Mathematics

Our Mathematics programme nurtures critical thinking and problem-solving skills, empowering students to apply mathematical concepts in real-world contexts.

Through a balanced approach to theory and application, learners build confidence in tackling challenges and exploring innovative solutions across diverse domains.

Early Years Programme

Primary Years Programme

Middle Years Programme

Diploma Programme

Early Years Programme

Foundational Concepts of Mathematics

Early Years Mathematics introduces young learners to foundational concepts through engaging, hands-on experiences that spark curiosity and build confidence.

By exploring patterns, shapes, numbers, and measurement in playful and meaningful contexts, children develop essential problem-solving skills and a love for mathematical thinking that serves as a strong foundation for future learning

Grade 3

Content:

Design Cycle/Design Process
Problem / issue identification
Design proposal
Idea/solution generation
Testing methods
Success evaluation
Improvement explanation

Skills

Creating/editing of 2D graphics
Presenting / communicating
Producing and editing film
Developing brand / identity
Using structure as function

Early Years 3

Content

Numbers and Number Systems

Introduction to various forms of numbers
Basic understanding of number systems

Estimation and Counting

Estimating groups up to five
Exploring counting methods and quantities

Measurement

Introduction to non-standard units of measurement
Understanding time as a unit of measurement

Mathematical Vocabulary

Introducing basic terms and language used in mathematics

Data Handling

Introduction to collecting data
Understanding and interpreting basic data collections

Geometry

Identifying basic 2D shapes
Understanding positional language

Problem Solving

Introduction to mathematical problem-solving methods and approaches

Skills

Numeracy Skills

Using number words and numerals to represent quantities in real-life situations
Counting with and without the aid of physical objects

Comparison

Recognizing and comparing sets or quantities to determine if they’re equal, more, or less than another set
Using language terms like “first” and “last” to determine positions

Addition and Subtraction Concepts

Relating addition to combining objects and subtraction to taking objects away
Basic understanding of one-to-one correspondence

Geometric Understanding

Describing and organizing shapes based on their properties

Temporal Skills

Identifying events using temporal terms
Sequencing events in order

Data Interpretation

Collecting and organizing information to derive meaning
Describing data and understanding basic data representations

Early Years 4

Content

Numbers and Number Systems

Introduction to forms of numbers
Basic understanding of number systems

Estimation and Counting

Estimating groups of objects
Introduction to fractional parts in making a whole

Measurement

Exploring non-standard units of measurement
Delving deeper into time as a unit of measurement

Mathematical Vocabulary

Further enhancing basic terms and language used in mathematics

Data Handling

Introduction to data collection
Recognizing and naming basic 2D shapes

Geometry

Enhancing understanding of positional language

Problem Solving

Using mathematical approaches to solve basic problems

Skills

Numeracy Skills

Using number words and numerals to represent real-life quantities
Estimating objects up to five
Rote counting up to 20 without objects

Comparison and Quantity Judgement

Recognizing sets or quantities and determining if they’re equal to, more than, or less than another set
Understanding position with terms like “first” and “last”

Basic Arithmetic Concepts

Modeling simple joining and separating of whole numbers
Relating addition to the combination of objects and subtraction to taking objects away

Geometric and Spatial Understanding

Describing and categorizing shapes based on their properties
Recognizing events and sequencing them

Data Interpretation

Collecting and understanding information to grasp the world around
Organizing and interpreting data collections

Problem-Solving Skills

Identifying and analyzing problems

Early Years 5

Content

Numbers and Number Systems

Deepening understanding of forms of numbers and number systems
Enhancing the application of mathematical language

Basic Arithmetic

Concepts of addition and subtraction with the integration of number lines

Estimation and Evaluation

Building proficiency in estimating and evaluating sets of objects
Introducing the concept of fractions

Measurement

Grasping non-standard units of measurement
Understanding time as a measure

Patterns and Geometry

Recognizing and describing patterns
Identifying and categorizing 2D shapes

Data Interpretation

Introduction to data handling, sampling techniques, and graphical representations

Spatial Understanding

Grasping concepts related to space and position

Probability

Basic understanding of probability and chance events.

Skills

Numeracy Skills

Identifying and vocalizing numbers from 0 to 30
Counting objects in a set
Comparison of quantities using terms like “more,” “less,” “first,” “equals,” etc.

Arithmetic Skills

Employing ordinal numbers in real scenarios
Modeling subtraction using objects and writing number sentences
Solving basic arithmetic problems using number lines

Estimation and Measurement

Estimating quantities in a set of 20 or less
Recognizing quantities without counting (subitizing)
Exploring fractions in daily scenarios
Comparing objects using comparative terms
Measuring with non-standard units

Time and Sequence

Sequencing events and understanding measurement instruments like clocks
Reading time in both digital and analog formats

Classification and Patterns

Sorting objects based on attributes
Recognizing patterns in everyday scenarios

Geometric and Spatial Understanding

Identifying common 2D shapes
Using positional language to place and describe objects

Data Interpretation

Collecting and organizing data
Using tally marks for data representation

Probability

Estimating the likelihood of events

Primary Years Programme (PYP)

Mathematics Progression Strands Code

Term	Code
Number and place value	NPV
Number Facts	NF
Addition and subtraction	AS
Multiplication and division	MD
Fractions	F
Geometry (shape and space)	G
Command Terms	CT
MAP Testing Relevant Practice	MAP

Grade 3

Content:

Design Cycle/Design Process
Problem / issue identification
Design proposal
Idea/solution generation
Testing methods
Success evaluation
Improvement explanation

Skills

Creating/editing of 2D graphics
Presenting / communicating
Producing and editing film
Developing brand / identity
Using structure as function

Grade 1

Content

Numbers and Number Sense

Introduction to numbers up to 100
Basic number lines

Estimation and Counting

Estimating numbers in a group of 100 or less
Counting to evaluate the reasonableness of the estimate

Fractions and Parts of a Whole

Introduction to halves, thirds, and fourths
Recognizing these fractions in different contexts

Measurement

Exploring non-standard units of measurement
Comparing and ordering objects based on length, capacity, and mass

Time and Calendar

Months of the year, weeks, and days
Telling time using digital and analogue clocks

Patterns and Functions

Recognizing, creating, and explaining repeating patterns
Completing basic number sentences using addition or subtraction

Geometry

Introduction to 2D and 3D shapes
Classifying shapes based on properties

Position and Direction

Understanding positional words (up/down, left/right)
Basic introduction to directions (North, East, South, West)

Data Handling

Collecting, organizing, and interpreting data
Introduction to data display methods (tallies, tables, bar graphs)

Probability

Understanding chance in daily events
Predicting outcomes based on simple data

Skills

Numeracy Skills

Reading, writing, and comparing numbers
Decomposing numbers
Estimating and counting objects in groups

Fractional Understanding

Identifying basic fractions as part of a whole or group using models

Measurement Skills

Using non-standard units of measurement in real-life scenarios
Identifying and using standard units of measurement
Identifying measurement tools

Time Management

Recognizing the sequence of days, weeks, months, and understanding the calendar
Telling time to specific intervals (e.g., half and quarter hours)
Telling time on analog and digital clocks

Pattern Recognition

Classifying objects based on attributes
Understanding and creating repeating patterns

Geometric Understanding

Naming, sorting, and sketching 2D shapes
Identifying, classifying, and drawing 3D shapes
Describing locations and movements using positional terms

Data Handling and Interpretation

Organizing and interpreting data in various formats
Displaying data using graphs
Predicting outcomes based on collected data

N1.1.(NPV). Number and Place Value (NPV)

Count within 100, forwards and backwards, starting with any number
Reason about the location of numbers to 20 within the linear number system, including comparing using <, >, and =

N1.2.(NF). Number Facts

Develop fluency in addition and subtraction facts within 10
Count forwards and backwards in multiples of 2, 5, and 10, up to 10 multiples, beginning with any multiple, and count forwards and backwards through the odd numbers

