Topics
Mathematics
Knowing Our Numbers
 Introduction to Knowing Our Numbers
 Comparing Numbers
 Compare Numbers in Ascending and Descending Order
 Compare Number by Forming Numbers from a Given Digits
 Compare Numbers by Shifting Digits
 Introducing a 5 Digit Number  10,000
 Revisiting Place Value of Numbers
 Expansion Form of Numbers
 Introducing the Six Digit Number  1,00,000
 Larger Number of Digits 7 and Above
 An Aid in Reading and Writing Large Numbers
 Using Commas in Indian and International Number System
 Round off and Estimation of Numbers
 To Estimate Sum Or Difference
 Estimating Products of Numbers
 Simplification of Expression by Using Brackets
 BODMAS  Rules for Simplifying an Expression
 Roman Numbers System and Its Application
Whole Numbers
 Concept for Natural Numbers
 Concept for Whole Numbers
 Successor and Predecessor of Whole Number
 Operation of Whole Numbers on Number Line
 Properties of Whole Numbers
 Closure Property of Whole Number
 Associativity Property of Whole Numbers
 Division by Zero
 Commutativity Property of Whole Number
 Distributivity Property of Whole Numbers
 Identity of Addition and Multiplication of Whole Numbers
 Patterns in Whole Numbers
Playing with Numbers
 Arranging the Objects in Rows and Columns
 Factors and Multiples
 Concept of Perfect Number
 Concept of Prime Numbers
 Concept of Coprime Number
 Concept of Twin Prime Numbers
 Concept of Even and Odd Number
 Concept of Composite Number
 Concept of Sieve of Eratosthenes
 Tests for Divisibility of Numbers
 Divisibility by 10
 Divisibility by 5
 Divisibility by 2
 Divisibility by 3
 Divisibility by 6
 Divisibility by 4
 Divisibility by 8
 Divisibility by 9
 Divisibility by 11
 Common Factor
 Common Multiples
 Some More Divisibility Rules
 Prime Factorisation
 Highest Common Factor
 Lowest Common Multiple
Basic Geometrical Ideas
 Concept for Basic Geometrical Ideas (2 d)
 Concept of Points
 Concept of Line
 Concept of Line Segment
 Concept of Ray
 Concept of Intersecting Lines
 Parallel Lines
 Concept of Curves
 Different Types of Curves  Closed Curve, Open Curve, Simple Curve.
 Concept of Polygons  Side, Vertex, Adjacent Sides, Adjacent Vertices and Diagonal
 Concept of Angle  Arms, Vertex, Interior and Exterior Region
 Concept of Triangles  Sides, Angles, Vertices, Interior and Exterior of Triangle
 Concept of Quadrilaterals  Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles
 Concept of Circle  Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
Understanding Elementary Shapes
 Introduction to Understanding Elementary Shapes
 Measuring Line Segments
 Concept of Angle  Arms, Vertex, Interior and Exterior Region
 Right, Straight, and Complete Angle by Direction and Clock
 Acute, Right, Obtuse, and Reflex angles
 Measuring Angles
 Perpendicular Line and Perpendicular Bisector
 Classification of Triangles (On the Basis of Sides, and of Angles)
 Equilateral Triangle
 Isosceles Triangles
 Scalene Triangle
 Acute Angled Triangle
 Obtuse Angled Triangle
 Right Angled Triangle
 Types of Quadrilaterals
 Properties of a Square
 Properties of Rectangle
 Properties of a Parallelogram
 Properties of Rhombus
 Properties of Trapezium
 Three Dimensional Shapes
 Prism
 Concept of Pyramid
 Polygons
Integers
Fractions
Decimals
 Concept of Decimal Numbers
 Place Value in the Context of Decimal Fraction
 Concept of Tenths, Hundredths and Thousandths in Decimal
 Representing Decimals on the Number Line
 Interconversion of Fraction and Decimal
 Comparing Decimal Numbers
 Using Decimal Number as Units
 Addition of Decimal Numbers
 Subtraction of Decimals Fraction
Data Handling
Mensuration
Algebra
Ratio and Proportion
Symmetry
Practical Geometry
 Introduction to Practical Geometry
 Construction of a Circle When Its Radius is Known
 Construction of a Line Segment of a Given Length
 Constructing a Copy of a Given Line Segment
 Drawing a Perpendicular to a Line at a Point on the Line
 Drawing a Perpendicular to a Line Through a Point Not on It
 Drawing the Perpendicular Bisector of a Line Segment
 Constructing an Angle of a Given Measure
 Constructing a Copy of an Angle of Unknown Measure
 Constructing a Bisector of an Angle
 Angles of Special Measures  30°, 45°, 60°, 90°, and 120°
Notes
Some More Divisibility Rules:
a) Common divisibility examples:
Let us observe a few more rules about the divisibility of numbers.

If a number is divisible by another number then it is divisible by each of the factors of that number. Consider 24. It is divisible by 8 and the factors of 8 i.e. 1, 2, 4, and 8 also divide 24.

If a number is divisible by two coprime numbers then it is divisible by their product also. The number 80 is divisible by 4 and 5. It is also divisible by 4 × 5 = 20, and 4 and 5 are coprimes.
Similarly, 60 is divisible by 3 and 5 which are coprimes. 60 is also divisible by 3 × 5 = 15. 
If two given numbers are divisible by a number, then their sum is also divisible by that number. The numbers 16 and 20 are both divisible by 4. The number 16 + 20 = 36 is also divisible by 4.

If two given numbers are divisible by a number, then their difference is also divisible by that number. The numbers 35 and 20 are both divisible by 5. Is their difference 35 – 20 = 15 also divisible by 5.
Shaalaa.com  Divisibility Rule Involving Factors & Multiples  Part 1
Series: Some More Divisibility Rules
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