#### Topics

##### Number System

##### Sets

- Concept of Sets
- Representation of Sets
- Types of Sets: Finite/Infinite and Empty
- Cardinality of a Set

##### Number System(Consolidating the Sense of Numberness)

- Concept for Number System(Consolidating the Sense of Numberness)
- Consolidating the Sense of Numberness up to 5 Digits, Size, Estimation of Numbers, Identifying Smaller, Larger, Etc.

##### Estimation

- Concept of Estimation
- Estimation of Outcome of Number Operations

##### Numbers in India and International System (With Comparison)

- Numbers in Indian and Comparison
- Numbers in International Systems and Comparison

##### Place Value

- Concept for Place Value - Recapitulation and Extension

##### Natural Numbers and Whole Numbers (Including Patterns)

##### Negative Numbers and Integers

- Negative and Positive Numbers
- Need for Negative Numbers
- Connection of Negative Numbers in Daily Life
- Representation of Negative Numbers on Number Line
- Ordering of Negative Numbers, Integers.
- Representation of Integers on the Number Line
- Operation of Addition and Subtraction of Integers
- Addition of Integers
- Comparison of Integers
- Concept for Ordering of Integers

##### Number Line

- Operation of Whole Numbers on Number Line
- Seeing Patterns for Operations on Numbers.
- Identifying And Formulating Rules for Operations on Numbers.

##### HCF and LCM

- Concept for HCF and LCM
- Prime Factorization for HCF and LCM
- Division Method for HCF and LCM
- Property HCF x LCM = Product of Two Numbers

##### Playing with Numbers

- Arranging the Objects in Rows and Columns
- Simplification of Expression by Using Brackets
- Factors and Multiples
- Concept of Even and Odd Number
- Concept for Co-prime Numbers, Prime Factorisation

##### Ratio and Proportion

##### Ratio

- Concept of Ratio
- Difference Between Fraction and Ratio.

##### Proportion (Including Word Problems)

- Proportion as Equality of Two Ratios
- Concept of Ratio
- Concept of Proportion

##### Unitary Method

- Concept for Unitary Method (With Only Direct Variation Implied)

##### Fractions

- Concept of Fractions
- Concept of Fraction as a Part of Whole
- Representation of Fractions (Pictorially and on Number Line).
- Concept for Fraction as a Division.
- Concept of Proper Fractions
- Concept for Equivalent Fractions
- Concept of Fractions
- Operations on Fractions (Avoid Large and Complicated Unnecessary Tasks). (Moving Towards Abstraction in Fractions).

##### Decimal Fractions

- Concept of Decimal Numbers
- Concept of Decimal Numbers
- Place Value in the Context of Decimal Fraction
- Concept for Inter Conversion of Fractions
- Word Problems Involving Addition and Subtraction of Decimals (Two Operations Together on Money, Mass, Length and Temperature).

##### Percent (Percentage)

- Concept of Percent and Percentage
- Idea of Percent as Fraction with 100 as Denominator

##### Idea of Speed, Distance and Time

- Relation Between Speed, Time and Distance
- Idea of Speed and Simple Daily Life Problems Related to Speed, Time and Distance

##### Algebra

##### Fundamental Concepts

- Fundamental Concepts for Algebra
- Introduction to Constants, Variable and Unknown Through Patterns
- Concept for Appropriate Word Problems and Generalisations

##### Fundamental Operations (Related to Algebraic Expressions)

- Operation on Algebraic Expression
- Algebra Terminology - Literal Numbers, Terms, Expressions, Factor, Coefficient, Polynomials, Degree, like and Unlike Terms
- Concept for Unknowns Through Examples with Simple Contexts (Single Operations)

##### Substitution (Including Use of Brackets as Grouping Symbols)

- Concept of Substitution

##### Framing Algebraic Expressions (Including Evaluation)

##### Simple (Linear) Equations (Including Word Problems)

- Concept of Simple (Linear) Equations (Including Word Problems)
- Linear Equation in One Variable

##### Geometry

##### Fundamental Concepts

- Concepts of Fundamental (Geometry)
- Concept for Basic Geometrical Ideas (2 -d)
- Concept for Linkage with and Reflection in Everyday Experiences.
- Concept of Line
- Concept for Open and Closed Figures.
- Concept for Interior and Exterior of Closed Figures.
- Curvilinear and Linear Boundaries
- Concept of Angle - Arms, Vertex, Interior and Exterior Region

