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
What exactly is BODMAS?
BODMAS is a set of rules or an order for performing an arithmetic expression in order to make evaluation easier. Mathematics is all about logic, and certain rules must be followed at all times. BODMAS is one of them, and if it is not followed, the entire answer can go wrong, resulting in unnecessary marks loss.
BODMAS can also be defined as standard rules for simplifying expressions containing multiple operators.
Numbers and operators are the two main components of mathematical expressions:

Numbers: Numbers are the values used in calculations and to represent quantities. Natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, and complex numbers are all types of numbers.

Operators: The Operators are two characters combined to form an expression or equation. Addition, multiplication, division, and subtraction are the most common. When there is only one operator in an expression, solving it is simple, but when there are multiple operators, it becomes more difficult.
According to BODMAS, when solving an expression, we must first solve it with brackets, then with exponents, division, multiplication, addition, and subtraction. While solving the equations, the order must be remembered. You will get the wrong answer if you do not follow this rule.
Notes
BODMAS Rules for Simplifying an Expression:
Mathematics is a logicbased discipline. As so often, there are some simple rules to follow that help you work out the order in which to do the calculation. These are known as the ‘Order of Operations’.
BODMAS is a useful acronym that tells you the order in which you solve mathematical problems. It's important that you follow the rules of BODMAS because without it your answers can be wrong.
The BODMAS acronym is for

Brackets (parts of a calculation inside brackets always come first).

Orders (numbers involving powers or square roots).

Division.

Multiplication.

Addition.

Subtraction.
Numeric Expressions: BODMAS
Order of operations in Numeric Expressions
To evaluate: 8 × (5 + 3)^{2} ÷ 16 + 4
= 8 × (5 + 3)^{2} ÷ 16 + 4...….{Solve everything which is inside the brackets}
= 8 × (8)^{2} ÷ 16 + 4...….{Power}
= 8 × 64 ÷ 16 + 4...….{Divide}
= 8 × 4 + 4...….{Multiply}
= 32 + 4.....{Add}
= 36.
Remember:
Brackets may be used more than once to clearly specify the order of the operations. Different kinds of brackets, such as round brackets ( ), square brackets [ ], curly brackets { }, may be used for this purpose. When solving brackets, solve the innermost bracket first and follow it up by solving the brackets outside in turn.
Example
Solve: 2 × {25 × [(113  9) + (4 ÷ 2 × 13)]}
2 × {25 × [(113  9) + (4 ÷ 2 × 13)]}
= 2 × {25 × [104 + (4 ÷ 2 × 13)]}
= 2 × {25 × [104 + (2 × 13)]}
= 2 × {25 × [104 + 26]}
= 2 × {25 × 130}
= 2 × 3250
= 6500.
Notes
How to Apply BODMAS?
The BODMAS rule can be used when an expression contains multiple operators. In that case, we first simplify the brackets from the inside to the outside ( ), then evaluate the exponents or roots, simplify multiplication and division, and finally perform addition and subtraction operations while moving from left to right.
Let’s start simplifying expressions in the following order

Bracket: Calculate everything inside the bracket first.
For example:
4 × (12 − 10)
=4 × 2
=8
The correct answer is 8 by using the BODMAS rule.

Order of: Solve the power, square etc.
For example:
7 + 4^{2}
=7 + 16
=23
The correct answer is 23 by using the BODMAS rule.

Division and Multiplication: Since multiplication and division are equally important, they should be completed from left to right.
For example:
9 + 24 ÷ 3 × 4
=9 + 8 × 4
=9 + 32
=41
The correct answer is 41 by using the BODMAS rule.

Addition and Subtraction: Since addition and subtraction are equally important, they should be completed from left to right.
24 + (8 − 5)
=24 + 3
=27
The correct answer is 27 by using the BODMAS rule.
Notes
BODMAS without Brackets
If there are no brackets, we can apply this rule to indices, then multiplication and division, and finally addition and subtraction. The first instructs you to multiply, then divide, while the second instructs you to do the opposite.
Here is a BODMAS Example with Answer.
Q. Simplify 3 + 4 × 2 + 4 − 1
Ans. BODMAS says Multiplication first,
so multiply, 4 × 24 × 2
3 + 8 + 4 − 1
Solving addition next,
3 + 8 + 4 = 15
Now perform subtraction at last
15 − 1 = 14
The correct answer is 14 by using the BODMAS rule.
Notes
BODMAS Rule Problems
Problem 1: Simplify 12 ÷ 4 × 2 + 33 − (9 + 4)
Solution: Use the BODMAS Rule (left to right whichever operations come first, we will follow that).
12 ÷ 4 × 2 + 2^{2} − (9 + 4)
First, we will simplify bracket,
= 12 ÷ 4 × 2 + 2^{2} − 13
Now we will simplify powers,
= 12 ÷ 4 × 2 + 4 − 13
Now we will divide 12 by 4,
= 3 × 2 + 4 − 13
Now we will multiply 3 and 2,
=6 + 4 − 13
Now we will add and subtract,
=10 − 13
=3
Problem 2: Simplify the expression by using the BODMAS rule:
(9 × 3 ÷ 9 + 1) × 3
Solution: Step 1: Using BODMAS Rule (left to right whichever operations come first we will follow that). Here, first, we simplify the bracket and inside the bracket, we will multiply first then division (we can do vice versa) and then addition. Thus, we need to multiply 9 by 3 in the given expression,
(9 × 3 ÷ 9 + 1) × 3 and we get,
(27 ÷ 9 + 1) × 3
Step 2: Now, we need to divide 27 by 9 inside the bracket, and we get, (3 + 1) × 3
Step 3: Remove the parentheses after adding 3 and 1, we get, 4 × 34 × 3
Step 4: Multiply 4 by 3 to get the final answer, which is 12.
∴ (9 × 3 ÷ 9 + 1) × 3 = 12