# Mathematics and Numeracy

Mathematics is the language in which logic is written. Logic helps you solve problems and make the right decisions. It is only when you can read the language of logic, can you lead with logic.

Mathematics and numeracy are core competencies.

By engaging in mentally stimulating problems, children begin to understand mathematical language and then use it to talk about their work. This practice lays the foundation for real-life problem-solving.

Children learn to:

- understand numbers
- manage information
- understand processes in mathematics and data handling
- think critically
- solve problems and
- make decisions

### My Wondrous World

Children often ask profound questions about themselves and the nature of the world around them.

Why is the ocean salty?

Why do we see rainbows?

How do frogs and butterflies metamorphosize?

This area of learning helps children find age-appropriate answers to some of these questions and also ignites new ones.

This program helps to develop a cohesive and comprehensive view of the world, including:

- interdependence of science, history, and geography
- synergy between the human, animal, and plant kingdoms
- cultures of the world
- impact of technology
- developments, innovations, and discoveries in the world over time

### Gearing up for the Future

Big data, machine learning & artificial intelligence, hold the keys to our future. It is imperative for children to develop quantitative aptitude and computational ability.

The Math World Program helps children think with and visualize data. They calculate and solve analytical problems. The iterative processes which they learn also form the fundamentals for coding and software skills.

The course covers Mathematics, Analytical & Logical Reasoning, General Knowledge, and Olympiad Preparation.

"View the world as a kaleidoscope of possibilities."

The Math World program seamlessly integrates mathematics, analytical reasoning, logical thinking, and knowledge of the world.

The course encourages a child’s natural curiosity through exploration-based learning and planned activities across mathematics, arts, geography, history, science, and technology. These activities include exercises on analytical thinking and reasoning, design thinking, perceptual and spatial awareness.

###### Orbit 1 -

Age Group: 3.5 - 5.5 Years

- Number of Sessions in Academic Year: 36 sessions
- Duration of each session: 90 minutes per session

###### Foundation Basics - Syllabus +

###### Mathematics and Numeracy +

- Addition - An Introduction
- Cardinal Numbers
- Numbers and number names
- Count and match
- Comparing numbers
- Arranging numbers

- Data Handling
- Geometry and Shapes
- Measurements
- Weight
- Length

- One-to-one correspondence
- Order of Events
- Ordinal Numbers
- Ranks
- Positions

- Number Line
- Patterns on the number line
- Solving problems on the number line

- Skip Counting

###### Analytical Reasoning and Critical Thinking +

- Comparing and Contrasting
- Grouping and Sorting
- Number and Picture Series
- Pattern Identification
- Odd One Out
- Finding Differences

###### World Knowledge +

- Calendar Events and Time
- Seasons
- Months, Days, Weeks

- Communities, People and Places
- Fictional Books, Stories and Characters
- Famous Personalities
- Human Anatomy
- India - An Exploration
- Inventors and Inventions
- Landforms
- Life on Earth
- Modes of Transportation
- Mythological Stories and Characters
- Natural Phenomena
- Places Around Us
- Religions and Beliefs
- Safeguarding the Environment
- Space and the birth of the world
- Technological Growth
- Understanding Cultures and Traditions
- Water Bodies

###### Foundation Advanced - Syllabus +

###### Mathematics and Numeracy +

- Abacus
- Representation of numbers on the abacus

- Addition
- Cardinal Numbers
- Numbers and number names
- Count and match
- Comparing numbers
- Arranging numbers

- Data Handling
- Expanded Forms
- Geometry and Shapes
- 2D and 3D Shapes

- Graphs and Pictorial Representations
- Measurements
- Weight
- Length

- Number Line
- Patterns on the number line
- Solving problems on the number line

- One-to-one correspondence
- Order of Events
- Ordinal Numbers
- Ranks
- Positions

- Skip Counting
- Subtraction
- Time

###### Analytical Reasoning and Critical Thinking +

- Comparing and Contrasting
- Classification and Sorting
- Number and Picture Series
- Pattern Identification
- Odd One Out
- Finding Differences