##### Angles (With Their Types)

- Types of Angles- Acute, Obtuse, Right, Straight, Reflex, Complete and Zero Angle.
- Measure of Angles
- Types of Angles- Acute, Obtuse, Right, Straight, Reflex, Complete and Zero Angle.
- Introduction to Lines and Angles

##### Properties of Angles and Lines (Including Parallel Lines)

- Concept of Properties of Angles and Lines
- Measure of Line Segment
- Pair of Lines – Intersecting and Perpendicular Lines, Parallel Lines

##### Triangles (Including Types, Properties and Constructions)

- Concept of Triangles - Sides, Angles, Vertices, Interior and Exterior of Triangle
- Classification of Triangles (On the Basis of Sides, and of Angles)

##### Quadrilateral

##### Polygons

- Concept of Polygons - Side, Vertex, Adjacent Sides, Adjacent Vertices and Diagonal
- Simple Polygons (Upto Octagons Regulars as Well as Non-regular).
- Sum of Angles of a Polynomial
- Sum of Exterior Angles of a Polynomial
- Regular Polynomial

##### The Circle

##### Revision Exercise Symmetry (Including Constructions on Symmetry)

- Concept of Revision Exercise Symmetry (Including Constructions on Symmetry)
- Concept of Reflection Symmetry
- Concept of Observation and Identification of 2-d Symmetrical Objects for Reflection Symmetry.
- Operation of Reflection (Taking Mirror Images) of Simple 2-d Objects
- Recognising Reflection Symmetry (Identifying Axes).

##### Recognition of Solids

- Concept of Recognition of Solids
- Identification of 3-d Shapes: Cubes, Cuboids, Cylinder, Sphere, Cone, Prism (Triangular and Square), Pyramid (Triangular and Square)
- Identification and Locating in the Surroundings.
- Faces, Edges and Vertices
- Nets for Building 3-d Shapes - Cube, Cuboids, Cylinders, Cones, Pyramid, and Prism
- Faces, Edges and Vertices

##### Mensuration

##### Perimeter and Area of Plane Figures

- Concept of Perimeter
- Concept of Perimeter
- Shapes of Different Kinds with the Same Perimeter.
- Concept of Area
- Conversion of Units (Mass, Time, Money, and Capacity) from to Smaller to Larger and Vice-versa
- Counter Examples to Different Misconcepts Related to Perimeter and Area.
- Perimeter of a Rectangle
- Deducing the Formula of the Perimeter for a Rectangle and Then a Square Through Pattern and Generalisation.

##### Data Handling

##### Data Handling (Including Pictograph and Bar Graph)

- Concept of Data Handling (Including Pictograph and Bar Graph)
- Collection of Data to Examine a Hypothesis
- Collecting Data
- Concept of Pictograph
- Organisation of Data

##### Mean and Median

## Notes

**Concept for Basic Geometrical Ideas:**

The term ‘Geometry’ is the English equivalent of the Greek word ‘Geometron’. ‘Geo’ means Earth and ‘metron’ means Measurement.

**What are Dimensions?**

Dimensions in mathematics are the measure of the size or distance of an object or region or space in one direction. In simpler terms, it is the measurement of the length, width, and height of anything.

In our day to day life, we see several objects like books, balls, ice-cream cones, etc., around us which have different shapes.

Any object or space can be

One-dimensional (or 1D)

Two-dimensional (or 2D)

Three-dimensional (or 3D)

For example,

**1. Zero Dimensional:**

A point is a zero-dimensional object as it has no length, width, or height. It has no size. It tells about the location only. A point is dimensionless.

**2. One Dimensional:**

A line segment drawn on a surface is a one-dimensional object, as it has only length and no width.

For example,

**3. Two Dimensional:**

The 2-dimensional shapes or objects in geometry are flat plane figures that have two dimensions – length and width. Two-dimensional or 2-D shapes do not have any thickness and can be measured in only two faces.

A plane figure can be made of straight lines, curved lines, or both straight and curved lines. The circle, the square, the rectangle, the quadrilateral, and the triangle are examples of plane figures.