Topics
Number System
Integers
- Concept of 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)
- Concept of Fractions
- Concept for Fraction as an Operator
- Concept of Reciprocal or Multiplicative Inverse
Decimal Fractions (Decimals)
- The Decimal Number System
- Concept of Multiplication
- Division of Decimal Numbers
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)
- Concept of Unitary Method (Including Time and Work)
- Unitary Method Continued, Consolidation, General Expression for Unitary Method .
- Relation Between Speed, Time and Distance
Percent and Percentage
- Basic Concept of Percentage
- Concept for Understanding Percentage as a Fraction with Denominator 100
- Conversion between Percentage and Fraction
- Converting Decimals to 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)
- Simple Linear Equations in One Variable
- Simple Linear Equations in One Variable
- 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
- Concept for Cardinal Property of Sets
Geometry
Lines and Angles (Including Construction of Angles)
- Introduction to Lines and Angles
- Concept for Pairs of Angles
- Properties of Parallel Lines
- Construction of a Line Parallel to a Given Line from a Point Outside It .
Triangles
- Concept 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)
- Concept of Symmetry
- Concept of Reflection Symmetry
- Concept for Idea of Rotational Symmetry, Observations of Rotational Symmetry of 2-d Objects. (900, 1200, 1800)
Recognition of Solids (Representing 3-d in 2-d)
- Concept of Recognition of Solids
- Faces, Edges and Vertices
- 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
- 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
- Concept of Data Handling
- Concept for Collection and Organisation of Data – Choosing the Data to Collect for a Hypothesis Testing
- Arithmetic Mean - Raw Data
- Arithmetic Mean - Range
- Concept of Median
- Concept of Mode
- Concept for Constructing
- Interpretation of Bar Graphs
Probability
- Basic Ideas 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.
Multiplication
Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers. Multiplication is used to simplify the task of repeated addition of the same number.
Multiplying a given number by a three-digit number:
Example (1): There are 754 students in a school. If one child’s uniform costs 368 rupees, what will be the cost of the uniforms for all the children in the school?
7 5 4
x 3 6 8
6 0 3 2 - - - - - - Multiplying by 8 units
+ 4 5 2 4 0 - - - - - - Multiplying by 6 tens
+ 2 2 6 2 0 0 - - - - - - Multiplying by 3 hundreds
2 7 7 4 7 2
Multiplying by 8 units : 7 5 4
x 8
6 0 3 2
Multiplying by 6 tens: 7 5 4
× 6 0
4 5 2 4 0
Multiplying by 3 hundreds: 7 5 4
x 3 0 0
2 2 6 2 0 0
The total cost of the uniforms is ₹ 2,77, 472.
Here, 754 is the multiplicand, 368 is the multiplier, and 2,77,472 is the product.