N1.3.(AS). Addition and Subtraction

Compose numbers to 10 from 2 parts, and partition numbers to 10 into parts, including recognising odd and even numbers
Read, write, and interpret equations containing addition (+), subtraction (-), and equals (=) symbols, and relate additive expressions and equations to real-life contexts

N1.6.(G). Geometry

Recognise common 2D and 3D shapes presented in different orientations, and know that rectangles, triangles, cuboids, and pyramids are not always similar to one another
Compose 2D and 3D shapes from smaller shapes to match an example, including manipulating shapes to place them in particular orientations

N1.7.(CT). Command Terms

Term	Command Term
Number	Represent
Pattern and Function	Describe
Shape and Space	Investigate
Data Handling	Sort
Measurement	List

N1.8.(MAP). MAP Testing Relevant Practice

(n/a)

Grade 2

Content

Number and Arithmetic

Understanding forms of numbers and number systems
Mastery of basic arithmetic operations: addition, subtraction, multiplication, and division
Application of arithmetic in problem-solving and estimation

Advanced Number Concepts

Dive into fractions, decimals, ratios, and proportions

Measurement and Time

Grasping concepts of measurement using different units
Time as a tool of measurement

Algebra and Patterns

Introduction to basic algebraic concepts
Recognizing and describing patterns

Geometry

Exploring the world of shapes and coordinate geometry
Introduction to symmetry

Data and Probability

Fundamental skills in data handling
Basic understanding of statistics, probability, sampling techniques, and graphical representation

Skills

Numeracy Skills

Mastery of numbers up to 1000: reading, writing, comparing, and ordering
Advanced understanding of place value
Subtracting 2-digit numbers using various methods, including regrouping
Mental arithmetic skills for simple addition and subtraction

Arithmetic Proficiency

Modeling multiplication as repeated addition with quick recall for certain multiplication tables
Familiarity with division through sharing and repeated subtractions
Using models and number lines for arithmetic problem-solving

Measurement and Estimation

Rounding numbers and analyzing their reasonableness
Mastery of measurement using standard units
Telling time accurately using different types of clocks

Geometric Understanding

Classifying objects by multiple attributes
Recognizing and sketching 2D shapes and regular polygons
Identifying points on a grid using ordered pairs
Grasping properties of reflective symmetry

Data Interpretation

Gathering data using various methods
Organizing and interpreting structured data
Displaying data through various graphical methods

Probability

Identifying and describing chance events in daily scenarios

N2.1.(NPV). Number and Place Value (NPV)

Recognize the place value of each digit in two-digit numbers, and compose and decompose two-digit numbers using standard and non-standard partitioning
Reason about the location of any two-digit number in the linear number system, including identifying the previous and next multiple of 10

N2.2.(NF). Number Facts

Secure fluency in addition and subtraction facts within 10, through continued practice

N2.3.(AS). Addition and Subtraction

Add and subtract across 10
Recognize the subtraction structure of ‘difference’ and answer questions of the form, “How many more…?”
Add and subtract within 100 by applying related one-digit addition and subtraction facts: add and subtract only ones or only tens to/from a two-digit number
Add and subtract within 100 by applying related one-digit addition and subtraction facts: add and subtract any two 2-digit numbers

N2.4.(MD). Multiplication and Division

Recognize repeated addition contexts, representing them with multiplication equations and calculating the product within the 2, 5, and 10 multiplication tables
Relate grouping problems where the number of groups is unknown to multiplication equations with a missing factor, and to division equations (quotitive division)

N2.5.(F). Fractions

Term	Command Term
Number	Represent
Pattern and Function	Discover
Shape and Space	Contrast
Data Handling	Identify
Measurement	State

N2.6.(G). Geometry

Use precise language to describe the properties of 2D and 3D shapes, and compare shapes by reasoning about similarities and differences in properties

N2.8.(MAP) MAP Testing Relevant Practice:

Grade 3

Content

Number Concepts

Deep dive into number forms and understanding of number systems.
A study of fractions, decimals, ratios, and proportions.

Arithmetic Operations

Advanced arithmetic, encompassing addition and subtraction of both whole and part numbers.
Mastery of multiplication and division, building upon the foundation set in the previous grades.

Measurement and Estimation

A thorough understanding of units of measurement.
Mastery of time, its units, and applications.

Geometrical Concepts

Studies of shapes and angles.
Understanding perimeter and area.

Advanced Topics

Introduction to algebraic concepts.
Exploring patterns and their relevance in mathematical operations.

Skills

Numeracy Proficiency

Recognition of ancient number systems from different cultures/periods.
Ability to read, write, and compare numbers up to 10,000 and beyond.
Advanced understanding of the place value of 4-digit numbers.
Enhanced skills in subtracting whole numbers using various methods, including regrouping.

Multiplication and Division

Deepening understanding of multiplication as repeated addition, arrays, and skip counting.
Confidence and accuracy when multiplying and dividing numbers.
Skills to multiply by tens and hundreds and divide 2-digit whole numbers without remainders.

Measurement and Time

Ability to count, write, and comprehend money amounts in different formats.
Proficiency in using different measurement units and tools.
Accurate reading of measurements from various scales.
Advanced skills in time management and reading different types of clocks.

Estimation and Rounding

Expertise in estimating quantities, sums, and differences in real-world scenarios.
Rounding numbers to the nearest tens and hundreds with increasing skill.

Geometrical Understanding

Explore geometry, identifying different shapes and angles.
Calculating area and perimeter.

Fractional Understanding

A deepening understanding of fractions, their interpretations, and applications.
Identifying equivalent fractions and working with fractions with sums equal to one whole.

Pattern Recognition

Ability to identify and describe patterns and their underlying rules.

N3.1.(NPV). Number and Place Value (NPV)

Know that 10 tens are equivalent to 1 hundred, and that 100 is 10 times the size of 10; apply this to identify and work out how many 10s there are in other three-digit multiples of 10.
Recognise the place value of each digit in three-digit numbers, and compose and decompose three-digit numbers using standard and non-standard partitioning.
Reason about the location of any three-digit number in the linear number system, including identifying the previous and next multiple of 100 and 10.

N3.2.(NF). Number Facts

Secure fluency in addition and subtraction facts that bridge 10, through continued practice.
Recall multiplication facts, and corresponding division facts, in the 10, 5, 2, 4, and 8 multiplication tables, and recognise products in these multiplication tables as multiples of the corresponding number.
Apply place-value knowledge to known additive and multiplicative number facts (scaling facts by 10).

N3.3.(AS). Addition and Subtraction

Calculate complements to 100.
Add and subtract up to three-digit numbers using columnar methods.
Manipulate the additive relationship:
- Understand the inverse relationship between addition and subtraction, and how both relate to the part–part–whole structure.
- Understand and use the commutative property of addition, and understand the related property for subtraction.

N3.4.(MD). Multiplication and Division

Apply known multiplication and division facts to solve contextual problems with different structures, including quotative and partitive division.

N3.5.(F). Fractions

Interpret and write proper fractions to represent 1 or several parts of a whole that is divided into equal parts.
Find unit fractions of quantities using known division facts (multiplication tables fluency).
Reason about the location of any fraction within 1 in the linear number system.
Add and subtract fractions with the same denominator, within 1.

N3.6.(G). Geometry

Recognise right angles as a property of shape or a description of a turn, and identify right angles in 2D shapes presented in different orientations.
Draw polygons by joining marked points, and identify parallel and perpendicular sides.

N3.4.(MD). Multiplication and Division

Apply known multiplication and division facts to solve contextual problems with different structures, including quotative and partitive division.

N3.5.(F). Fractions

Interpret and write proper fractions to represent 1 or several parts of a whole that is divided into equal parts.
Find unit fractions of quantities using known division facts (multiplication tables fluency).
Reason about the location of any fraction within 1 in the linear number system.
Add and subtract fractions with the same denominator, within 1.

N3.6.(G). Geometry

Recognise right angles as a property of shape or a description of a turn, and identify right angles in 2D shapes presented in different orientations.
Draw polygons by joining marked points, and identify parallel and perpendicular sides.

