Aims
The aims of the teaching and study of mathematics are to encourage and enable students to:
 develop inquiring minds and curiosity about mathematics
 acquire knowledge, conceptual understanding and skills to solve problems and make informed decisions
 develop skills of inquiry to design and carry out investigations and evaluate evidence to draw conclusions
 communicate mathematical ideas, arguments and practical experiences accurately in a variety of ways
 think analytically, critically and creatively to solve problems, judge arguments and make educated decisions
 appreciate the benefits and limitations of mathematics and its application in technological developments
 demonstrate attitudes and develop values of honesty and respect for themselves, others, and their shared environment.
Objectives
The objectives of mathematics listed below are final objectives and they describe what students should be able to do by the end of the course. These objectives have a direct correspondence with the final assessment criteria
A. Number
Numercy is an essential skill. A numerate has an understanding of number concepts and the skills of estimation and calculation.
Students should understand that numercy is a form of communication which has developed since humankind’s earliest beginnings, and that the evolution of mathematics is multicultural.
Number Concepts:
Level 
Concepts 
Mathematics 
 Forms of numbers (eg: numerals, decimals, standard form
 Ordinality
 Cardinality
 Pattern
 Number sets
 Magnitude
 Irrationals
 Sequences and higherlevel number sets
 Surd form (rationals)
 Logarithms

Extended mathematics 

Number Skills:
Level 
Skills 
Mathematics 
 Performing basic operations
 Estimating
 Approximating
 Renaming
 Classifying
 Apportioning
 Performing and discussing problemsolving strategies
 Communicating and reasoning orally and in writing
 Writing and solving problems involving the concepts at this level
 Performing higherlevel operations (other binary operations, powers and roots with degree equal to or greater than 3)
 Performing and discussing higherlevel problemsolving strategies
 Communicating and reasoning orally and in writing using mathematical language and conventions
 Writing and solving problems involving the concepts at this level

Extended mathematics 

B. Algebra
An understanding of pattern recognition is fundamental to further learning in mathematics. Students who wish to continue studying mathematics beyond MYP will require a knowledge of algebraic concepts and skills and apply them in practical and everyday situations.
Algebra Concepts:
Level 
Concepts 
Mathematics 
 Numerals and variables
 Relations, functions and their graphical representations
 Expressions
 Equations
 Coordinate systems
 Repeated addition as multiplication
 Repeated multiplication as exponents
 Inequalities
 Sequences – recursive and generative rules
 Coordinates systems in three dimensions
 Matrices
 Logarithms
 Higherlevel relations, functions and their graphical representations – exponential, logarithmic, circles, rational

Extended mathematics 

Algebra Skills:
Level 
Skills 
Mathematics 
 Expanding – linear and quadratic
 Factoring – linear and quadratic
 Simplifying
 Substituting
 Solving equations – linear, simple quadratic, simultaneous – by a variety of methods including the use of graphing calculators
 Sketching and interpreting graphs
 Performing and discussing problemsolving strategies
 Communicating and reasoning orally and in writing
 Writing and solving problems involving the concepts at this level
 Solving higherlevel equations including more difficult quadratics and simultaneous equations
 Manipulating rational and logarithmic expressions
 Performing and discussing higherlevel problemsolving strategies
 Communicating and reasoning orally and in writing using mathematical language and conventions
 Writing and solving problems involving problems at this level

Extended mathematics 

C. Geometry and Trigonometry
The study of geometry and trigonometry enhances spatial awareness and gives insights into the realms of construction and navigation. Teachers and students should not limit their study to Euclidean geometry, but should be familiar with other geometries such as:
 transformation geometry – cultural and social use and its appearance in nature
 fractal geometry – iterative constructions
 nonEuclidean geometry – global navigation and topology and its relationship to discrete mathematics.
Geometry and Trigonometry Concepts:
Level 
Concepts 
Mathematics 
 Shapes and their properties
 Measuring
 Similarity and Congruence
 Isometric Transformations
 Enlargement
 Angles
 Pythagoras’ theorem
 Trigonometry including the use of graphs
 Vectors
 Nets
 Similarity and congruence theorems
 Nonisometric transformations
 Trigonometric identities
 3D coordinate and vector spaces
 Trigonometric graphs

