# Mathematics

The mathematics program should ensure that all students have an opportunity to become mathematically literate, are capable of extending their learning, have an equal opportunity to learn, and become informed citizens capable of understanding issues in a technological society. Knowledge of mathematics is an essential element in the development of the whole person.

Mathematics is more than a collection of concepts and skills to be memorized and mastered. Mathematics includes problem-solving, reasoning, and communicating, as well as valuing the breadth of its connections. Thus, an appropriate mathematics curriculum includes the investigation of the connections and interplay among various mathematical topics and their applications at every grade level.

All students can become mathematically powerful. They can learn to formulate and solve problems with a variety of strategies, to verify and interpret results, and to generalize solutions. Their understanding of mathematical concepts can enable them to identify and generate examples and counter-examples as well as recognize the various meanings and interpretations of concepts. They can learn to use models, diagrams, and symbols to represent concepts and to translate from one mode of representation to another. They can recognize when a mathematical procedure is appropriate and reliably and efficiently execute procedures, including appropriate methods of computation. They can verify the results of procedures as well as generate new procedures and extend or modify familiar ones.

All students should be provided access to the full range of mathematical topics. Knowledge of patterns, relations, and functions; of geometry and measurement; of probability and statistics; and of increasingly important topics in discrete mathematics are a necessary foundation for all students. Since students' interests, goals, and achievements change as they mature and advance through school, the mathematics program should be designed to keep options open. While recognizing that individuals have different career objectives, and may well pursue careers as yet undefined, we acknowledge that all students have the right to learn significant mathematics and to develop power over mathematical ideas.

The goals of the mathematics program are that all students:

• learn to value mathematics;
• become confident in their ability to do mathematics;
• become mathematical problem-solvers;
• learn to communicate mathematically; and
• learn to transfer mathematical skills to other areas in the curriculum.

### Elementary

Today's technologically sophisticated world requires a greater mastery and understanding of mathematical concepts and skills than ever before. The latest curriculum materials are used in teaching, and concepts are taught as far as possible through concrete experiences, so that children encounter in a natural way the basic mathematical ideas that exist in their environment. The students at ISA receive a thorough programme in mathematics that incorporates a wide spectrum of subjects from the basic four operations to topics such as geometry, measurement, and fractions. Instruction in math also includes regular opportunities to practice previously taught skills, as well as exercises that challenge students to extend the knowledge they have at the start of each lesson. At all stages, students develop their problem solving skills and are encouraged to use mathematics in practical situations.

### Middle School

#### Math 6

The sixth grade Mathematics course develops, maintains and applies skills introduced during the Elementary School years, as well as introducing them to new concepts which will be further developed over the next few courses. This course encourages and enables students to gain confidence in their own mathematical abilities, as well as teaches them how to effectively communicate and apply their knowledge to both theoretical and practical situations. In this course, students will study the following topics: Number Systems; Operations with Whole Numbers; Points, Lines & Angles; Number Properties; Geometric Shapes; Fractions; Decimal Numbers; Percentages; Integers; Area & Volume; Transformations and Coordinate Geometry. Finally, students will also review and study aspects of measurement systems and time.

#### Math 7

This course will cover topics introduced in early courses with more in-depth study: fractions, decimals, geometry, percentages, ratios, and proportions. Students will also be introduced to several new concepts of Algebra including the use of integers, algebraic expressions, and equations. Problem-solving and critical thinking skills are emphasised throughout the course. The purpose of Math 7 is to reinforce a sound mathematical foundation, which will allow the student to progress to higher mathematics courses that involve more abstract thought processes.

#### Math 8 Core

This course is designed to provide students with a strong mathematical foundation and build student’s mathematical confidence. Students will explore working with single and multi-step algebraic equations in addition to continuing to review pre-algebra skills. An emphasis is placed on the understanding of process over memorisation of pattern, whilst developing numeracy skills. Students further explore the topics of integers, exponents, fractions, rational and irrational numbers, mathematical properties, number theory, ratios, proportions, percentages, graphing, probability and geometry. The focus of this course is not only on computation but also problem-solving and logical thinking.

#### Math 8 Extended

This course is designed to provide a foundation for IB and IGCSE math courses and to teach students to be successful at solving mathematical problems. Emphasis is placed on problem-solving in the context of real-life situations as well as integrating technology into everyday life and using it as a problem-solving tool. Some of the topics covered include: properties of the real numbers; graphing and solving linear equations and inequalities; the concept of a function; quadratic and exponential expressions and radicals; and connections with geometry.

### High School

#### Maths 9 Core (Algebra & Geometry)

1 credit

Prerequisite: Maths 8C or 8E

This course is the first of two in a sequence designed for students whose primary interests may be more in the humanities and soft sciences. Students will acquire and develop foundational mathematical skills and learn to apply them to other subjects and to real world problems. Students should have, and will be expected to use a graphing calculator on a regular basis. The first portion of the IGCSE International Mathematics 0607 Core syllabus will be studied. Topics of coverage will include, but not necessarily limited to, number, algebra, functions, geometry, two-dimensional transformations, mensuration and coordinate geometry.