Grade 4

Content

Numerical Foundations

Deep dive into various forms of number and number systems, including understanding Roman numerals.
Advanced place value explorations with emphasis on understanding 5-digit numbers.

Basic Operations

Advanced techniques in addition and subtraction, especially involving decimals.
Mastery in multiplication and division, reinforcing and extending the range of calculations.

Fractional and Decimal Understanding

Dive deeper into fractions and decimals with emphasis on real-life applications and comparisons.
Introduction to factors and multiples, leading to recognition of prime and composite numbers.

Advanced Numerical Concepts

Estimation techniques for real-life situations.
Introductory lessons on ratio and proportion.
Introduction to exponents and their applications.

Measurement

Advanced lessons in measurement and understanding different units of measurement.
Explorations into capacity, volume, and mass, including conversions.
Mastery of time, involving calculations and understanding durations.

Algebraic Foundations

Introductory algebra concepts.
Recognition and creation of patterns using various representations.

Geometrical Concepts

Introduction to geometry fundamentals and basic trigonometry.
Advanced studies on shapes, angles, perimeter, and area.
Mastery in metric conversion for various units of measurement.

Coordinate Geometry and Transformations

Introduction to the coordinate plane and basic operations.

Data Management and Probability

Lessons on graphing, data handling, sampling techniques, and graphical representation.
Introductory lessons on probability, leading to understanding chances and predictions.

Skills

Grade 4 Mathematics emphasizes instilling a robust foundation in various mathematical concepts.

Students will:

Be adept in recognizing different forms of numbers, including the Roman numeral system.
Be proficient in reading, writing, and comparing numbers beyond the 100,000 mark.
Understand the intricacies of addition, subtraction, multiplication, and division, especially with larger numbers and decimals.
Have a clear concept of fractions, decimals, factors, and multiples and their applications.
Develop a clear understanding of measurement, especially volume, mass, and time, and how to convert between different units.
Build a foundation in algebra, especially in pattern recognition and representation.
Dive deep into geometry, learning about different shapes, angles, and how to calculate areas and perimeters.
Start their journey into coordinate geometry, transformations, and basic trigonometry.
Get hands-on experience with data, understanding how to graph it, interpret it, and even gather it through surveys.
Get introduced to probability, laying the groundwork for more advanced statistical studies in later grades.

N4.1.(NPV). Number and Place Value (NPV)

Know that 10 hundreds are equivalent to 1 thousand, and that 1,000 is 10 times the size of 100; apply this to identify and work out how many 100s there are in other four-digit multiples of 100.
Recognise the place value of each digit in four-digit numbers, and compose and decompose four-digit numbers using standard and non-standard partitioning.
Reason about the location of any four-digit number in the linear number system, including identifying the previous and next multiple of 1,000 and 100, and rounding to the nearest of each.
Divide 1,000 into 2, 4, 5, and 10 equal parts, and read scales/number lines marked in multiples of 1,000 with 2, 4, 5, and 10 equal parts.

N4.2.(NF). Number Facts

Recall multiplication and division facts up to 12×12, and recognise products in multiplication tables as multiples of the corresponding number.
Recall multiplication facts, and corresponding division facts, in the 10, 5, 2, 4, and 8 multiplication tables, and recognise products in these multiplication tables as multiples of the corresponding number.
Apply place-value knowledge to known additive and multiplicative number facts (scaling facts by 10).

N4.3.(AS). Addition and Subtraction

Understand that 2 numbers can be related additively or multiplicatively, and quantify additive and multiplicative relationships (multiplicative relationships restricted to multiplication by a whole number).
Use a given additive or multiplicative calculation to derive or complete a related calculation, using arithmetic properties, inverse relationships, and place-value understanding.

N4.4.(MD). Multiplication and Division

Multiply and divide whole numbers by 10 and 100 (keeping to whole number quotients); understand this as equivalent to making a number 10 or 100 times the size.
Manipulate multiplication and division equations, and understand and apply the commutative property of multiplication.
Understand and apply the distributive property of multiplication.

N4.5.(F). Fractions

Reason about the location of mixed numbers in the linear number system.
Convert mixed numbers to improper fractions and vice versa.
Add and subtract improper and mixed fractions with the same denominator, including bridging whole numbers.

N4.6.(G). Geometry

Draw polygons, specified by coordinates in the first quadrant, and translate within the first quadrant.
Identify regular polygons, including equilateral triangles and squares, as those in which the side lengths are equal and the angles are equal.
Find the perimeter of regular and irregular polygons.
Identify line symmetry in 2D shapes presented in different orientations. Reflect shapes in a line of symmetry and complete a symmetric figure or pattern with respect to a specified line of symmetry.

N4.7.(CT) Command Terms I:

Term	Command Term
Number	Calculate
Pattern & Function	Demonstrate
Shape & Space	Construct
Data Handling	Compare
Measurement	Solve

N4.7.(CT) Command Terms II:

Term	Command Term
Number	Calculate
Pattern & Function	Demonstrate
Shape & Space	Construct
Data Handling	Compare
Measurement	Solve

N4.8.(MAP) MAP Testing Relevant Practice:
n/a

Grade 5

Content

Numerical Foundations

Comprehensive study of number forms and the evolution of number systems.
Advanced studies in addition and subtraction with emphasis on diverse place values.
Mastery in understanding the place value system, especially in decimals.

Factors, Multiples, and Estimation

A deeper dive into factors and multiples, emphasizing the understanding of HCF and LCM.
Mastery in estimation techniques, focusing on real-world applications.

Fractional & Decimal Understanding

Advanced studies in fractions, ratio, and proportion.
Dive deeper into decimal studies, understanding tenths, hundredths, and thousandths.

Advanced Numerical Concepts

Extended lessons on exponents and roots.
Exploration of patterns through pattern and function.

Measurement and Conversions

Advanced concepts in measurement using standard units.
Emphasis on understanding and applying metric conversions in real-world situations.
Mastery of time concepts, ensuring full understanding of 12 and 24-hour clocks.

Geometry and Space

Explorations into geometrical elements, including shapes, angles, and triangle properties.
Introductory trigonometry.
Advanced studies in perimeter, area, and volume.

Coordinate Geometry and Transformations

Further studies on the coordinate plane and locating positions.
Understanding geometric transformations, such as translations, reflections, rotations, and enlargements.

Statistics, Data, and Probability

Lessons on statistics, data handling, graphing, and data sampling techniques.
Introduction to graphical representation with emphasis on various graph forms.
Mastery of probability concepts, focusing on predictions, experiments, and interpretations.

Skills

In Grade-5 Mathematics, Students Will:

Be adept in comparing and operating on whole numbers, fractions, and decimals.
Master addition and subtraction techniques, especially with diverse place values.
Recall multiplication and division facts efficiently.
Understand and identify factors and multiples, especially HCF and LCM.
Develop proficiency in estimation using fractions, decimals, and percentages.
Convert between fractions, decimals, and percentages.
Understand the relationship between exponents and roots.
Analyze, describe, and classify various shapes using appropriate geometric vocabulary.
Master measurements, especially in real-world contexts, and understand the precision and accuracy of tools.
Convert units of measurement and understand their applications.
Analyze patterns, functions, and represent rules through various means.
Apply geometric knowledge in calculating perimeters, areas, and volumes.
Work with coordinate geometry to solve positional problems.
Understand and apply transformations to geometric figures.
Collect, organize, interpret, and conclude data through various graphical representations.
Understand statistical measures such as mean, median, mode, and range.
Master the concept of probability and differentiate between predictions and experiment results.

