Topics
Number System
Number System (Including Estimation and Approximation)
Number System(Consolidating the Sense of Numberness)
Theme 1 : Numbers
Ratio and Proportion
Numbers in Indian and International Systems (With Comparison)
Theme 2 : Ratio, Proportion and Arithmetic Problems
Estimation
Numbers in India and International System (With Comparison)
Natural Numbers and Whole Numbers (Including Number Line and Patterns)
Theme 3 : Algebra
Algebra
Theme 4 : Geometry
Negative Numbers and Integers
Geometry
Place Value
Sets
Natural Numbers and Whole Numbers (Including Patterns)
Mensuration
Theme 5 : Mensuration
Theme 6 : Statistics
Data Handling
Negative Numbers and Integers
Fractions
Number Line
Decimal Fractions
HCF and LCM
Playing with Numbers (Including H.C.F. and L.C.M.)
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)
Percent (Percentage)
Sets
Idea of Speed, Distance and Time
Ratio
Fundamental Concepts (With operations on Algebraic Expressions)
Proportion (Including Word Problems)
Unitary Method
Framing Algebraic Expressions (Including Substitution and Linear Equations)
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
Fundamental Concepts (Including Angles and their Properties)
Triangles (Including Types and Properties of Triangles)
Decimal Fractions
Quadrilaterals
Percent (Percentage)
Idea of Speed, Distance and Time
Circles
Fundamental Concepts
Constructions
Symmetry
Fundamental Operations (Related to Algebraic Expressions)
Recognition of Solids
Substitution (Including Use of Brackets as Grouping Symbols)
Framing Algebraic Expressions (Including Evaluation)
Perimeter and Area of Plane Figures
Simple (Linear) Equations (Including Word Problems)
Data Handling (Including Mean and Median)
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
- Definition: Prime Numbers
- Definition: Twin Prime Numbers
- Definition: Composite Number
- Activity: Prime or Composite? Build and Decide!
- Classification of Numbers Based on Their Factors
- Key Points Summary
Definition: Prime Numbers
A prime number is a natural number greater than 1 that has exactly two factors: 1 and the number itself.
2, 3, 5, 7, 11, and so on are examples of prime numbers.
Definition: Twin Prime Numbers
If the difference between two coprime numbers is 2, the numbers are said to be twin prime numbers. For example: (3, 5)
Definition: Composite numbers
Numbers having more than two factors are called composite numbers. 4, 6, 8, 9, 10, and so on are examples of composite numbers.
Prime or Composite? Build and Decide!
Step 1: Guna arranges 12 figs
Guna tries to arrange 12 figs in different rectangular shapes.
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Arrangement 1: 1 × 12
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Arrangement 2: 2 × 6
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Arrangement 3: 3 × 4
He finds 3 different rectangular arrangements.
Step 2: Anshu arranges 7 figs
Anshu tries to arrange 7 figs in rectangles.
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Arrangement: 1 × 7
She finds only one rectangular arrangement.
Conclusion:
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If a number can form many rectangular arrangements, it has many factors → it is composite (like 12).
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If a number can form only one rectangular arrangement, it has only two factors → it is prime (like 7).
- Number of arrangements = Number of factor pairs.
Classification of Numbers Based on Their Factors
|
Numbers |
Factors |
Number of Factors |
| 1 | 1 | 1 |
| 2 | 1, 2 | 2 |
| 3 | 1, 3 | 2 |
| 4 | 1, 2, 4 | 3 |
| 5 | 1, 5 | 2 |
| 6 | 1, 2, 3, 6 | 4 |
| 7 | 1, 7 | 2 |
| 8 | 1, 2, 4, 8 | 4 |
| 9 | 1, 3, 9 | 3 |
| 10 | 1, 2, 5, 10 | 4 |
| 11 | 1, 11 | 2 |
| 12 | 1, 2, 3, 4, 6, 12 | 6 |
- The number 1 has only one factor (i.e., itself).
- 1 is neither a prime nor a composite number.
- There are numbers having more than two factors like 4, 6, 8, 9, 10, and so on. These numbers are composite numbers.
Key Points Summary
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A prime number has exactly two factors.
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1 is neither prime nor composite.
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Twin primes come in pairs, two apart.