Extended mathematics 

Geometry and Trigonometry Skills:
Level 
Skills 
Mathematics 
 Naming and classifying
 Applying area/volume formulae
 Constructing
 Rotating, reflecting, translating, and enlarging
 Solving problems by applying Pythagoras’ Theorem, trigonometric ratios and rules, properties of shapes and angles
 Performing and discussing problemsolving strategies
 Communicating and reasoning orally and in writing
 Writing and solving problems involving the concepts at this level
 Justifying theorems for congruence, similarity, shape and angles
 Justifying simple trigonometric identities and applying them to solve problems
 Performing and discussing higherlevel problem solving strategies
 Communicating and reasoning orally and in writing using mathematical language and conventions
 Writing and solving problems involving the concepts at this level

Extended mathematics 

D. Statistics and Probability
Statistical literacy is an awareness and understanding of the concepts and skills involved in collecting, collating and analyzing data. Students will use these skills in their investigations and use a variety of technologies. They will become aware of both the power and limitations of statistics used to support and counter opinions and propaganda, how statistics may serve to emancipate and oppress, and how statistics may be used to both inform and misinform.
Students will become aware of the difference between what happens in theory (probability) and what is observed to happen (statistics).
Statistics and Probability Concepts:
Level 
Concepts 
Mathematics 
 Discrete and continuous data
 Qualitative and quantitative data
 Graphical analysis and graphical representation
 Mathematical analysis
 Sampling
 Probability
 Measures of central tendency (e.g. mean, mode, median)
 Two variables data
 Linear regression
 Normal distribution
 Conditional probability
 Measures of spread (e.g. standard deviation)

Extended mathematics 

Statistics and Probability Skills:
Level 
Skills 
Mathematics 
 Sampling
 Constructing plots and graphs appropriately
 Calculating and locating statistics
 Making inferences and drawing conclusions
 Calculating probabilities of simple events
 Performing and discussing problemsolving strategies
 Communicating and reasoning orally and in writing
 Writing and solving problems involving the concepts at this level
 Analyzing timeseries data and other bivariate data
 Calculating probabilities of combined and conditional events
 Making inferences about statistical analyses and probability
 Performing and discussing higherlevel problemsolving strategies
 Communicating and reasoning orally and in writing using mathematical language and conventions
 Writing and solving problems involving the concepts at this level

Extended mathematics 

E. Discrete Mathematics
An understanding of systems has become increasingly important for people to effectively participate in today’s postindustrial/technological age.
Students should develop a sense of logic and be able to articulate this through Venn diagrams, structure diagrams and flow charts. This is a major contribution by mathematics to approaches to learning in the MYP.
Discrete mathematics is a relatively new branch of mathematics which has its roots in abstract algebra and has adopted the language and notations of graph theory. Students should be aware of the realworld applications of discrete mathematics which may include road or rail networks, computer networks, communication networks, optimal routes, time and projectmanagement techniques and critical path analysis.
Discrete Mathematics Concepts:
Level 
Concepts 
Mathematics 
 Sets
 Venn Diagrams
 Logic
 Trees
 Networks
 Topology
 Directed Networks

Extended mathematics 

Discrete Mathematics Skills:
Level 
Skills 
Mathematics 
 Performing set operations
 Constructing logical diagrams
 Locating paths and tours
 Solving problems involving optimal solutions
 Performing and discussing problemsolving strategies
 Communicating and reasoning orally and in writing
 Writing and solving problems involving the concepts at this level
 Classifying and describing topological objects
 Performing and discussing higherlevel problemsolving strategies
 Communicating and reasoning orally and in writing using mathematical language and conventions
 Writing and solving problems involving the concepts at this level

Extended mathematics 
