Percentage Problems Related to Environment

Number System (Including Estimation and Approximation)

Number System(Consolidating the Sense of Numberness)

• Comparing Numbers
• To Form The Smallest and The Greatest Numbers Using Given Digits
• Operations on Larger Numbers

Numbers in Indian and International Systems (With Comparison)

Estimation

• Basic Concept of Estimation and Approximation of Numbers
• Rounding off a Number
• Estimation in Basic Operations

Numbers in India and International System (With Comparison)

• Concept of Unit, Number, Numeral and Numeration
• Hindu-Arabic (Indian) System of Numeration
• International System of Numeration
• Indian vs. International Place Value System

Natural Numbers and Whole Numbers (Including Number Line and Patterns)

Place Value

• Concept of Place Value
• Largest and Smallest Numbers

Negative Numbers and Integers

Sets

Natural Numbers and Whole Numbers (Including Patterns)

• Natural Numbers
• Whole Numbers
• Successor and Predecessor of Whole Number
• Properties of Whole Numbers
• Mathematical Patterns
• Patterns in Whole/Natural Numbers
• Magic Square
• Matchstick Pattern

Negative Numbers and Integers

• Concept of Negative Numbers
• Integers
• Ordering of Integers
• Addition of Integers
• Subtraction of Integers
• Integers

Fractions

Number Line

• Number Line
• Representation of Natural numbers, Whole Numbers and Integers On Number Line
• Comparing Numbers
• Addition and Subtraction on a Number Line

Decimal Fractions

Playing with Numbers (Including H.C.F. and L.C.M.)

HCF and LCM

• Factors and Common Factors
• Prime and Composite Numbers
• Eratosthenes’ Method of Finding Prime Numbers
• Prime Factorisation
• Highest Common Factor (HCF)
• Methods of Finding HCF
• Multiples and Common Multiples
• Lowest Common Multiple
• Methods of Finding LCM

Playing with Numbers

• Simplification of Brackets
• Finding Factors Using Rectangular Arrangements and Division
• Factors and Common Factors
• Multiples and Common Multiples
• Concept of Even and Odd Number
• Tests for Divisibility of Numbers
• Divisibility by 2
• Divisibility by 4
• Divisibility by 8
• Divisibility by 3
• Divisibility by 6
• Divisibility by 9
• Divisibility by 5
• Divisibility by 11

Ratio and Proportion (Including Unitary Method)

Sets

• Concept of Sets
• Representation of a Set
• Types of Sets
• Cardinality of a Set

Percent (Percentage)

Idea of Speed, Distance and Time

Ratio

• Quantitative Comparison Using Basic Operations
• Ratio
• Simplifying Ratios
• Problems based on Ratio
• All About Ratios: Dividing, Comparing, and Modifying Quantities

Fundamental Concepts (With operations on Algebraic Expressions)

Proportion (Including Word Problems)

• Proportion
• Concept of Continued Proportion

Unitary Method

• Unitary Method
• Types of Variation

Framing Algebraic Expressions (Including Substitution and Linear Equations)

Fundamental Concepts (Including Angles and their Properties)

Fractions

• Concept of Fraction
• Types of Fractions
• Concept of Proper and Improper Fractions
• Concept of Mixed Fractions
• Like and Unlike Fraction
• Concept of Equivalent Fractions
• Conversion between Improper and Mixed fraction
• Conversion between Unlike and Like Fractions
• Simplest Form of a Fractions
• Comparing Fractions
• Addition of Fraction
• Subtraction of Fraction
• Multiplication of Fraction
• Division of Fractions
• Using Operator 'Of' with Multiplication and Division
• BODMAS Rule
• Problems Based on Fraction

Decimal Fractions

• The Decimal Number System
• Like and Unlike Decimal Numbers
• Conversion between Decimal Fraction and Common Fraction
• Addition of Decimal Fraction
• Subtraction of Decimal Numbers
• Multiplication of Decimal Numbers
• Division of Decimal Numbers
• Application of Decimals in Real Life
• Word Problems based on Decimals

Triangles (Including Types and Properties of Triangles)

Quadrilaterals

Percent (Percentage)