N5.1.(NPV). Number and Place Value (NPV)

Know that 10 tenths are equivalent to 1 one, and that 1 is 10 times the size of 0.1. Know that 100 hundredths are equivalent to 1 one, and that 1 is 100 times the size of 0.01. Know that 10 hundredths are equivalent to 1 tenth, and that 0.1 is 10 times the size of 0.01.
Recognise the place value of each digit in numbers with up to 2 decimal places, and compose and decompose numbers with up to 2 decimal places using standard and non-standard partitioning.
Reason about the location of any number with up to 2 decimal places in the linear number system, including identifying the previous and next multiple of 1 and 0.1 and rounding to the nearest of each.
Divide 1 into 2, 4, 5, and 10 equal parts, and read scales/number lines marked in units of 1 with 2, 4, 5, and 10 equal parts.
Convert between units of measure, including using common decimals and fractions.

N5.2.(NF). Number Facts

Secure fluency in multiplication table facts, and corresponding division facts, through continued practice.
Apply place-value knowledge to known additive and multiplicative number facts (scaling facts by 1 tenth or 1 hundredth).

N5.3.(AS). Addition and Subtraction

Solve problems involving ratio relationships.

N5.4.(MD). Multiplication and Division

Multiply and divide numbers by 10 and 100; understand this as equivalent to making a number 10 or 100 times the size, or 1 tenth or 1 hundredth times the size.
Find factors and multiples of positive whole numbers, including common factors and common multiples, and express a given number as a product of 2 or 3 factors.
Multiply any whole number with up to 4 digits by any one-digit number using a formal written method.
Divide a number with up to 4 digits by a one-digit number using a formal written method, and interpret remainders appropriately for the context.

N5.5.(F). Fractions

Find non-unit fractions of quantities.
Find equivalent fractions and understand that they have the same value and the same position in the linear number system.
Recall decimal fraction equivalents for 1/2, 1/4, 1/5, and 1/10, and for multiples of these proper fractions.

N5.6.(G). Geometry

Compare angles, estimate and measure angles in degrees (°), and draw angles of a given size.
Compare areas and calculate the area of rectangles (including squares) using standard units.

N5.7.(CT) Command Terms I:

Term	Command Term
Number	Communicate
Pattern & Function	Apply
Shape & Space	Measure
Data Handling	Solve
Measurement	Deduce

N5.7.(CT) Command Terms II:

Term	Command Term
Number	Use
Pattern & Function	Compare & Contrast
Shape & Space	Find
Data Handling	Show
Measurement	Justify

N4.8.(MAP) MAP Testing Relevant Practice:
n/a

Grade 5 Extended

Content

N5.1.ex.(NPV). Number and Place Value (NPV)

Understand the relationship between powers of 10 from 1 hundredth to 10 million, and use this to make a given number 10, 100, 1,000, 1 tenth, 1 hundredth, or 1 thousandth times the size (multiply and divide by 10, 100, and 1,000).
Recognise the place value of each digit in numbers up to 10 million, including decimal fractions, and compose and decompose numbers up to 10 million using standard and non-standard partitioning.
Reason about the location of any number up to 10 million, including decimal fractions, in the linear number system, and round numbers as appropriate, including in contexts.
Divide powers of 10, from 1 hundredth to 10 million, into 2, 4, 5, and 10 equal parts, and read scales/number lines with labelled intervals divided into 2, 4, 5, and 10 equal parts.

N5.2.ex.(NF). Number Facts

N5.3.ex.(AS). Addition and Subtraction

Solve problems with 2 unknowns.

N5.4.ex.(MD). Multiplication and Division

N5.5.ex.(F). Fractions

Recognise when fractions can be simplified, and use common factors to simplify fractions.
Express fractions in a common denomination and use this to compare fractions that are similar in value.
Compare fractions with different denominators, including fractions greater than 1, using reasoning, and choose between reasoning and common denomination as a comparison strategy.

N1.6.ex.(G). Geometry

Draw, compose, and decompose shapes according to given properties, including dimensions, angles, and area, and solve related problems.

Middle Years Programme (MYP)

Mathematics in the MYP

Mathematics promotes a powerful universal language, analytical reasoning and problem-solving skills that contribute to the development of logical, abstract and critical thinking.

Mathematics in the MYP is tailored to the needs of students, seeking to intrigue and motivate them to want to learn its principles.

Students should see authentic examples of how mathematics is useful and relevant to their lives and be encouraged to apply it to new situations.

Grade 6

Content:

Design Cycle/Design Process
Problem / issue identification
Design proposal
Idea/solution generation
Testing methods
Success evaluation
Improvement explanation

Skills

Creating/editing of 2D graphics
Presenting / communicating
Producing and editing film
Developing brand / identity
Using structure as function

Grade 6

Content

Numbers and Number Systems

Representing quantities in different forms
Exponents and roots
Classifying numbers (factors and multiples)

Fractions

Representing fractions in different forms
Simplifying fractions
Using number operations (subtraction, multiplication, division, and addition)
Using mathematical strategies to solve real-life problems involving fractions

Fractions as Percentages

Representing percentages in different forms (decimals, fractions, ratio)
Converting between equivalent forms of numbers (fractions, decimals, percentages)

Algebraic Expressions and Equations

Using correct terminology
Representing patterns in different forms (diagrams, sequences, tables, words)

Geometric Constructions

Perimeter, area, and volume

Data Management

Integers

Skills

Problem Solving
Analytical/critical thinking
Interpretation and representation of data
Mathematical reasoning (pattern recognition and generalisation)
Communication of mathematical concepts
Application of mathematical strategies to real-life situations

Grade 7

Content

Ratio and Proportions

Constant of proportionality
Representing proportional relationships using tables, equations, and graphs

Probability

Representing probability in fraction, decimal, and percentage forms
Modeling sample space using lists, tables, and tree diagrams
Calculating theoretical probability

Integers

Performing the operations of multiplication, division, addition, and subtraction with integers
Plotting points on the Cartesian plane

Algebraic Expressions

Solving algebraic equations (two-step)
Representing inequalities on a number line

Geometry

Finding the perimeter and area of 2D shapes, including circles and trapezoids
Calculating the surface area and volume of prisms

Rate and Unit Rate

Converting between different units and currencies
Understanding the constant rate of change

Data Analysis

Creating stem-and-leaf plots and box-and-whisker plots
Understanding measures of central tendency and measures of dispersion
Analyzing univariate data and drawing conclusions

Skills

Problem-Solving

Analytical thinking
Interpretation and representation of data
Mathematical reasoning
Communication of mathematical concepts
Application of mathematical strategies to real-life situations

Ratios

Understanding how ratios associate quantities that vary together

Equations

Solving versus satisfying an equation

Geometry

Visualization and representation of 3D shapes
Moving between different units

Data Analysis

Understanding data distribution and how they can be analyzed or compared

Probability

Differentiating between theoretical and experimental probabilities

Grade 8

Content

Numbers Unit and Number Sense

Rational numbers
Negative and zero exponents
Standard form or scientific notation

Triangles

Pythagoras theorem
Introduction to similarity and trigonometric ratios

Equations and Lines

Equation of a straight line
Arithmetic sequences and investigating patterns
Drawing straight lines
Basic coordinate geometry, including midpoint and distance formula
Parallel and perpendicular lines

Linear Equations

Solving linear equations
Simultaneous equations (graphically and algebraically)

Linear Regression

Introduction to linear regression and real-life applications
Coefficient correlation and its interpretation
Line of best fit by hand and by technology

STEAM-Related Unit

3D shapes and pencil case design
Surface areas, nets, and volumes of 3D shapes, including prisms, spheres, cones, and irregular shapes (open-ended)

Geometry

Geometric transformations
Tessellations

Skills

Problem-Solving
Analytical thinking
Interpretation and representation of data
Mathematical reasoning
Communication of mathematical concepts
Application of mathematical strategies to real-life situations
Creativity in STEAM-related design projects

Grade 9

Content

The Number System

Laws of exponents and scientific notation
Units and measurement
Surds, roots, and radicals
Absolute value

Relations and Functions

Linear functions and graph review
Coordinate geometry review (parallel and perpendicular lines, gradient, and different forms of the equation of a straight line)
Review of linear algebra and expressions

