on understanding and applying data collection, data organization and data representation to analyze and sort data, including measures of central tendency. Statistics from technology is part of this course.

Algebra topics focus on representing and analyzing mathematical situations and structures using algebraic representations. Algebra topics include rational expressions, functions and relations, exponential functions, logarithms, quadratics, polynomials, and imaginary numbers. Algebraic thinking is encouraged through numerical, graphical, symbolic, and verbal means.

Geometry builds upon students’ understanding of the physical world through a more formal structure, i.e. proofs. Students will use logic, reasoning, mathematical proofs and precise language to evaluate situations and select problem-solving strategies for plane figure properties. Using reasoning and proof, students discover a multitude of properties and connections among geometric concepts.

Logic focuses on algorithms and algorithmic thinking and the concept of using reasoning to solve mathematical problems in contextual situations.

Algebra II – Full-year course - graduation requirement
This course prepares students for Pre-Calculus, Trigonometry or IB Math SL. Using algebraic manipulation, graphing and application, students will extend their understanding of algebra and functions. Students will master algebraic methods and properties so as to use mathematical modeling to solve problems.

Students will analyze and interpret the behavior and nature of the following functions: linear, quadratic, polynomial, rational, radical, exponential, logarithmic, absolute value, and piece-wise. Students will learn systems of equations, matrices, vectors, sequences, series, conics, and data analysis.

Algebraic thinking is encouraged through numerical, graphical, symbolic, and verbal means. The TI-nspire or the TI-84 graphing calculator is required.

Pre-Calculus– Full-year course

This course prepares students for IB Math HL, IB Math SL or AP Calculus AB. One semester will be dedicated to trigonometry, while the second semester will go deeper into functions: linear, quadratic, polynomial, rational, radical, exponential, logarithmic, absolute value, and piece-wise. Students will increase their understanding of systems of equations, matrices, vectors, sequences, series, conics, and data analysis. For example, students will learn linear programming, which is an advanced systems of equations topic.

Algebraic thinking is encouraged through numerical, graphical, symbolic, and verbal means. The TI-nspire or the TI-84 graphing calculator is required.

11th and 12th Grade IB Group 5 Mathematics Courses:

Standard Level Mathematics – Two-year sequence
IB Math SL is a two-year course offered to students who recognize a need for a sound background in mathematics for their future studies. These students have a thorough knowledge of college preparatory mathematics.

IB Math SL consists of seven core areas: 1) algebra, 2) functions and equations, 3) circular functions and trigonometry, 4) matrices, 5) vectors, 6) statistics and probability, and 7) calculus.

First year IB Math SL year covers trigonometry, and reviews pre-calculus topics, i.e. math areas 1 thru 5 above. Second year IB Math SL covers limits, continuity, differential and integral calculus, probability and statistics. The calculus component compares to first semester college calculus.

IB Math SL requires that students focus on written English language skills through written papers and projects. Students will write two math research papers their first year and two their second year. These allow students to increase their understanding of mathematical concepts and processes through mathematical writing. The best two math papers will be submitted to the IB for diploma consideration.

At the end of the second year, students sit for the IB Math SL Exam, which covers the entire two year course. To earn the IB Diploma, the IB Math SL exam counts as 80% of their IB Math SL grade, while the student’s best two research papers count as 20%. This grade is separate from the Verde Valley School IB Math SL course grade which depends only on work performed throughout the year. It is possible for a student to pass the VVS course and fail the IB written exam.

A graphing calculator is required: either the TI-nspire or the TI-84 graphing calculator. The TI-nspire is versatile in that it can be used as a TI-84 and is recommended. The TI-84 Silver Plus is also recommended.


Higher Level Mathematics – Two-year sequence
IB Math HL is for students who intend math-related careers in such areas as science, engineering or business. These students have a strong interest in mathematics and enjoy the challenge of engaging problems. IB Math HL is a rigorous, two-year course that requires college-level performance and work habits, i.e. late work receives a grade of zero.

IB Math HL includes seven core areas: algebra, functions and equations, circular functions and trigonometry, matrices, vectors, statistics and probability, and calculus. These are the same IB Math SL math areas but in IB Math HL, each topic is covered in much greater depth. The calculus component may be compared to AP Calculus AB, equivalent to first semester college calculus. Due to the greater number of topics, IB Math HL students sit for one additional math class each week.

In addition, students also must complete one of the following four option areas: statistics and probability, sets, relations and groups, series and differential equations, or discrete mathematics. Generally, discrete mathematics will be the IB Math HL option topic, but the option topic could change. For example, the option topic will be differential equations if a majority of students intend to study engineering.

IB Math HL requires that students focus on written English language skills through written papers and projects. Students will write two math research papers their first year and two their second year. These allow students to increase their understanding of mathematical concepts and processes through mathematical writing. The best two math papers will be submitted to the IB for diploma consideration.

At the end of the second year, students sit for the five-hour IB Math HL Exam, which covers the entire two year course. To earn the IB Diploma, the IB Math HL exam counts as 80% of their IB Math HL grade, while the student’s best two research papers count as 20%. This grade is separate from the Verde Valley School IB Math HL course grade which depends only on work performed throughout the year. It is possible for a student to pass the VVS course and fail the IB written exam.

A graphing calculator is required: the TI-nspire, TI-84 or TI-89 graphing calculator. The TI-89 is the most powerful but is not recommended because it is difficult to learn to use. The TI-84 is recommended.

IB Math Studies SL - Two-year sequence
IB Math SL is for IB students whose future careers will not include a focus on mathematics, such as the humanities. IB Math Studies SL will build confidence and encourage an appreciation of mathematics in students who do not anticipate a need for theoretical mathematics. Emphasis is placed on the application of mathematics to real-life situations. Students entering this course should have a good understanding of algebra, geometry, and foundational trigonometry.

IB Mathematical Studies SL includes these topics: introduction to the graphic display calculator, number and algebra, sets, logic and probability, functions, geometry and trigonometry, statistics, introductory differential calculus, and financial mathematics. Students learn how information is gathered, organized and analyzed by the use of statistical methods. Note: IB Math Studies SL includes statistics topics that are not in IB Math SL or IB Math HL; therefore, it should not be considered an "easier" math course.

Students must also complete a personal project, i.e. a statistical project. This project is an individual piece of work involving the collection of information and/or generation of measurements, and the analysis and evaluation of the information or measurements. This project will be submitted to the IB for diploma consideration..

At the end of the second year, students sit for the IB Math Studies SL Exam, which covers the entire two year course. To earn the IB Diploma, the IB Math Studies SL exam counts as 80% of their IB Math SL grade, while the student’s personal research paper count as 20%. This grade is separate from the Verde Valley School IB Math Studies SL course grade which depends only on work performed throughout the year. It is possible for a student to pass the VVS course and fail the IB written exam.

A graphing calculator is required: the TI-nspire, or the TI-84. Note that the TI-nspire may be used as a TI-84 calculator.