###### World Knowledge +

- Calendar Events and Time
- Seasons
- Months, Days, Weeks

- Communities, People and Places
- Fictional Books, Stories and Characters
- Famous Personalities
- Human Anatomy
- India - An Exploration
- Inventors and Inventions
- Landforms
- Life on Earth
- Modes of Transportation
- Mythological Stories and Characters
- Natural Phenomena
- Places Around Us
- Religions and Beliefs
- Safeguarding the Environment
- Space and the birth of the world
- Technological Growth
- Understanding Cultures and Traditions
- Water Bodies

###### Orbit 2 +

Age Group: 6 - 9 Years

- Number of Sessions in Academic Term: 72 sessions
- Duration of each session: 75 minutes per session

###### Level 1 - Syllabus +

###### Mathematics and Numeracy +

- Abacus
- Representation of numbers on the abacus
- Addition and subtraction on the abacus

- Addition
- Addition using a number line
- Addition with and without carry-forward
- Addition on the abacus

- Data Handling and Information Management
- Graphing and representing data
- Interpreting data for information

- Division
- Introduction to division
- Division facts

- Geometry
- Identification of shapes
- Movement of objects as per shape
- Properties of shapes

- Measurement
- Types of Measurement
- Units of Measurement
- Instruments of Measurement
- Measuring Objects

- Money
- Currencies of the world
- Forms of money
- Denominations of Indian currency
- Counting and using money
- Comparing prices

- Multiplication
- Tables
- Multiplying numbers
- Multiplication facts

- Number Line
- Solving problems on the number line
- Patterns on the number line

- Numbers
- Numbers upto 1000
- Comparing numbers
- Arranging numbers
- Place value and face value
- Expanded and standard forms
- Odd and even numbers
- Skip counting

- Ordinal Numbers
- Counting in ordinal numbers
- Positions and places

- Subtraction
- Subtraction on the number line
- Subtraction with and without borrowing
- Subtraction on the abacus

- Time
- Fractions
- Introduction to fractions
- Visual representation of fractions

###### Analytical Reasoning and Critical Thinking +

- Alphanumeric Series
- Reasoning Analogies
- Artificial Language
- Blood Relations
- Calendars
- Coding and Decoding Alphanumeric Problems
- Playing with Dice
- Maps and Directions
- Embedded Images
- Mirror Images
- Odd one out
- Pictures Series and Sequences
- Seating Arrangements

###### World Knowledge +

- Country Deep Dives
- Fictional Books, Stories and Characters
- Famous Personalities
- Great Empires and Civilizations
- Human Anatomy
- India - An Exploration
- Inventors and Inventions
- Landforms
- Life on Earth
- Mythological Stories and Characters
- Natural Phenomena
- Religions and Beliefs
- Safeguarding the Environment
- Space and the birth of the world
- Technological Growth
- Water Bodies
- Understanding Cultures and Traditions

###### Level 2 - Syllabus +

###### Mathematics and Numeracy +

- Abacus
- Representation of numbers on the abacus
- Addition and subtraction on the abacus

- Addition
- Addition with and without carry-forward (3 digit numbers)
- Addition on the abacus
- Addition in expanded form

- Data Handling and Information Management
- Graphing and representing data
- Interpreting data for information

- Division
- Introduction to division
- Division by grouping and repeated subtraction
- Division facts
- Long division
- Inverse relationships - multiplication and division

- Geometry
- Identification of shapes
- 2D vs 3D shapes
- Movement of objects as per shape
- Properties of shapes

- Measurement
- Types of Measurement
- Units of Measurement
- Instruments of Measurement
- Measuring Objects
- Addition and subtraction of measurements
- Introduction to capacity and volume

- Money
- Currencies of the world
- Forms of money
- Denominations of Indian currency
- Counting and using money
- Comparing prices

- Multiplication
- Tables
- Multiplying numbers
- Multiplication facts
- Multiplication on the number line
- Multiplication of 2 and 3 digit numbers

