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
- Introduction
- Flat Surfaces (Planes)
- Curved Surfaces
- Key Points Summary
Introduction
A surface is the outer boundary that separates a solid object from the space around it.
Imagine your textbook. The outer covers and pages are the surfaces that separate the paper inside from the air in the room!
A surface has two main measurements:
-
Length
-
Width (or Breadth)
It has ZERO thickness or depth. Mathematically, a surface is a two-dimensional (2D) object.
Flat Surfaces (Planes)
A flat surface is perfectly smooth and level. In geometry, we call a flat surface a Plane.
Real-Life Examples:
-
A classroom blackboard or whiteboard.
-
The top of a dining table.
-
The surface of a wall or floor.
Curved Surfaces
A curved surface is one that is bent or rounded and is not a plane.
Real-Life Examples:
-
The outer skin of a cricket ball or an orange.
-
The surface of a water bottle or glass.
-
The surface of a football or globe.
Key Points Summary
Surface
- The outer boundary of a 3D solid.
- 2D (Length and Width)
Flat Surface
- A smooth, level surface (called a Plane).
- Example: Top of a table.
Curved Surface
- A rounded or bent surface.
- Example: A football.