• Basic Concept of Percentage
• Conversion between Percentage and Fraction or Decimal
• Expressing Quantities as Percentages
• Increase or Decrease in Percent
• Percentage Problems Related to Environment

Circles

Idea of Speed, Distance and Time

• Speed, Distance and Time
• Uniform Speed, Variable Speed, and Conversions

Symmetry

Fundamental Concepts

• Introduction to Algebra
• Constants and Variables in Mathematics
• Classification of Terms in Algebra
• Algebraic Expressions
• Factors and Common Factors
• Powers and Exponents
• Basic Concept of Polynomial and its Degree

Constructions

Fundamental Operations (Related to Algebraic Expressions)

• Addition of Like and Unlike Terms
• Subtraction of Like and Unlike Terms
• Addition of Polynomials
• Subtraction of Polynomials
• Multiplication of Algebraic Expressions
• Division of Algebraic Expressions

Substitution (Including Use of Brackets as Grouping Symbols)

• Basic Concept of Substitution
• Brackets in Mathematics

Recognition of Solids

Framing Algebraic Expressions (Including Evaluation)

• Algebraic Expressions
• Evaluation of Algebraic Expressions

Perimeter and Area of Plane Figures

Data Handling (Including Mean and Median)

Simple (Linear) Equations (Including Word Problems)

• Concept of Linear Equations
• Rules for Solving a Linear Equation
• Methods of Solving Linear Equations
• Word Problems on Linear Equations

Fundamental Concepts

• Fundamentals of Geometrical Concepts
• Concept of Points
• Concept of Lines
• Rays
• Line Segments
• Mathematical Concept of Surface
• Planes
• Parallel Lines
• Intersecting Lines
• Concept for Open and Closed Figures
• Plane Closed Figures
• The Perpendicular
• The Perpendicular Bisector

Angles (With Their Types)

• Concept of Angle
• Angle and Its Formation
• Measuring Angles
• Types of Angles
• Concept of Pairs of Angles
• The Sum of the Angles Around a Point is Always 360°

Properties of Angles and Lines (Including Parallel Lines)

• Properties of Adjacent and Vertically Opposite Angles
• Parallel Lines
• Concept of Transversal Lines
• Construction of an Angle
• Drawing a Perpendicular to a Line

Triangles (Including Types, Properties and Constructions)

• Basic Concepts of Triangles
• Exterior Angle of a Triangle and Its Property
• Classification of Triangles based on Angles
• Classification of Triangles based on Sides
• Altitudes of a Triangle
• Median of a Triangle
• Construction of Triangles

Quadrilateral

• Quadrilaterals
• Angle sum Property of Quadrilateral
• Types of Quadrilaterals

Polygons

• Basic Concept of Polygons
• Sum of Interior Angles of a Polygon
• Sum of Exterior Angles of a Polygon
• Basic Concept of Regular Polygon

The Circle

• Basic Concept of Circle
• Secant and Tangent
• Arc of the Circle
• Sector of a Circle
• Segment of a Circle
• The Interior and the Exterior of a Circle
• Circumcircle of a Triangle
• Incircle of a Triangle

Symmetry (Including Constructions on Symmetry)

• Concept of Symmetry
• Reflection Symmetry in 2-D Shapes
• Construction of Symmetric Points and Lines

Recognition of Solids

• Identification of 3-d Shapes
• Faces, Edges and Vertices of Polyhedron
• Nets of 3D Figures
• Oblique Sketches of 3D Shapes

Perimeter and Area of Plane Figures

• Basic Concepts in Mensuration
• Concept of Perimeter
• Perimeter of a Rectangle
• Perimeter of Squares
• Perimeter of an Equilateral Triangle
• Problems based on Perimeter
• Shapes with the Same Perimeter
• Concept of Area
• Area of Rectangle
• Area of Square
• Problems based on Area

Data Handling (Including Pictograph and Bar Graph)

• Mathematical Data Collection and Organisation
• Frequency Distribution and Its Applications
• Pictographs
• Bar Graphs

Mean and Median

• Concept of Mean (Average)
• Basic Concept of Median