#### Maths 9 Extended (Algebra & Geometry)

1 credit

Prerequisite: Maths 8C or 8E

This course is the first of two in a sequence designed for students that enjoy the challenge of a more rigorous math course, whose foundational math skills are in place, and whose interests may lie more in business administration, chemistry, physics, biology, engineering and mathematics. Students must be willing to accept the challenge of a more rigorous math course and the rapid pace that comes along with it. Students will acquire and further develop mathematical skills and learn to apply them to other subjects and to real world problems. Students should have, and will be expected to use a graphing calculator on a regular basis. The first portion of the IGCSE International Mathematics 0607 Extended syllabus will be studied. Topics of coverage will include, but not necessarily limited to, number, algebra, functions, geometry, two-dimensional transformations, mensuration and coordinate geometry.

#### Maths 10 Core (Algebra & Geometry)

1 credit

Prerequisite: Maths 9C or 9E

This course focuses primarily on developing a thorough understanding of algebraic topics and techniques and applying algebraic, geometric and technological approaches to solve problems. Many topics previously introduced in Algebra Geometry 9C are reviewed and extended in order to prepare students for the demands of IB mathematics courses. Emphasis is placed on utilising a variety of mathematical concepts and skills to solve problems. Some of the topics covered include: study of number systems; graphing and solving linear and quadratic equations and inequalities; systems of equations and inequalities; analysis of a range of functions – linear, quadratic, square root, absolute value, and exponential; operations with polynomial, exponents and radicals; sequences and series; basic trigonometry; and an introduction to probability and statistics. In this course the student will become proficient in utilising technological tools such as graphing calculators in their mathematical work.

#### Maths 10 Extended (Algebra & Geometry)

1 credit

Prerequisite: Maths 9E

This course is the second of two in a sequence designed for students that enjoy the challenge of a more rigorous math course, whose foundational math skills are in place, and whose interests may lie more in business administration, chemistry, physics, biology, engineering and mathematics. Students must be willing to accept the challenge of a more rigorous math course and the rapid pace that comes along with it. Students will acquire and further develop mathematical skills and learn to apply them to other subjects and to real world problems. Students should have, and will be expected to use a graphing calculator on a regular basis. The second portion of the IGCSE International Mathematics 0607 Extended syllabus will be studied. Topics of coverage will include, but not necessarily limited to, trigonometry, sets, functions, probability and statistics.

#### IB Mathematical Studies (SL)

2 credits/2 years

Prerequisite: Maths 10C or 10E

This course is available only at standard level, and is equivalent in status to mathematics SL, but addresses different needs. It has an emphasis on applications of mathematics, and the largest section is on statistical techniques. It is designed for students with varied mathematical backgrounds and abilities. It offers students opportunities to learn important concepts and techniques and to gain an understanding of a wide variety of mathematical topics. Students taking this course are well prepared for a career in social sciences, humanities, languages or arts. These students may need to utilize the statistics and logical reasoning that they have learned as part of the mathematical studies SL course in their future studies.

#### IB Mathematics Standard Level

2 credits/2 years

Prerequisite: Maths 10C or 10E

IB Mathematics Standard Level is a rigorous two-year course designed for students who already possess knowledge of basic mathematical concepts, and who are equipped with the skills needed to apply mathematical techniques correctly. The course allows students to study and investigate the following mathematical topics: functions; number theory and related topics; algebra, geometry and trigonometry; vectors; differential and integral calculus; probability and statistics. It is intended to provide a solid mathematical basis for those students planning to pursue further studies in such fields as chemistry, economics, biology and business administration.

#### IB Maths HL

2 credits/2 years

Prerequisite: Maths 10E and teacher recommendation

IB Mathematics Higher Level is a rigorous two-year course intended for students with a strong background in mathematics and who are competent in a range of analytical and technical skills. The majority of these students will be expecting to include mathematics as a major component of their university studies, either as a subject in its own right or within courses such as physics, engineering and technology. Others may take this subject because they have a strong interest in mathematics and enjoy meeting its challenges and engaging with its problems. Topics covered include: differential and integral calculus; advanced calculus topics such as power series; further integration techniques; probability and statistics; complex numbers; and vector geometry.

#### IB Mathematics: Application & Interpretation SL and HL (from Aug 2019)

2 credits/2 years

Prerequisite: For SL: 10 C or 10 E For HL: 10 E and teacher recommendation

This course recognizes the increasing role that mathematics and technology play in a diverse range of fields in a data-rich world. As such, it emphasizes the meaning of mathematics in context by focusing on topics that are often used as applications or in mathematical modelling.

The course makes extensive use of technology to allow students to explore and construct mathematical models and will develop mathematical thinking, often in the context of a practical problem and using technology to justify conjectures.

Students who wish to take the applications and interpretation course at HL will need solid algebraic skills and should get pleasure and satisfaction when exploring challenging problems. They must also be committed to putting additional time into their studies of mathematics.

The five topics of study for both the HL and SL course are: Number and algebra, functions, geometry and trigonometry, statistics and probability, and Calculus. It should be noted that the SL course is a subset of the HL course.