#### Topics

##### Mathematics

##### Knowing Our Numbers

- Introduction to Knowing Our Numbers
- Comparing 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
- Round off and Estimation of Numbers
- To Estimate Sum Or Difference
- Estimating Products of Numbers
- Simplification of Expression by Using Brackets
- BODMAS - Rules for Simplifying an Expression
- Roman Numbers System and Its Application

##### Whole Numbers

- Concept for Natural Numbers
- Concept for Whole Numbers
- Successor and Predecessor of Whole Number
- Operation of Whole Numbers 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 of Whole Numbers
- Patterns in Whole Numbers

##### Playing with Numbers

- Arranging the Objects in Rows and Columns
- 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
- 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
- Prism
- Concept of Pyramid
- Polygons

##### 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°

- Method using ruler and compasses
- Method using a ruler and a set-square

## Notes

**Perpendicular to a Line Through a Point Not on It:**

**A. By folding the paper:**

- Draw a line MN on a paper. Take a point P anywhere outside the line.

- Keeping the line MN in view, fold the paper along the line MN.

- Now fold the paper through point P in such a way that the part of line MN on one side of the fold falls on the part of line MN on the other side of the fold.

- Unfold the paper. Name the point of intersection of the two folds Q. Draw the line PQ. This line falls on a fold in the paper.

Using a protractor, measure every angle formed at the point Q.

Line PQ is perpendicular to line MN.

Line PQ ⊥ line MN.

**A. Method using ruler and compasses:**

**Step 1: **Given a line l and a point P not on it.

**Step 2:** With P as a centre, draw an arc that intersects line l at two points A and B.

**Step 3:** Using the same radius and with A and B as centers, construct two arcs that intersect at a point, say Q, on the other side.

**Step 4: **Join PQ. Thus, `bar"PQ"`** **is perpendicular to l.** **

**B. Method using a ruler and a set-square (An optional activity):**

**Step 1: **Let l be the given line and P be a point outside l.

**Step 2:** Place a set-square on l such that one arm of its right angle aligns along l.

**Step 3:** Place a ruler along the edge opposite to the right angle of the set-square.

**Step 4:** Hold the ruler fixed. Slide the set-square along the ruler till the point P touches the other arm of the set-square.

**Step 5:** Join PM along the edge through P, meeting l at M.

Now, `bar"PM"` ⊥ l.