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
- Concept of Place Value
- Expansion Form of Numbers
- Introducing the Six Digit Number - 1,00,000
- Introducing seven-digit numbers
- Crores
- 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
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
- Eratosthenes’ method of finding prime numbers
- 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
- Introduction to Parallel Lines
- Concept of Curves
- Different Types of Curves - Closed Curve, Open Curve, Simple Curve.
- Concept of Polygons
- Concept of Angle
- Concept of Triangles
- Concept of Quadrilaterals
- Concept of Circle
Understanding Elementary Shapes
- Introduction to Understanding Elementary Shapes
- Measuring Line Segments
- Right, Straight, and Complete Angle by Direction and Clock
- Concept of Angle
- Measuring Angles
- Perpendicular Line and Perpendicular Bisector
- Classification of Triangles (On the Basis of Sides, and of Angles)
- Classification of Triangles based on Sides- Equilateral, Isosceles, Scalene
- Classification of Triangles based on Angles: Acute-Angled, Right-Angled, Obtuse-Angled
- 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
- Concept of Polygons
Integers
Fractions
Decimals
- The Decimal Number System
- Concept of Place Value
- Concept of Tenths, Hundredths and Thousandths in Decimal
- Representing Decimals on the Number Line
- Conversion between Decimal Fraction and Common Fraction
- Comparing Decimal Numbers
- Using Decimal Number as Units
- Addition of Decimal Fraction
- Subtraction of Decimal Fraction
Data Handling
Mensuration
Algebra
Ratio and Proportion
Symmetry
Practical Geometry
- Introduction to Geometric Tool
- 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 from a point outside the line
- The Perpendicular Bisector
- Constructing an Angle of a Given Measure
- Construction of an angle bisector using a compass
- Concept of Angle Bisector
- Angles of Special Measures - 30°, 45°, 60°, 90°, and 120°
- Decimals in money
- Decimals in length measurement
- Decimals in weight measurement
Notes
Using Decimal number as units:
1. Decimals in money:
We know that 100 paise = Rs. 1.
Therefore, 1 paise = Rs. ` 1/100` = Rs. 0.01.
2. Decimals in length measurement:
10 millimetre(mm) = 1 centimetre(cm)
100 centimetre(cm) = 1 metre(m)
1000 millimetre(mm) = 1 metre(m)
1 Kilometr e (Km) = 1000 metre(m)
1 centimetre(cm) = `1/(100) "m" or 0.01 "m"`
3. Decimals in weight measurement:
We know that 1000 g = 1 kg
Therefore, 1 g = `1/(1000)` kg = 0.001 kg.
Example
Express as rupees using decimals.
65 paise
65 paise = Rs. `65/100` = Rs. 0.65
Example
Express as cm using decimals.
7 cm and 5 mm
7 cm and 5 mm
= 7 cm + `5/10`cm
= `7 5/10`
= 7.5 cm
Example
Express as metres using decimals.
5 m and 875 mm
5 m and 875 mm
= 5 + `875/1000`
= `5 875/1000`
= 5.875 m.
Example
Express as metres using decimals.
5 m and 20 cm
5 m and 20 cm
= 5 + `20/100`
= `5 20/100`
= 5.20 m
Example
Express as kg using decimals.
2350 g
2350 g
= 2000 g + 350 g
= `2000/1000 "kg" + 350/1000 "kg"`
= 2 kg + 0.350 kg
= 2.350 kg
i.e. 2350 g = 2 kg 350 g = 2.350 kg.
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