- Number Line
- Solving problems on the number line
- Patterns on the number line

- Numbers
- Numbers upto 10,000
- Comparing numbers
- Counting by 10s, 100s
- Arranging numbers
- Place value and face value
- Expanded and standard forms
- Odd and even numbers
- Skip counting

- Ordinal Numbers
- Counting in ordinal numbers
- Positions and places

- Subtraction
- Subtraction on the number line (3 digit numbers)
- Subtraction with and without borrowing
- Subtraction on the abacus
- Checking of subtraction problems

- Time
- Units of time
- Using clocks
- Reading calendars

- Fractions
- Introduction to fractions
- Visual representation of fractions
- Comparing fractions

###### Analytical Reasoning and Critical Thinking +

- Alphanumeric Series
- Reasoning Analogies
- Artificial Language
- Blood Relations
- Calendars
- Cause and Effect
- Coding and Decoding Alphanumeric Problems
- Data Sufficiency
- Embedded Images
- Playing with Dice
- Probability - An Introduction
- Maps and Directions
- Mirror Images
- Odd one out
- Pictures Series and Sequences
- Seating Arrangements
- Shape Constructions
- Syllogisms
- Venn Diagrams
- Water Images

###### World Knowledge +

- Country Deep Dives
- Fictional Books, Stories and Characters
- Famous Personalities
- Great Empires and Civilizations
- Geographical Features
- Human Anatomy
- India - An Exploration
- Inventors and Inventions
- Landforms
- Life on Earth
- Monuments and Structures
- Mythological Stories and Characters
- Religions and Beliefs
- Safeguarding the Environment
- Symbols
- Natural Phenomena
- Space and the birth of the world
- Technological Growth
- Water Bodies
- Understanding Cultures and Traditions

###### Level 3 - Syllabus +

###### Mathematics and Numeracy +

- Abacus
- Representation of numbers on the abacus
- Addition and subtraction on the abacus

- Addition
- Addition facts
- Addition with and without carry-forward (4 digit numbers)
- Addition on the abacus
- Addition in expanded form

- Data Handling and Information Management
- Graphing and representing data
- Interpreting data for information

- Division
- Introduction to division
- Division by grouping and repeated subtraction
- Division facts
- Long division
- Inverse relationships - multiplication and division

- Fractions
- Introduction to fractions
- Visual representation of fractions
- Like and unlike fractions
- Comparing fractions
- Addition and subtraction of fractions
- Multiplication and division of fractions

- Geometry
- Identification of shapes
- 2D vs 3D shapes
- Movement of objects as per shape
- Properties of shapes
- Symmetry, tilings and tangrams
- Dot grids and positions

- Measurement
- Types of Measurement
- Units of Measurement
- Instruments of Measurement
- Capacity and volume
- Addition and subtraction of measurements
- Conversions of length, weight, volume

- Money
- Currencies of the world
- Forms of money
- Denominations of Indian currency
- Counting and using money (with and without decimals)
- Comparing prices
- Conversion of money
- Calculating rate charts and bills

- Multiplication
- Tables
- Patterns in tables
- Multiplying numbers
- Multiplication facts
- Multiplication on the number line
- Multiplication of 2 and 3 digit numbers
- Estimating products

- Numbers
- Numbers upto 1,00,000
- Comparing numbers
- Arranging numbers
- Counting by 10s, 100s, 1000s
- Place value and face value
- Expanded and standard forms
- Odd and even numbers
- Introduction of decimal numbers
- Skip counting
- Rounding off numbers
- Forming Numbers

- Ordinal Numbers
- Counting in ordinal numbers
- Positions and places

- Roman Numerals
- History and symbols of Roman numerals
- Counting of Roman numerals
- Reading and writing Roman numerals

- Subtraction
- Subtraction on the number line
- Subtraction with and without borrowing (4 digit numbers)
- Subtraction on the abacus
- Checking of subtraction problems
- Finding missing digits
- Estimation of differences

