Mathematics Class 6 ICSE CISCE Topics and Syllabus

• Concept of Sets 
  • Representation of a set

  1. Roster Method
  2. Set-Builder Method
  3. Venn Diagram

  • Number of elements of a set
  • Types of Sets

  1. Empty Set
  2. Singleton set
  3. Finite set
  4. Infinite set
  5. Subset
  6. Superset
  7. Proper Subset
  8. Power Set
  9. Equal sets
  10. Equivalent sets
  11. Universal set

  • Operations on sets

  1. Complement of a set
  2. Union of Sets
  3. Intersection of sets
     - De Morgan's Laws
  4. Difference of Sets

  •  Intervals

  1. Open Interval
  2. Closed Interval
  3. Semi-closed Interval
  4. Semi-open Interval
• Representation of Sets 
• Types of Sets: Finite/Infinite and Empty 
• Cardinality of a Set 

• Idea of sets.
• Representation of sets.
• Types of sets: Finite/infinite and empty.
• Cardinality of a set

• Concept for Number System(Consolidating the Sense of Numberness) 
• Consolidating the Sense of Numberness up to 5 Digits, Size, Estimation of Numbers, Identifying Smaller, Larger, Etc. 

Consolidating the sense of numberness up to 5 digits, size, estimation of numbers, identifying smaller, larger, etc.

• Concept of Estimation 
• Estimation of Outcome of Number Operations 

Estimation of outcome of number operations.

• Numbers in Indian and Comparison 
• Numbers in International Systems and Comparison 

Numbers in Indian and International Systems and their comparison

• Concept for Place Value - Recapitulation and Extension 

Place value - recapitulation and extension

• Concept for Natural Numbers 
• Concept for Whole Numbers 

• Natural numbers
• Whole numbers

• Negative and Positive Numbers 
• Need for Negative Numbers 
• Connection of Negative Numbers in Daily Life 
• Representation of Negative Numbers on Number Line 
• Ordering of Negative Numbers, Integers. 
• Representation of Integers on the Number Line 
• Operation of Addition and Subtraction of Integers 
• Addition of Integers 
• Comparison of Integers 
• Concept for Ordering of Integers 

• Need for negative numbers.
• Connection of negative numbers in daily life.
• Representation of negative numbers on number line.
• Ordering of negative numbers, Integers.
• Identification of integers on the number line,
• Operation of addition and subtraction of integers,
• Addition and subtraction of integers on the number line
• Comparison of integers,
• ordering of integers.

• Operation of Whole Numbers on Number Line 
• Seeing Patterns for Operations on Numbers. 
• Identifying And Formulating Rules for Operations on Numbers. 

• Number line.
• Seeing patterns, identifying and formulating rules for operations on numbers.

• Concept for HCF and LCM 
• Prime Factorization for HCF and LCM 
• Division Method for HCF and LCM 
• Property HCF x LCM = Product of Two Numbers 

• HCF and LCM, prime factorization and division method for HCF and LCM, the property LCM × HCF = product of two numbers

• Arranging the Objects in Rows and Columns 
• Simplification of Expression by Using Brackets 
• Factors and Multiples 
• Concept of Even and Odd Number 
• Concept for Co-prime Numbers, Prime Factorisation 

• Simplification of brackets.
• Multiples and factors,
• divisibility rule of 2, 3, 4, 5, 6, 8, 9, 10, 11. (All these through observing patterns. Children would be helped in deducing some and then asked to derive some that are a combination of the basic patterns of divisibility)
• Even/odd and prime/composite numbers, Co-prime numbers, prime factorisation, every number can be written as products of prime factors.

• Concept of Ratio 
• Difference Between Fraction and Ratio. 

Difference between fraction and ratio.

Concept of Ratio.

• Proportion as Equality of Two Ratios 
• Concept of Ratio 
• Concept of Proportion 
  • Proportion
  • Continued or mean proportion
  • Proportionality law

• Concept for Unitary Method (With Only Direct Variation Implied) 

Unitary method (with only direct variation implied).

