Topics
Number System(Consolidating the Sense of Numberness)
Number System
Estimation
Ratio and Proportion
Algebra
Numbers in India and International System (With Comparison)
Geometry
Place Value
Mensuration
Natural Numbers and Whole Numbers (Including Patterns)
Data Handling
Negative Numbers and Integers
Number Line
HCF and 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
Sets
Ratio
Proportion (Including Word Problems)
Unitary Method
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
Percent (Percentage)
Idea of Speed, Distance and Time
Fundamental Concepts
Fundamental Operations (Related to Algebraic Expressions)
Substitution (Including Use of Brackets as Grouping Symbols)
Framing Algebraic Expressions (Including Evaluation)
Simple (Linear) Equations (Including Word Problems)
Fundamental Concepts
Angles (With Their Types)
Properties of Angles and Lines (Including Parallel Lines)
Triangles (Including Types, Properties and Constructions)
Quadrilateral
Polygons
The Circle
Symmetry (Including Constructions on Symmetry)
Recognition of Solids
Perimeter and Area of Plane Figures
Data Handling (Including Pictograph and Bar Graph)
Mean and Median
- Historical Note
- Step-by-Step Guide to Eratosthenes’ Prime Number Method
- Key Points Summary
Historical Note
Eratosthenes was an ancient Greek mathematician. He invented a simple, clever way to find all prime numbers up to any limit, known as the Sieve of Eratosthenes.
Step-by-Step Guide to Eratosthenes’ Prime Number Method
Step 1: Leave 1 as it is neither prime nor composite
Step 2: Encircle 2, cross out all the multiples of 2, other than 2 itself, i.e. 4, 6, 8, and so on.
Step 3: You will find that the next uncrossed number is 3. Encircle 3 and cross out all the multiples of 3, apart from 3 itself.
Step 4: The next uncrossed number is 5. Encircle 5 and cross out all the multiples of 5 other than 5 itself.
Step 5: Continue this process till all the numbers in the list are either encircled or crossed out. All the encircled numbers are prime numbers. All the crossed-out numbers, other than 1, are composite numbers. The total number of primes up to 100 is 25.
This method is called the Sieve of Eratosthenes.
Key Points Summary
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A prime number has exactly two factors: 1 and itself.
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The Sieve of Eratosthenes helps us find all primes up to a certain number.
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1 is not a prime number.
