#### Topics

##### Number System

##### Sets

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

##### Estimation

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

##### Place Value

##### 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

##### HCF and LCM

##### Playing with Numbers

##### Ratio and Proportion

##### Ratio

##### Proportion (Including Word Problems)

##### Unitary Method

##### 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

##### Percent (Percentage)

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

##### Algebra

##### 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)

##### 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)

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

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

##### Quadrilateral

##### Polygons

##### 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)

##### Mean and Median

#### notes

**Simplification of Expression by Using Brackets:**

Use of brackets allows us to avoid confusion in the problems where we need to carry out more than one number operation.

First, turn everything inside the brackets () into a single number and then do the operation outside which in this case is to multiply by 10.

8 × 100 + 3 × 100 = 100 × (8 + 3) = 100 × 11 = 1100.

**Expanding brackets:**

**i) 102 × 103**

= (100 + 2) × (100 + 3) = (100 + 2) × 100 + (100 + 2) × 3

= 100 × 100 + 2 × 100 + 100 × 3 + 2 × 3

= 10,000 + 200 + 300 + 6 = 10,000 + 500 + 6

= 10,506

**(ii) 17 × 109**

= (10 + 7) × 109 = 10 × 109 + 7 × 109

= 10 × (100 + 9) + 7 × (100 + 9)

= 10 × 100 + 10 × 9 + 7 × 100 + 7 × 9

= 1000 + 90 + 700 + 63 = 1,790 + 63

= 1,853.

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