- Time
- Units of time
- Using clocks
- Reading calendars

###### Analytical Reasoning and Critical Thinking+

- Alphanumeric Series
- Reasoning Analogies
- Artificial Language
- Blood Relations
- Calendars
- Cause and Effect
- Coding and Decoding Alphanumeric Problems
- Data Sufficiency
- Embedded Images
- Playing with Dice
- Probability - An Introduction
- Maps and Directions
- Mirror Images
- Odd one out
- Pictures Series and Sequences
- Seating Arrangements
- Shape Constructions
- Statements and Assumptions
- Statements and Conclusions
- Syllogisms
- Venn Diagrams
- Water Images

###### World Knowledge +

- Country Deep Dives
- Fictional Books, Stories and Characters
- Famous Personalities
- Great Empires and Civilizations
- Geographical Features
- India - An Exploration
- Inventors and Inventions
- Landforms
- Life on Earth
- Monuments and Structures
- Mythological Stories and Characters
- Religions and Beliefs
- Safeguarding the Environment
- Natural Phenomena
- Space and the birth of the world
- Technological Growth
- Water Bodies
- Understanding Cultures and Traditions

###### Orbit 3 +

- Number of Sessions in Academic Term: 72 sessions
- Duration of each session: 75 minutes per session

###### Level 4 - Syllabus +

###### Mathematics and Numeracy +

- Addition and subtraction
- Properties of addition and subtraction
- Missing digits in addition and subtraction
- Checking answers
- Mental math
- Problem solving

- Data handling
- Reading and interpreting pictographs, bar charts and pie charts
- Representing data into pictographs, bar charts and pie charts

- Decimals
- Writing decimal numbers
- Word form of decimal numbers
- Place value of decimal numbers
- Expanded form and standard form of decimal numbers
- Converting fractions into decimal numbers and vice versa

- Division
- Division of 3-digit numbers by 1- digit numbers
- Division of 4 digit numbers by 1 digit numbers
- Division of 5 digit numbers by 1-digit numbers
- Division of 3-digit numbers by 2-digit numbers
- Division of 4-digit numbers by 2-digit numbers
- Rules of divisibility
- Creating division stories
- Finding missing numbers
- Problem solving

- Fractions
- Fraction of a collection
- Addition and subtraction of fractions
- Multiplication and division of fractions
- Equivalent fractions
- Comparing and ordering fractions
- Converting improper fractions to mixed fractions and vice versa
- Converting into lowest terms

- Geometry and Symmetry
- Circle and its parts
- Draw the missing half
- Identifying polygons and polygon types
- Calculating the radius and diameter of circles
- Drawing missing halves
- Tessellation

- Lines and shapes
- Measurement
- Measure length
- Drawing line segments
- Estimation of length, weight & capacity
- Conversion of units
- Addition and subtraction of length, weight and capacity
- Problem solving

- Multiplication
- Multiplication of 4, 3, 2 and 1 digit numbers
- Finding estimated and actual products
- Properties of multiplication
- Problem solving

- Multiples and factors
- Finding LCM
- Prime and composite numbers
- Prime factorization
- Finding GCF

- Numbers ( 5- digit, 6- digit)
- Number sequence
- Expanded and standard form
- International number system
- Estimation
- Problem solving
- Building numbers
- Place value system
- Comparing and ordering numbers
- Roman numerals

- Shapes and designs
- Perimeter and area
- Perimeter of squares, rectangles and triangles
- Perimeter of irregular shapes
- Finding area using square models
- Comparison of area
- Area of squares and rectangles
- Problem solving

- Time
- 24- hour clock & 12 hour clock
- Read and analyse time table
- Calendar
- Conversion of time

- Money
- Conversion
- Add, Sub, Mul, Div money
- Problem Solving
- Profit and Loss
- Bill

- Integers
- Rules of integer formula.
- Addition and Subtraction of integers.