• Concept of Fraction as a Part of Whole 
• Representation of Fractions (Pictorially and on Number Line). 
• Concept for Fraction as a Division. 
• Types of Fraction 
  • Concept of Proper Fractions 
  • Concept for Equivalent Fractions 
    • Equivalent Fractions
    • Cross Product
• Concept of Fractions 
• Operations on Fractions (Avoid Large and Complicated Unnecessary Tasks). (Moving Towards Abstraction in Fractions). 

• Revision of what a fraction is.
• Fraction as a part of whole.
• Representation of fractions (pictorially and on number line).
• Fraction as a division.
• Proper, improper & mixed fractions.
• Equivalent fractions
• Comparison of fractions
• Operations on fractions (Avoid large and complicated unnecessary tasks). (Moving towards abstraction in fractions).

• Concept of Decimal Numbers 
• Place Value in the Context of Decimal Fraction 
• Concept for Inter Conversion of Fractions 
• Word Problems Involving Addition and Subtraction of Decimals (Two Operations Together on Money, Mass, Length and Temperature). 

• Review of the idea of a decimal fraction.
• Place value in the context of decimal fraction.
• Inter conversion of fractions and decimal fractions (avoid recurring decimals at this stage).
• Word problems involving addition and subtraction of decimals (two operations together on money, mass, length and temperature).

• Concept of Percent and Percentage 
• Idea of Percent as Fraction with 100 as Denominator 

Idea of percent as fraction with 100 as denominator

• Relation Between Speed, Time and Distance 
• Idea of Speed and Simple Daily Life Problems Related to Speed, Time and Distance 

Idea of speed and simple daily life problems related to speed, time and distance

• Fundamental Concepts for Algebra 
• Introduction to Constants, Variable and Unknown Through Patterns 
• Concept for Appropriate Word Problems and Generalisations 

Introduction to constants, variable and unknown through patterns and through appropriate word problems and generalisations (For example 1+3=22, 1+3+5=32,
1+3+5+7=42 , sum of first n odd numbers = n2.).

• Operation on Algebraic Expression 
• Algebra Terminology - Literal Numbers, Terms, Expressions, Factor, Coefficient, Polynomials, Degree, like and Unlike Terms 
• Concept for Unknowns Through Examples with Simple Contexts (Single Operations) 

Terminology associated with algebra- like literal numbers, terms, expressions, factor, coefficient, polynomials, degree, like and unlike terms

Introduction to unknowns through examples with simple contexts (single operations)

• Concept of Substitution 

• Algebraic Expressions 
  • Variable
  • Constant
  • Algebraic Expressions
  • Value of Expression
  • Number line and an expression
• Evaluation of Algebraic Expressions by Substituting a Value for the Variable. 

Framing algebraic expressions.

Evaluation of algebraic expressions by substituting a value for the variable.

• Concept of Simple (Linear) Equations (Including Word Problems) 
• Linear Equation in One Variable 

Introduction to linear equation in one variable.

• Concepts of Fundamental (Geometry) 
• Concept for Basic Geometrical Ideas (2 -d) 
• Concept for Linkage with and Reflection in Everyday Experiences. 
• Concept of Line 
• Concept for Open and Closed Figures. 
• Concept for Interior and Exterior of Closed Figures. 
• Curvilinear and Linear Boundaries 
• Concept of Angle - Arms, Vertex, Interior and Exterior Region 

Basic geometrical ideas (2 -D): Introduction to geometry. Its linkage with and reflection in everyday experiences.

Line, line segment, ray.

Open and closed figures.

Interior and exterior of closed figures.

Curvilinear and linear boundaries

Angle — Vertex, arm, interior and exterior.

• Measure of Angles 
• Types of Angles- Acute, Obtuse, Right, Straight, Reflex, Complete and Zero Angle. 
• Introduction to Lines and Angles 

Measure of angles

Types of angles- acute, obtuse, right, straight, reflex, complete and zero angle.