Quadratic Functions and Algebra

Quadratic expressions (factorization and rearranging)
Representing quadratic functions
Solving quadratic equations (by factor or by quadratic formula)
Quadratic graphs (general form, vertex form, and x-intercept form)

Modelling with Functions

Modelling with linear, exponential, and quadratic functions
Applications and limitations of models

Univariate Statistics

Quantifying data
Histograms, box plots, cumulative frequency graphs
Sampling techniques

Bivariate Data

Causation vs. correlation
Line of best fit with and without technology
Data processing: quartiles and percentiles
Measures of dispersion: interquartile range
The role of context in statistical inquiry
Outliers
Critical literacy in statistics, considering sources and evaluating techniques

Data Analysis

Data distribution and how they can be analyzed or compared

Skills

Problem-solving
Analytical thinking
Interpretation and representation of data
Mathematical reasoning
Communication of mathematical concepts
Application of mathematical strategies to real-life situations
How proportional relationships lead to linear equations and modelling
Algorithmic thinking

Grade 9 Extended

Content

Mathematical Concepts

Lower and upper bounds
Absolute values
Representing inequalities, including compound and double inequalities
Solving inequalities, including compound and double inequalities
Solving simultaneous equations, including algebraically and graphically

Functions and Geometry

Mapping
Function notation
Domain and range
Linear functions of the form $f(x) = mx + c$
Parallel and perpendicular lines
Number sequences (prediction, description)
Coordinate geometry, including distance, midpoint, and gradient formulae
Pythagoras’ theorem

Quadratic Functions and Expressions

Factorizing quadratic expressions
Solving quadratic equations using factorization, the quadratic formula, and graphically
Transformation of quadratic functions, including translation, reflection, and dilation

Exponential Functions

Representation and shape of exponential functions and their horizontal asymptotes

Measurement and Algebra

Metric conversions
Rearranging formulae
Surds, roots, and radicals, including simplifying
Laws of exponents, including integer, negative, and fractional/rational exponents
Standard form (scientific notation)

Sequences and Patterns

Find, justify, and prove general rules/formulae for sequences

Data and Statistics

Sampling techniques and response rates
Data manipulation and misinterpretation
Graphical representations, including:
- Bivariate graphs/scatter graphs
- Box-and-whisker plots
- Cumulative frequency graphs
- Histograms for continuous fixed interval groups
Lines of best fit
Data processing, including:
- Mean, median (measures of central tendency), and mode for continuous data
- Quartiles and percentiles for discrete and continuous data
Measure of dispersion, including standard deviation (application and relationship with the mean)
Use of technology to find the numerical value for correlation and its meaning
Describing correlation, including positive, negative, none, strong, and weak

Skills

Advanced problem-solving
Analytical thinking
Interpretation and representation of data
Mathematical reasoning
Communication of mathematical concepts
Application of mathematical strategies to real-life situations
Critical thinking

Grade 10

Content

Geometry and Measurement

Surface area and volume calculation combined with algebraic manipulation
Similar triangles (SSS, SAS, etc.) and similar shapes using the scale factor of enlargement, area, and volume
Geometric transformations (reflection, translation, rotation, and enlargement)

Probability and Game Theory

Probability (sample space, tree diagrams, independent and mutually exclusive, and combined events)
Game theory (focused on comparison of theoretical and experimental probability)
Set operations and Venn diagrams
Probability of single and combined events

Trigonometry

Right-angle trigonometry
Simple use of sine rule, cosine rule, and area of a non-right-angled triangle

Circle Geometry

Properties of circles
Circle theorems (angle-related and side-length-related)

Digital Resources and Assessments

Familiarization with the e-assessment packs and sharing relevant digital resources

Sequences

Arithmetic, geometric/exponential, quadratic, cubic, quartic
Rational sequences where the numerator and/or denominator may be linear, quadratic, or geometric

Skills

Problem-solving
Analytical thinking
Interpretation and representation of data
Mathematical reasoning
Communication of mathematical concepts
Application of mathematical strategies to real-life situations
Familiarity with on-screen examinations, such as MYP eAssessments

Grade 10 Extended

Content

Number Systems and Notation

Set of positive integers and zero (N)
Integers (Z)
Rational numbers (Q)
Irrational numbers (Q’)
Real numbers (R)

Number Sequences

Prediction and description
Find, justify, and prove general rules/formulae for sequences
Use notation and formulae for arithmetic and geometric sequences to continue a sequence, find specific terms, and identify the progression

Logarithms

Laws of logarithms
Use of technology to find values

Proportions and Equations

Direct and inverse proportion
Exponential equations
Rational functions of the form $f(x) = \frac{ax+b}{cx+d}$
Linear programming, including inequalities

Functions

Representation and shape of cubic, rational, trigonometric, and logarithmic functions and their asymptotes

Circle Geometry

Circle theorems, including angles, radius, diameter, and tangent
Length of arc and chord
Perimeter and area of sectors and segments

Geometry and Measurement

Volume, surface area, and nets of pyramids, cones, and compound three-dimensional shapes
Rotation around a given point
Similarity and congruence, including proving similar and congruent triangles
Movement on a plane— isometric transformations, enlargements, and tessellations
Enlargement around a given point
Enlargement by a rational factor
Identical representation of transformations

Triangles

Triangle properties (right-angle trigonometry, area of non-right triangles)
Bearings
Trigonometric ratios in right-angled triangles
Sine rule and cosine rule, including applications

Probability

Probability calculations with Venn diagrams, tree diagrams, and sample space
Probability calculations for dependent and independent events (using the addition and multiplication rules), including conditional probability
Mutually exclusive events
Combined events
Relative frequency

Digital Resources and Assessments

Familiarization with the e-assessment packs and sharing relevant digital resources

Skills

Advanced problem-solving
Analytical thinking
Interpretation and representation of data
Mathematical reasoning
Communication of mathematical concepts
Application of mathematical strategies to real-life situations
Critical thinking
Familiarity with on-screen examinations, such as MYP e-assessments

Diploma Programme (DP)

Diploma Programme: Mathematics Analysis & Approaches SL

The Mathematics: Analysis and Approaches (SL) is a two-year, pre-university course designed for students who have an interest in mathematics and seek to develop a strong foundation in mathematical concepts and techniques. This course focuses on fostering students’ knowledge and understanding of mathematical concepts, principles, and nature in a comprehensible, coherent, and rigorous way. Students are encouraged to apply their mathematical knowledge to solve problems in both abstract and real-world contexts while developing intercultural understanding, open-mindedness, and respect for diverse perspectives.

The aims of the Mathematics: analysis and approaches (SL) course are to develop students’ curiosity, enjoyment, and appreciation for mathematics, as well as to strengthen their understanding of mathematical concepts and principles. The course seeks to cultivate students’ logical and creative thinking, patience, persistence, and confidence in problem-solving, while also fostering their ability to communicate mathematical ideas clearly and concisely across various contexts. By emphasizing the interconnectedness of mathematics with other disciplines and promoting the integration of technology, students will be better prepared to transfer their mathematical skills and knowledge to alternative situations, other areas of knowledge, and their local and global communities. Additionally, the course encourages awareness of the moral, social, and ethical implications of mathematical work and applications, as well as fostering appreciation for the universality of mathematics and its multicultural, international, and historical perspectives.