- Patterns
- Predicting patterns
- Cast out nine
- Read the code

- Probability

###### Analytical and Logical Reasoning +

- Patterns
- Alphabet test
- Coding and decoding
- Ranking tests
- Mirror images
- Geometrical shapes and solid
- Directions and Spatial Awareness
- Days and dates
- Analogies and classification
- Seating arrangements
- Odd one out
- Blood relations
- Playing with dice
- Data sufficiency
- Probability
- Syllogisms

###### Level 5 - Syllabus +

###### Mathematics and Numeracy +

- Large Numbers
- Number sequence
- Number name
- Indian and international place value system
- Expanded form,standard form
- Predecessor,successor
- Compare and order
- Number pattern
- Count in 100’s, 1000’s
- Roman numeral
- Estimation of large numbers

- Addition And Subtraction
- Addition and subtraction of large numbers
- Subtraction across zeroes
- Find missing digits in addition and subtraction problems
- Problem solving

- Multiplication And Division
- Related vocabulary
- Properties of multiplication and division
- Patterns in multiplication
- Multiplication and division of large numbers
- Tests of divisibility
- Problem solving

- Factors And Multiples
- Related vocabulary
- Properties related to factors and multiples
- Find factors and multiples
- Find LCM and GCF
- Factor tree method and long division method
- Prime,co-prime,twin prime and composite numbers
- Problem solving

- Fraction
- Convert mixed fraction to improper fraction and vice versa
- Lowest term
- Equivalent fraction
- Compare and arrange fraction
- Multiply and divide fractions
- Add and subtract fractions
- Problem solving

- Decimal
- Words to numerals and vice versa
- Place value
- Convert decimals into fractions and vice versa
- Compare and order
- Add and subtract decimals
- Multiply and divide decimals
- Convert percentage to fractions and vice versa
- Find percentage
- Ratio and proportion
- Compare ratios

- Shapes
- Symmetry
- Turns
- Number pattern
- Shape pattern
- Slide,reflection
- Net of 3D shapes

- Geometry
- Identify ray,line and line segment
- Draw line segment using ruler
- Types of angles
- Measure angles using protractor
- Draw angles using protractor
- Types of lines
- Types of triangles
- Circle and its parts
- Calculate radius and diameter of a circle
- Draw circles with given radius

- Measurement
- Conversion of units
- Addtion and subtraction of length,weight and capacity
- Multiplication and division of length ,mass and capacity
- Problem solving
- Convert 12-hour clock to 24- clock
- Conversion between year,month,day,hour,minute and seconds
- Calculate time duration
- Temperature

- Mensuration
- Perimeter of regular and irregular shapes
- Area of square,rectangle and triangle
- Finding missing dimensions
- Perimeter and area of composite figures
- Area of path
- Problem solving

- Unitary method
- Problem solving

- Algebra
- Find the value of unknown quantity in an equation
- Identify monomial, binomial and polynomial
- Like terms,unlike terms
- Converting statements to algebraic expression and vice versa

- Data handling
- Read and interpret pictographs,bar charts and pie charts
- Represent data into pictographs, bar charts and pie charts

- Time, temperature and money
- Addition ,subtraction and multiplication of time
- Reading time tables-Bus and Railway
- Word problems
- Temperature
- Money
- Bills

- Profit and loss and unitary method
- Profit and loss
- Unitary method

- Percentage
- Converting percentage to fraction
- Converting percentage to decimal
- Converting fraction to percentage
- Converting decimal to percentage
- Percentage of a number or a quantity

- Lines,Angles and Triangles
- Measuring angles using a protractor
- Construction of angles using a protractor
- Types of lines
- Triangles

- Perimeter , Area and Volume
- Perimeter
- Area
- Finding area by formula
- Permeter and area
- Volume

- Circle
- Arc of a circle
- Drawing a circle of the given radius
- Measuring circumference of a circle
- Relation between diameter and circumference

###### Analytical and Logical Reasoning +

- Patterns
- Analogy
- Geometrical shapes
- Mirror images
- Directions and spatial awaness
- Ranking and ordering
- Alphabets and coding
- Coding and decoding
- Days and dates
- Probability theory
- Data sufficiency
- Playing with dice
- Odd one out
- Statement and conclusions
- Syllogisms
- Venn diagrams

