#### 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

**Types of Angles:**

1. An **acute angle** measures between 0° and 90°.

2. The **right angle** is exactly equal to 90°.

3. An angle greater than 90° but less than 180° is called an **obtuse angle**.

4. A **straight angle** is equal to 180°.

5. An angle which is greater than 180° but less than 360° is called a **reflex angle**.

6. The angle between the two sticks lie one upon the other is called a **zero angle**. The measure of the zero angles is written as 0°.

7. Turning by two straight angles (or four right angles) in the same direction makes a full turn. This one complete turn is called one revolution. The angle for one revolution is a complete angle. Complete angle is one complete revolution or equal to 360°.

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##### Series: Types of Angles- Acute, Obtuse, Right, Straight, Reflex, Complete and Zero Angle

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Relation Between Right Angle, Straight Angle & Complete Angle

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The Measure Of Right Angle, Straight Angle & Complete Angle

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Some Important Points Related To Right Angle

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