Grade 6

Content:

Design Cycle/Design Process
Problem / issue identification
Design proposal
Idea/solution generation
Testing methods
Success evaluation
Improvement explanation

Skills

Creating/editing of 2D graphics
Presenting / communicating
Producing and editing film
Developing brand / identity
Using structure as function

Grades 11 & 12

Content

Number and Algebra: 19 Hours

Using standard form
Arithmetic sequences and series
Geometric sequences and series
Financial applications (compound interest, annual depreciation)
Introduction to logarithms
Simple proof
Laws of exponents and logarithms
Sum of infinite geometric sequence
Binomial theorem where $n$

Functions: 21 Hours

Equations of straight lines (parallel and perpendicular)
Functions: notation, domain, range, and inverse as reflection
Graphing and key features of graphs
Intersections using technology
Composite functions, identity, and finding inverse
Quadratic functions: solutions of quadratic equations and inequalities
Discriminant and nature of roots
Reciprocal and simple rational functions
Equations of asymptotes
Exponential and logarithmic functions
Solving equations graphically and analytically
Transformation of functions

Geometry and Trigonometry: 25 Hours

3D space: volume, angles, distance, and midpoints
2D and 3D trigonometry: sine rule, cosine rule, area
Applications: angles of elevation and depression, bearings
Circle: radians, arcs, sectors
Unit circle definitions of sin, cos, tan
Exact trig ratios
Ambiguous case of sine rule
Pythagorean identity
Double angles
Circular functions: graphs, composites, transformations
Solving trigonometric equations

Statistics and Probability: 27 Hours

Concepts, reliability, and sampling techniques
Histograms, cumulative frequency graphs, and box plots
Mean, median, and mode
Mean of grouped data
Standard deviation, quartiles, interquartile range
Pearson’s correlation coefficient and scatter diagrams
Equation of $y$
Probability concepts: expected numbers, combined, mutually exclusive, conditional, independence
Probability diagrams
Discrete random variables, binomial distribution, and normal distribution
X on Y regression line
Conditional and independent probabilities
Test for independence
Z values and inverse normal to find mean and standard deviation

Calculus: 28 Hours

Introduction to differential calculus
Increasing and decreasing functions
Differentiating polynomials
Tangents and normals
Introduction to integration
Areas between curve and x-axis
Chain, product, and quotient rules
Second derivative and testing for max and min
Optimization and points of inflection
Kinematics problems
Indefinite integration, reverse chain, and substitution

Skills

Knowledge and Understanding

Recall, select, and use knowledge of mathematical facts, concepts, and techniques in a variety of familiar and unfamiliar contexts.

Problem Solving

Recall, select, and use knowledge of mathematical skills, results, and models in both abstract and real-world contexts to solve problems.

Communication and Interpretation

Transform common realistic contexts into mathematics.
Comment on the context.
Sketch or draw mathematical diagrams, graphs, or constructions both on paper and using technology.
Record methods, solutions, and conclusions using standardized notation.
Use appropriate notation and terminology.

Technology

Use technology accurately, appropriately, and efficiently both to explore new ideas and to solve problems.

Reasoning

Construct mathematical arguments through the use of precise statements, logical deduction, and inference.
Manipulate mathematical expressions effectively.

Inquiry Approaches

Investigate unfamiliar situations, both abstract and from the real world.
Organize and analyze information.
Make conjectures, draw conclusions, and test their validity.

Assessments

External Assessments
Paper 1

Technology not allowed.
Includes two sections:
- Section A: Compulsory short-response questions based on the syllabus.
- Section B: Compulsory extended-response questions based on the syllabus.
Duration: 1.5 hours.
Contribution: 40% of the final grade.

Paper 2

Technology allowed.
Includes two sections:
- Section A: Compulsory short-response questions based on the syllabus.
- Section B: Compulsory extended-response questions based on the syllabus.
Duration: 1.5 hours.
Contribution: 40% of the final grade.

Internal Assessments

Exploration Component:
- Requires 15 hours of work.
- Accounts for 20% of the final grade.

Diploma Programme: Mathematics Analysis & Approaches HL

The Mathematics: Analysis and Approaches (HL) course is a rigorous, two-year pre-university course designed for students with a strong interest and aptitude in mathematics. This course delves deeper into mathematical concepts and techniques, building on the foundation established in the SL course, and aims to prepare students for university-level mathematics and related fields. Students are encouraged to apply their mathematical knowledge to solve complex problems in both abstract and real-world contexts, and to develop a profound understanding of mathematical concepts, principles, and nature. The course places emphasis on intercultural understanding, open-mindedness, and respect for diverse perspectives.

The aims of the Mathematics: analysis and approaches (HL) course are to inspire students to develop a deep curiosity and enjoyment of mathematics, as well as an appreciation for its elegance, power, and relevance to real-world situations. The course seeks to enhance students’ understanding of mathematical concepts and principles, while fostering logical and creative thinking, patience, persistence, and confidence in problem-solving. By emphasizing effective communication of mathematical ideas across various contexts, the course encourages students to employ and refine their powers of abstraction, generalization, and application of mathematical concepts. The course also highlights the interconnectedness of mathematics with other disciplines and the integration of technology, enabling students to transfer their mathematical skills and knowledge to alternative situations, other areas of knowledge, and their local and global communities. Moreover, the course promotes awareness of the moral, social, and ethical implications of mathematical work and applications, as well as fostering appreciation for the universality of mathematics and its multicultural, international, and historical perspectives.

Grade 6

Content:

Design Cycle/Design Process
Problem / issue identification
Design proposal
Idea/solution generation
Testing methods
Success evaluation
Improvement explanation

Skills

Creating/editing of 2D graphics
Presenting / communicating
Producing and editing film
Developing brand / identity
Using structure as function

Grades 11 & 12

Content

Number and Algebra: 39 Hours
SL Content:

Using standard form, arithmetic sequences and series, geometric sequences and series
Financial applications (compound interest, annual depreciation)
Introduction to logarithms
Simple proof, laws of exponents and logarithms
Sum of infinite geometric sequence
Binomial theorem where $n$

HL Content:

Permutations and combinations
Binomial with negative and fractional indices
Partial fractions
Complex numbers (Cartesian form and Argand diagram, Polar and Euler form)
Complex roots of polynomials, conjugate roots
De Moivre’s theorem, powers and roots of complex numbers
Proof by induction, contradiction, counterexamples
Solution of systems of linear equations

Functions: 32 Hours
SL Content:

Equations of straight lines (parallel and perpendicular)
Functions: notation, domain, range, and inverse as reflection
Graphing and key features of graphs
Intersections using technology
Composite functions, identity, and finding inverse
Quadratic functions: solutions of quadratic equations and inequalities
Discriminant and nature of roots
Reciprocal and simple rational functions
Equations of asymptotes
Exponential and logarithmic functions
Solving equations graphically and analytically
Transformation of functions

HL Content:

Factor and remainder theorems
Sum and product of roots
Rational functions
Odd and even functions
Self-inverse, inverse, and domain restriction
Solutions of inequalities
Graphing modulus equations and inequalities

Geometry and Trigonometry: 51 Hours
SL Content:

3D space: volume, angles, distance, and midpoints
2D and 3D trigonometry: sine rule, cosine rule, area
Applications: angles of elevation and depression, bearings
Circle: radians, arcs, and sectors
Unit circle definitions of sin, cos, tan
Exact trig ratios
Ambiguous case of sine rule
Pythagorean identity
Double angles
Circular functions: graphs, composites, and transformations
Solving trigonometric equations

HL Content:

Reciprocal trig ratios and their Pythagorean identities
Inverse circular functions
Compound angle identities
Relationships between trig functions
Vector definitions and scalar (dot) product
Vector equation of line and classification of lines
Vector product and vector equations of a plane
Intersections of lines and planes

Statistics and Probability: 33 Hours
SL Content:

Concepts, reliability, and sampling techniques
Histograms, cumulative frequency graphs, and box plots
Mean, median, mode, and mean of grouped data
Standard deviation, quartiles, and interquartile range
Pearson’s correlation coefficient and scatter diagrams
Equation of $y$
Probability concepts: expected numbers, combined, mutually exclusive, conditional, independence
Probability diagrams
Discrete random variables, binomial distribution, and normal distribution
X on Y regression line
Conditional and independent probabilities
Test for independence
Z values and inverse normal to find mean and standard deviation

HL Content:

Bayes’ theorem
Properties of discrete and continuous random variables

Calculus: 55 Hours
SL Content:

Introduction to differential calculus
Increasing and decreasing functions
Differentiating polynomials, tangents, and normals
Integration introduction: areas between curve and x-axis
Chain, product, and quotient rules
Second derivative, testing for max and min
Optimization, points of inflection, and kinematics problems
Indefinite integration: reverse chain and substitution
Definite integrals: areas under curve onto x-axis and areas between curves

HL Content:

First principles, higher derivatives, and limits
L’Hopital’s rule, implicit functions, and related rates
Optimization and further derivatives
Indefinite integration of these functions
Partial fractions, integration by substitution, and integration by parts
Areas under curve onto the y-axis
Volume of revolution (about x and y axes)
First-order differential equations (Euler method, variables separable, integrating factor, homogeneous differential equations using substitution $y = vx$
Maclaurin series

Development of Investigational, Problem-Solving, and Modeling Skills and the Exploration of an Area of Mathematics: 30 Hours

Total Teaching Hours: 240 Hours

Skills

Knowledge and Understanding:
Recall, select, and use their knowledge of mathematical facts, concepts, and techniques in a variety of familiar and unfamiliar contexts.

