#### Topics

##### Knowing Our Numbers

##### Comparing Number

- Comparing Multiple Digit of Numbers
- Compare Numbers in Ascending and Descending Order
- Compare Number by Forming Numbers from a Given Digits
- Compare Numbers by Shifting Digits
- Introducing a 5 Digit Number - 10,000
- Revisiting Place Value of Numbers
- Expansion Form of Numbers
- Introducing the Six Digit Number - 1,00,000
- Larger Number of Digits 7 and Above
- An Aid in Reading and Writing Large Numbers
- Using Commas in Indian and International Number System

##### Large Numbers in Practice

##### Whole Numbers

- Concept for Natural Numbers
- Concept for Whole Numbers
- Successor and Predecessor of Whole Number
- Operation on of Whole Number on Number Line
- Properties of Whole Numbers
- Closure Property of Whole Number
- Associativity Property of Whole Numbers
- Division by Zero
- Commutativity Property of Whole Number
- Distributivity Property of Whole Numbers
- Identity of Addition and Multiplication
- Patterns in Whole Numbers

##### Playing with Numbers

- Introduction of Playing with Numbers
- Factors and Multiples
- Concept of Perfect Number
- Concept of Prime Numbers
- Concept of Co-prime Number
- Concept of Twin Prime Numbers
- Concept of Even and Odd Number
- Concept of Composite Number
- Concept of Sieve of Eratosthenes
- Tests for Divisibility of Numbers
- Divisibility by 10
- Divisibility by 5
- Divisibility by 2
- Divisibility by 3
- Divisibility by 6
- Divisibility by 4
- Divisibility by 8
- Divisibility by 9
- Divisibility by 11
- Common Factor
- Common Multiples
- Some More Divisibility Rules
- Prime Factorisation
- Highest Common Factor
- Lowest Common Multiple

##### Basic Geometrical Ideas

- Concept for Basic Geometrical Ideas (2 -d)
- Concept of Points
- Concept of Line
- Concept of Line Segment
- Concept of Ray
- Concept of Intersecting Lines
- Concept of Parallel Lines
- Concept of Curves
- Different Types of Curves - Closed Curve, Open Curve, Simple Curve.
- Concept of Polygons - Side, Vertex, Adjacent Sides, Adjacent Vertices and Diagonal
- Concept of Angle - Arms, Vertex, Interior and Exterior Region
- Concept of Triangles - Sides, Angles, Vertices, Interior and Exterior of Triangle
- Concept of Quadrilaterals - Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles
- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles

##### Understanding Elementary Shapes

- Introduction to Understanding Elementary Shapes
- Measuring Line Segments
- Concept of Angle - Arms, Vertex, Interior and Exterior Region
- Right, Straight, and Complete Angle by Direction and Clock
- Acute, Right, Obtuse, and Reflex angles
- Measuring Angles
- Perpendicular Line and Perpendicular Bisector
- Classification of Triangles (On the Basis of Sides, and of Angles)
- Equilateral Triangle
- Isosceles Triangles
- Scalene Triangle
- Acute Angled Triangle
- Obtuse Angled Triangle
- Right Angled Triangle
- Types of Quadrilaterals
- Properties of a Square
- Properties of Rectangle
- Properties of a Parallelogram
- Properties of Rhombus
- Properties of Trapezium
- Three Dimensional Shapes
- Concept of Prism
- Concept of Pyramid

##### Integers

##### Fractions

##### Decimals

- Concept of Decimal Numbers
- Place Value in the Context of Decimal Fraction.
- Concept of Tenths, Hundredths and Thousandths in Decimal
- Representing Decimals on the Number Line
- Interconversion of Fraction and Decimal
- Comparing Decimal Numbers
- Using Decimal Number as Units
- Addition of Decimal Numbers
- Subtraction of Decimals Fraction

##### Data Handling

##### Mensuration

##### Algebra

##### Ratio and Proportion

##### Symmetry

##### Practical Geometry

- Introduction to Practical Geometry
- Construction of a Circle When Its Radius is Known
- Construction of a Line Segment of a Given Length
- Constructing a Copy of a Given Line Segment
- Drawing a Perpendicular to a Line at a Point on the Line
- Drawing a Perpendicular to a Line Through a Point Not on It
- Drawing the Perpendicular Bisector of a Line Segment
- Constructing an Angle of a Given Measure
- Constructing a Copy of an Angle of Unknown Measure
- Constructing a Bisector of an Angle
- Angles of Special Measures - 30°, 45°, 60°, 90°, and 120°

#### notes

**Angles of Special Measures:**

There are some elegant and accurate methods to construct some angles of special sizes which do not require the use of the protractor.

**1. Constructing a 60° angle:**

**Step 1:** Draw a line l and mark a point O on it.

**Step 2:** Place the pointer of the compasses at O and draw an arc of convenient radius which cuts the line `bar"PQ"` at a point say, A.

**Step 3:** With the pointer at A (as centre), now draw an arc that passes through O.

**Step 4:** Let the two arcs intersect at B. Join OB. We get ∠BOA whose measure is 60°.

**2. ****Constructing a 30° angle:**

To construct an angle of 30°, we need to draw an angle of 60° as above then bisect it with the process of an angle bisector.

**3. Constructing a 90° angle:**

**Step 1: **Draw a line *l* and mark a point P on it. Now taking P as a centre and with a convenient radius, draw an arc of a circle which intersects line *l* at Q.

**Step 2: **Taking Q as a centre and with the same radius as before, draw an arc intersecting the previously drawn arc at R.

**Step 3: **Taking R as a centre and with the same radius as before, draw an arc intersecting the arc at S.

**Step 4: **Taking R and S as a centre, draw an arc of the same radius to intersect each other at T.

**Step 5:** Join PT, which is the required ray making 90° with line *l*.

**4. Constructing a 45° angle:**

Draw an angle of 90° then bisect it to make an angle of 45°.

**5. Constructing a 120° angle:**

An angle of 120° is nothing but twice of an angle of 60°.

Therefore, it can be constructed as follows :

**Step 1:** Draw any line PQ and take a point O on it.

**Step 2:** Place the pointer of the compasses at O and draw an arc of convenient

radius which cuts the line at A.

**Step 3: **Without disturbing the radius on the compasses, draw an arc with A as the centre which cuts the first arc at B.

**Step 4:** Again without disturbing the radius on the compasses and with B as centre, draw an arc which cuts the first arc at C.

**Step 5: **Join OC, ∠COA is the required angle whose measure is 120°.