###### Level 6 - Syllabus +

###### Mathematics and Numeracy +

- Knowing our Numbers
- Types of Numbers
- Indian and International System of Numeration
- Face Value and Place Value
- Comparison of Numbers
- Measurements
- Estimation
- Brackets
- Roman Numerals

- Whole Numbers
- Successor and Predecessor
- All Operations on a Number Line
- Properties of Whole Numbers
- Division Algorithm
- Patterns

- Playing with Numbers
- Factors and Multiples and their Properties
- Types of Numbers
- Sieve of Eratosthenes
- Divisibility Test
- LCM/HCF
- Co-prime Numbers
- Divisibility Properties
- Prime Factorization
- Problem Solving

- Basic Geometric Concepts
- Point, Line and Line segment
- Intersecting and Parallel Lines
- Collinear Points
- Concurrent Lines
- Distance between Two Parallel Lines
- Ray and its Properties
- Plane, Open and Closed figures
- Polygons, Angles, Triangles and Quadrilateral
- Circle: Parts of a Circle
- Semicircular Region
- Concentric Circle

- Understanding Elementary Shapes
- Line Segment and their Comparison
- Comparison and Magnitude of an Angle
- Special Angles
- Types of Angles
- Measuring Angles using Protractor
- Perpendicular Lines
- Classification of Triangles
- Types of Quadrilaterals
- Three-Dimensional Shapes

- Integers
- Integers and their Representation on a Number Line
- Ordering of Integers
- Absolute value of Integers
- Addition and Subtraction of Integers on a Number Line
- Addition and Subtraction of Integers without a Number Line
- Integers in Daily Life
- Problem Solving

- Fractions
- Representation of Fractions on a Number Line
- Types of Fractions
- Converting a Mixed Fraction into an Improper Fraction and vice versa
- Equivalent Fractions
- Simplest Form of a Fraction
- Comparison of Fractions
- Operations on Fractions
- Problem Solving

- Decimals
- Tenths, Hundredths and Thousandths
- Representation of Decimals on a Number Line
- Converting a Decimal into Fraction and vice versa
- Decimal Places
- Like and Unlike Decimals
- Comparison of Decimals
- Operations of Decimals
- Decimals in Real Life

- Data Handling
- Collection and Organization of Data
- Types of Data
- Pictorial Representation of Data
- Read and interpret Pictographs, Bar Charts, Histograms and Pie Charts
- Represent data in Pictographs, Bar Charts, Histograms and Pie Charts

- Mensuration
- Perimeter of Regular and Irregular Shapes
- Area of Square, Rectangle and Triangle
- Finding Missing Dimensions
- Perimeter and Area of Composite figures
- Area of Path
- Volume
- Problem Solving

- Algebra
- Find the value of an Unknown Quantity in an Equation
- Identify Monomial, Binomial and Polynomial
- Like Terms and Unlike Terms
- Converting Statements to Algebraic Expressions and vice versa
- Patterns
- Use of Variables
- Algebraic Expression and its Formation

- Ratio and Proportion
- Ratios
- Simplest Form of Ratio
- Equivalent Ratio
- Dividing a Number in the given Ratio
- Comparison of Ratios
- Proportions
- Unitary Method: Problem Solving

- Symmetry
- Symmetry
- Turns
- Number Pattern
- Shape Pattern
- Reflection
- Net of 3D shapes

- Construction
- Circle
- Line segment
- Perpendicular to a given line on a point lying on it
- Perpendicular to a given line on a point not lying on it
- Perpendicular Bisector of a Line segment
- Constructing an Angle equal to a given angle
- Bisector of an Angle
- Angles of Special Measures

- Probability Theory

###### Analytical and Logical Reasoning +

- Series completion
- Analogies and classification
- Coding and decoding
- Blood relations
- Directions and spatial awareness
- Venn diagram
- Alphanumeric sequences
- Mirror and water images
- Embedded figures
- Figure matrices
- Cubes and dice
- Dot Situation