Problem Solving:
Recall, select, and use their knowledge of mathematical skills, results, and models in both abstract and real-world contexts to solve problems.

Communication and Interpretation:

Transform common realistic contexts into mathematics.
Comment on the context.
Sketch or draw mathematical diagrams, graphs, or constructions both on paper and using technology.
Record methods, solutions, and conclusions using standardized notation.
Use appropriate notation and terminology.

Technology:
Use technology accurately, appropriately, and efficiently both to explore new ideas and to solve problems.

Reasoning:
Construct mathematical arguments through the use of precise statements, logical deduction, and inference, and by the manipulation of mathematical expressions.

Inquiry Approaches:

Investigate unfamiliar situations, both abstract and from the real world.
Organize and analyze information.
Make conjectures, draw conclusions, and test their validity.

Assessments:

External Assessments:

Paper 1:
- Technology not allowed.
- Divided into two sections:
  - Section A: Compulsory short-response questions based on the syllabus.
  - Section B: Compulsory extended-response questions based on the syllabus.
- Duration: 2 hours.
- Contribution: 30% of the final grade.
Paper 2:
- Technology allowed.
- Divided into two sections:
  - Section A: Compulsory short-response questions based on the syllabus.
  - Section B: Compulsory extended-response questions based on the syllabus.
- Duration: 2 hours.
- Contribution: 30% of the final grade.
Paper 3:
- Unique to the HL course.
- Technology allowed.
- Contains two compulsory extended-response

problem-solving questions.

Duration: 1 hour.
Contribution: 20% of the final grade.

Internal Assessments:

Exploration Component:
- Requires 15 hours of work.
- Contribution: 20% of the final grade.

Diploma Programme: Mathematics Applications & Interpretations SL

Mathematics: Applications and Interpretations is a two-year course designed to enable students to:

Enjoy mathematics and develop an appreciation of the elegance and power of mathematics.
Develop an understanding of the principles and nature of mathematics.
Develop logical, critical, and creative thinking, as well as patience and persistence in problem-solving.
Appreciate how developments in technology and mathematics have influenced each other.
Appreciate the contribution of mathematics to other disciplines.

Mathematics: Applications and Interpretations is a course for students interested in:

Developing mathematics for describing the world and solving practical problems.
Harnessing the power of technology alongside exploring mathematical models.
Seeing mathematics used in a practical context.

Students who choose Mathematics: Applications and Interpretations at SL or HL should:

Enjoy seeing mathematics applied to real-world contexts and solving real-world problems.

Students who wish to take Mathematics: Applications and Interpretations at HL should:

Have good algebraic skills and experience in solving real-world problems.
Derive pleasure and satisfaction from exploring challenging problems.
Be comfortable undertaking mathematical exploration using technology.

Grade 6

Content:

Design Cycle/Design Process
Problem / issue identification
Design proposal
Idea/solution generation
Testing methods
Success evaluation
Improvement explanation

Skills

Creating/editing of 2D graphics
Presenting / communicating
Producing and editing film
Developing brand / identity
Using structure as function

Grades 11 & 12

Content

Number and Algebra

Arithmetic sequences and series
Operations with numbers in the form $a \times 10^k$
Applications: Analysis, interpretation
Geometric sequences and series
Financial applications of geometric sequences and series
Laws of exponents
Approximation: upper and lower bounds of rounded numbers, percentage errors, estimation
Use technology to solve linear systems and polynomial equations

Key Concepts:
Number and algebra allow us to represent patterns, show equivalencies, and make generalizations that enable us to model real-world situations. Algebra is an abstraction of numerical concepts and employs variables to solve mathematical problems.

Functions

Different forms of the equation of a straight line: gradient, intercepts; parallel, perpendicular
Creating a sketch from information
Determining key features of graphs
Finding the point of intersection of two curves or lines using technology
Function domain, range, and graph; function notation; functions as mathematical models
Models of graphs:
- Develop and fit the model: choose an appropriate model, parameters, and reasonable domain
- Use the model: read, interpret, and make predictions

Key Concepts:
Models are depictions of real-life events using expressions, equations, or graphs, while a function is defined as a relation or expression involving one or more variables. Creating different representations of functions to model the relationships between variables, visually and symbolically as graphs, equations, and/or tables, represents different ways to communicate mathematical ideas.

Geometry and Trigonometry

Distance and midpoint between two points in 3-D space
Volume and surface area of simple and composite 3-D solids
Size of an angle between two intersecting lines or between a line and a plane
Use of sine, cosine, and tangent ratios to find the sides and angles of right-angled triangles
Sine rule, cosine rule, and area of a triangle
Applications of right and non-right angled trigonometry
The circle: length of an arc and area of a sector
Equations of perpendicular bisectors
Voronoi diagrams

Key Concepts:
Geometry and trigonometry allow us to quantify the physical world, enhancing our spatial awareness in two and three dimensions. This branch provides us with the tools for analysis, measurement, and transformation of quantities, movements, and relationships.

Statistics and Probability

Reliability of data sources and bias in sampling
Interpretation of outliers
Sampling techniques
Histograms; cumulative frequency graphs; finding median, quartiles, percentiles, range, IQR; box-and-whisker diagrams
Measures of central tendency (mean, median, and mode)
Measures of dispersion (interquartile range, standard deviation, and variance)
Pearson’s product-moment correlation coefficient
Binomial distribution
Use of diagrams (Venn, tree, sample space) and tables to calculate probabilities
Conditional probability
Normal distribution and curve
Spearman’s rank correlation coefficient
Expected and observed frequencies; $\chi^2$
The t-test; p-value to compare means of populations; using one-tailed and two-tailed tests

Key Concepts:
Statistics is concerned with the collection, analysis, and interpretation of quantitative data. It uses the theory of probability to estimate parameters, discover empirical laws, test hypotheses, and predict events. Statistical representations and measures allow us to represent data in many forms to aid interpretation. Probability enables us to quantify the likelihood of events occurring and evaluate risk. Both fields allow predictions, comparisons, and informed decisions but must be applied critically to differentiate between theoretical and observed data.

Calculus

Introduction to the concept of a limit
Derivative interpreted as gradient function and as rate of change
Increasing and decreasing functions
Power rule; extend power rule to polynomials
Tangents and normals
Optimization
Approximating areas using the trapezoidal rule

Key Concepts:
Calculus describes rates of change between two variables and the accumulation of limiting areas. Understanding these rates of change allows us to model, interpret, and analyze real-world problems and situations. Calculus helps us understand the behavior of functions and interpret the features of their graphs.

Skills

Knowledge and Understanding:

Recall, select, and use knowledge of mathematical facts, concepts, and techniques in a variety of familiar and unfamiliar contexts.

Problem Solving:

Recall, select, and use knowledge of mathematical skills, results, and models in both abstract and real-world contexts to solve problems.

Communication and Interpretation:

Transform common realistic contexts into mathematics.
Comment on the context.
Sketch or draw mathematical diagrams, graphs, or constructions both on paper and using technology.
Record methods, solutions, and conclusions using standardized notation.
Use appropriate notation and terminology.

Technology:

Use technology accurately, appropriately, and efficiently to explore new ideas and solve problems.