• Concept of Properties of Angles and Lines 
• Measure of Line Segment 
• Pair of Lines – Intersecting and Perpendicular Lines, Parallel Lines 

Measure of Line segment

Pair of lines – Intersecting and perpendicular lines, Parallel lines.

• Concept of Triangles - Sides, Angles, Vertices, Interior and Exterior of Triangle 
• Classification of Triangles (On the Basis of Sides, and of Angles) 

Triangle — vertices, sides, angles, interior and exterior, altitude and median.

Classification of triangles (on the basis of sides, and of angles).

• Interior and Exterior of a Quadrilateral. 
• Concept of Quadrilaterals - Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles 

Quadrilateral — Sides, vertices, angles, diagonals, adjacent sides and opposite sides (only convex quadrilateral are to be discussed), interior and exterior of a quadrilateral.

• Concept of Polygons - Side, Vertex, Adjacent Sides, Adjacent Vertices and Diagonal 
• Simple Polygons (Upto Octagons Regulars as Well as Non-regular). 
• Sum of Angles of a Polynomial 
• Sum of Exterior Angles of a Polynomial 
• Regular Polynomial 

Simple polygons (introduction) (Upto octagons regulars as well as non-regular).

• Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles 

Circle — Centre, radius, diameter, arc, sector, chord, segment, semicircle, circumference, interior and exterior.

• Concept of Revision Exercise Symmetry (Including Constructions on Symmetry) 
• Concept of Reflection Symmetry 
• Concept of Observation and Identification of 2-d Symmetrical Objects for Reflection Symmetry. 
• Operation of Reflection (Taking Mirror Images) of Simple 2-d Objects 
• Recognising Reflection Symmetry (Identifying Axes). 

Symmetry: (reflection)

Observation and identification of 2-D symmetrical objects for reflection symmetry.

Operation of reflection (taking mirror images) of simple 2-D objects

Recognising reflection symmetry (identifying axes).

• Concept of Recognition of Solids 
• Identification of 3-d Shapes: Cubes, Cuboids, Cylinder, Sphere, Cone, Prism (Triangular and Square), Pyramid (Triangular and Square) 
• Identification and Locating in the Surroundings. 
• Nets for Building 3-d Shapes - Cube, Cuboids, Cylinders, Cones, Pyramid, and Prism 
• Faces, Edges and Vertices 

Identification of 3-D shapes: Cubes, Cuboids, cylinder, sphere, cone, prism (triangular and square), pyramid (triangular and square), Identification and
locating in the surroundings.

Elements of 3-D figures. (Faces, Edges and vertices).

Nets for cube, cuboids, cylinders, cones and tetrahedrons.

• Concept of Perimeter 
• Shapes of Different Kinds with the Same Perimeter. 
• Concept of Area 
• Conversion of Units (Mass, Time, Money, and Capacity) from to Smaller to Larger and Vice-versa 
• Counter Examples to Different Misconcepts Related to Perimeter and Area. 
• Perimeter of a Rectangle 
• Deducing the Formula of the Perimeter for a Rectangle and Then a Square Through Pattern and Generalisation. 

• Concept of perimeter and introduction to area
• Introduction and general understanding of perimeter using many shapes.
• Shapes of different kinds with the same perimeter.
• Concept of area, Area of a rectangle and a square
• Conversion of units (Mass, time, money, and capacity) from to smaller to larger and vice-versa
• Counter examples to different misconcepts related to perimeter and area.
• Perimeter of a rectangle – and its special case – a square.
• Deducing the formula of the perimeter for a rectangle and then a square through pattern and generalisation.

• Concept of Data Handling (Including Pictograph and Bar Graph) 
• Collection of Data to Examine a Hypothesis 
• Collecting Data 
• Concept of Pictograph 
• Organisation of Data 
  • Ungrouped Data
  • Grouped Data

Collection of data to examine a hypothesis

Collection and organisation of data - examples of organising it in tally bars and a table.

Pictograph- Need for scaling in pictographs interpretation & construction of pictograph

• Concept of Median 

Mean and median of data not having more than ten observations