Topics
Number System
Integers
- Integers
- Multiplication and Division of Integers
- Properties of Operations on Integers
- Concept for Commutativity, Associativity, Existence of Identity
- Inverse and Distributivity
- Problem Solving Using Operations on Integers
- Statement Problems on Integers Using All Fundamental Operations.
Rational Numbers
- Rational Numbers
- Word Problems on Rational Numbers (All Operations)
- Decimal Representation of Rational Numbers
- Concept for Problem Solving Using Operations on Rational Numbers
- The Decimal Number System
Fractions (Including Problems)
Decimal Fractions (Decimals)
Exponents (Including Laws of Exponents)
- Concept of Exponents
- Concept for Exponents Only Natural Numbers.
- Laws of Exponents (Through Observing Patterns to Arrive at Generalisation.)
- Concept for Application of Laws of Exponents in Simple Daily Life Problems
Commercial Arithmetic
Ratio and Proportion (Including Sharing in a Ratio)
Unitary Method (Including Time and Work)
Percent and Percentage
Profit, Loss and Discount
- Concept of Discount
- Concept for Application to Profit and Loss (Single Transaction Only)
Simple Interest
Algebra
Fundamental Concepts (Including Fundamental Operations)
- Fundamental Concepts
- Terms, Factors and Coefficients of Expression
- Algebraic Expressions
- Performs Operations (Addition and Subtraction) on Algebraic Expressions with Integral Coefficients Only.
Simple Linear Equations (Including Word Problems)
- Word Problems on Linear Equations
- Concept for Inequalities
- Concept for Solution of Simple Inequalities in One Variable
Set Concepts (Some Simple Divisions by Vedic Method)
- Concept of Set Concepts
- Concept for Revision Idea of Sets
- Universal Set
- Cardinality of a Set
Geometry
Lines and Angles (Including Construction of Angles)
- Introduction to Lines and Angles
- Concept of Pairs of Angles
- Parallel Lines
- Construction of a Line Parallel to a Given Line from a Point Outside It .
Triangles
- Basic Concepts of Triangles
- Concept for Angle Sum Property
- Concept for Exterior Angle Property
- Concept for Construction of Simple Triangles.
Pythagoras Theorem
Symmetry (Including Reflection and Rotation)
Recognition of Solids (Representing 3-d in 2-d)
- Concept of Recognition of Solids
- Faces, Edges and Vertices of Polyhedron
- Concept for Mapping the Space Around Approximately Through Visual Estimation.
Congruency: Congruent Triangles
- Congruence of Triangles
- Concept for Congruence Through Superimposition
- Extend Congruence to Simple Geometrical Shapes E.G. Triangles, Circles.
- Criteria for Congruence of Triangles
Mensuration
- Basic Concepts in Mensuration
- Concept of Perimeter
- Circumference of a Circle
- Concept of Area
- Concept of Measurement Using a Basic Unit Area of a Square, Rectangle, Triangle, Parallelogram and Circle, Rings and Combined Figures.
Data Handling (Statistics)
Data Handling
Probability
- Concept of Probability
- Concept for Feel of Probability Using Data Through Experiments.
- Concept for Notion of Chance
- Concept for Tabulating and Counting Occurrences
- Comparing the Observation with that for a Coin. Observing Strings of Throws, Notion of Randomness.
- Definition: Cardinality
- Examples
- Real-Life Application
- Key Points Summary
CISCE: Class 6
Definition: Cardinality
Cardinality refers to the number of distinct elements in a set.
It is denoted by n(A)
- The cardinal number of the empty set is 0.
- The cardinal number of an infinite set is not defined
CISCE: Class 6
Examples
1. Set P = {2, 9, 11, 14}
- Has 4 elements,
- So its cardinal number is n(P) = 4.
2. Set E = {} (empty set)
- has 0 elements,
- n(E) = 0.
3. A = {2, 3, 5, 5, 3}
- Set A has 3 unique elements: {2, 3, 5}
- n(A) = 3
4. B = {letters in the word 'NOORAJAHAN'}
- Set B has 6 unique letters: {n, o, r, a, j, h}
- n(B) = 6
5. P = {counting numbers between 10 and 30 divisible by 5}
- Set P contains {15, 20, 25}
- n(P) = 3
CISCE: Class 6
Real-Life Application
Imagine you collect marbles of different colours:
Even if you have five red marbles and three blue ones, you only count red and blue as unique colours.
So, your set has two unique elements: n(Set) = 2
CISCE: Class 6
Key Points Summary
- Cardinality counts only different items in a set.
- Repeated items count once.
- An empty set’s cardinality is zero.