Reasoning:

Construct mathematical arguments through the use of precise statements, logical deduction, and inference.
Manipulate mathematical expressions effectively.

Inquiry Approaches:

Investigate unfamiliar situations, both abstract and from the real world.
Organize and analyze information.
Make conjectures, draw conclusions, and test their validity.

Diploma Programme: Mathematics Applications & Interpretations HL

Mathematics: Applications and Interpretations is a two-year course designed to enable students to:

Enjoy mathematics and develop an appreciation of the elegance and power of mathematics.
Develop an understanding of the principles and nature of mathematics.
Develop logical, critical, and creative thinking, as well as patience and persistence in problem-solving.
Appreciate how developments in technology and mathematics have influenced each other.
Appreciate the contribution of mathematics to other disciplines.

This course is designed for students interested in:

Developing their mathematics for describing the world and solving practical problems.
Harnessing the power of technology alongside exploring mathematical models.

Students who take Mathematics: Applications and Interpretations enjoy mathematics best when seen in a practical context.

Distinction Between SL and HL

Students who choose Mathematics: Applications and Interpretations at SL or HL should:

Enjoy seeing mathematics used in real-world contexts and solving real-world problems.

Students who wish to take Mathematics: Applications and Interpretations at HL should:

Have good algebraic skills and experience in solving real-world problems.
Find pleasure and satisfaction in exploring challenging problems.
Be comfortable undertaking this exploration using technology.

Grade 6

Content:

Design Cycle/Design Process
Problem / issue identification
Design proposal
Idea/solution generation
Testing methods
Success evaluation
Improvement explanation

Skills

Creating/editing of 2D graphics
Presenting / communicating
Producing and editing film
Developing brand / identity
Using structure as function

Grades 11 & 12

Content

Number and Algebra

Arithmetic sequences and series
Operations with numbers in the form $a \times 10^k$
Applications: analysis, interpretation
Geometric sequences and series
Financial applications of geometric sequences and series
Laws of exponents
Approximation: upper and lower bounds of rounded numbers, percentage errors, estimation
Use technology to solve linear systems and polynomial equations

HL Only:

Laws of logarithms
Simplifying expressions involving rational exponents
Complex numbers
Matrices
Conversion between Cartesian, polar, and exponential forms (by hand and with technology)
Calculating products, quotients, and integer powers in polar or exponential forms
Adding sinusoidal functions
Eigenvalues and eigenvectors

Key Concepts:
Number and algebra allow us to represent patterns, show equivalencies, and make generalizations, enabling us to model real-world situations. Algebra is an abstraction of numerical concepts and employs variables to solve mathematical problems.

Functions

Different forms of the equation of a straight line: gradient, intercepts; parallel, perpendicular
Creating a sketch from information
Determining key features of graphs
Finding the point of intersection of two curves or lines using technology
Function domain, range, and graph; function notation; functions as mathematical models
Models of graphs:
- Develop and fit the model: choose an appropriate model, parameters, and reasonable domain
- Use the model: read, interpret, and make predictions

HL Only:

Composite functions in context; notation and domain of inverse; find inverse
Transformations of graphs
Composite transformations
Scaling very large or small numbers using logarithms
Linearizing data using logarithms; interpretation of log-log and semi-log graphs

Key Concepts:
Models are depictions of real-life events using expressions, equations, or graphs. A function is defined as a relation or expression involving one or more variables. Creating different representations of functions—visually and symbolically as graphs, equations, and/or tables—represents different ways to communicate mathematical ideas.

Geometry and Trigonometry

Distance and midpoint between two points in 3-D space
Volume and surface area of simple and composite 3-D solids
Size of an angle between two intersecting lines or between a line and a plane
Use of sine, cosine, and tangent ratios to find sides and angles of right-angled triangles
Sine rule, cosine rule, and area of a triangle
Applications of right and non-right angled trigonometry
The circle: length of an arc; area of a sector
Equations of perpendicular bisectors
Voronoi diagrams

HL Only:

Radians
Definition of cosine, sine, and tangent; Pythagorean identity; ambiguous case
Vectors
Geometric transformations of points in 2-D using matrices
Graph theory: degree of a vertex, simple graphs, complete graphs, weighted graphs, directed graphs
Weighted adjacency tables
Tree and cycle algorithms with undirected graphs
Eulerian trails and circuits; Hamiltonian paths and cycles; minimum spanning trees
Chinese postman problem and algorithm
Travelling salesman problem; nearest neighbour algorithm; deleted vertex algorithm

Key Concepts:
Geometry and trigonometry allow us to quantify the physical world, enhancing our spatial awareness in two and three dimensions. This branch provides tools for analysis, measurement, and transformation of quantities, movements, and relationships.

Statistics and Probability

Reliability of data sources and bias in sampling
Interpretation of outliers
Sampling techniques
Histograms, cumulative frequency graphs, finding median, quartiles, percentiles, range, IQR; box-and-whisker diagrams
Measures of central tendency (mean, median, and mode)
Measures of dispersion (interquartile range, standard deviation, and variance)
Pearson’s product-moment correlation coefficient
Binomial distribution
Use of diagrams (Venn, tree, sample space) and tables to calculate probabilities
Conditional probability
Normal distribution and curve
Spearman’s rank correlation coefficient
Expected and observed frequencies; $\chi^2$
The t-test; p-value to compare means of populations (using one-tailed and two-tailed tests)

HL Only:

Reliability and validity tests
Non-linear regression
Coefficient of determination
Linear transformation of a single random variable
Expected value and variance of linear combinations of $n$
Critical values and regions; tests for population mean using normal and Poisson distributions
Transition matrices; powers of transition matrices
Regular Markov chains; initial state probability matrices
Calculation of steady state and long-term probabilities

Key Concepts:
Statistics is concerned with the collection, analysis, and interpretation of quantitative data. Probability theory allows us to estimate parameters, discover empirical laws, test hypotheses, predict events, evaluate risks, and make informed decisions. These fields, while powerful, require careful application and critical analysis to distinguish between theoretical and empirical data.

Calculus

Introduction to the concept of a limit
Derivative interpreted as gradient function and rate of change
Increasing and decreasing functions
Power rule; extend to polynomials
Tangents and normals
Optimization
Approximating areas using the trapezoidal rule

HL Only:

Derivatives of $\sin x, \cos x, \tan x, e^x, \ln x, x^n$
Second derivative
Integration by inspection or simple substitution
Area of the region enclosed by a curve and the x- or y-axes
Volumes of revolution
Kinematic problems involving displacement $s$
Solving by separation of variables
Slope fields and their diagrams
Euler’s method for approximate solutions to first-order differential equations
Numerical solutions of coupled systems
Phase portraits for solutions of coupled differential equations

Key Concepts:
Calculus describes rates of change between two variables and the accumulation of limiting areas. Understanding these rates of change allows us to model, interpret, and analyze real-world problems and situations. Calculus helps us understand the behaviour of functions and interpret the features of their graphs.

Skills

Knowledge and understanding: Recall, select, and use their knowledge of mathematical facts, concepts, and techniques in a variety of familiar and unfamiliar contexts.
Problem solving: Recall, select, and use their knowledge of mathematical skills, results, and models in both abstract and real-world contexts to solve problems.
Communication and interpretation:
- Transform common realistic contexts into mathematics.
- Comment on the context.
- Sketch or draw mathematical diagrams, graphs, or constructions both on paper and using technology.
- Record methods, solutions, and conclusions using standardized notation.
- Use appropriate notation and terminology.
Technology: Use technology accurately, appropriately, and efficiently to explore new ideas and solve problems.
Reasoning: Construct mathematical arguments through the use of precise statements, logical deduction, and inference, and by manipulating mathematical expressions.
Inquiry approaches: Investigate unfamiliar situations, both abstract and from the real world, involving organizing and analyzing information, making conjectures, drawing conclusions, and testing their validity

Downloadable Curriculum

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Glossary of Terms

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Learning & Assessment

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