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°
Definition
The branch of mathematics in which we studied numbers is arithmetic.
The branch of mathematics in which we studied shapes is geometry.
The study to use the letters and symbols in mathematics is called Algebra.
Notes
Introduction to Algebra:
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There are so many branches of mathematics -
The branch of mathematics in which we studied numbers is arithmetic.
The branch of mathematics in which we studied shapes is geometry.
The study to use the letters and symbols in mathematics is called Algebra. -
The word ‘algebra’ is derived from the title of the book, ‘Aljebar w’al almugabalah’.
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A branch of mathematics in which symbols, usually letters of the alphabet, represent numbers or members of a specified set and are used to represent quantities and to express general relationships that hold for all members of the set.
The main feature of algebra: (use of letters)
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The use of letters will allow us to write rules and formulas in a general way.
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By using letters, we can talk about any number and not just a particular number.
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Secondly, letters may stand for unknown quantities. By learning methods of determining unknowns, we develop powerful tools for solving puzzles and many problems from daily life.
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Thirdly, since letters stand for numbers, operations can be performed on them as on numbers. This leads to the study of algebraic expressions and their properties.
Matchstick Patterns:
The number of matchsticks required to make a pattern of Ls
No. of matchsticks used to make 1st L = 2
No. of matchsticks used to make 2nd L = 4
No. of matchsticks used to make 3rd L = 6
So, the pattern that we observe here is 2 × the number of Ls.
More Matchstick Patterns
The number of matchsticks required to make a pattern of Cs.
No. of matchsticks used to make 1st C = 3
No. of matchsticks used to make 2nd C = 6
No. of matchsticks used to make 3rd C = 9
So, the pattern that we observe here is 3 × the number of Cs.
Number of matchsticks required = 3n
