Topics
Term - 1
Numbers
- Fundamentals of Numbers
- Successor and Predecessor of Whole Number
- Introducing a 5 Digit Number - 10,000
- Introducing the Six Digit Number - 1,00,000
- Introducing seven-digit numbers
- Concept of Place Value
- Use of Commas
- Crores
- Comparing Numbers
- Ascending and Descending Order of Numbers
- Forming Numbers from Digits
- BODMAS Rule
- Rounding off a Number
- To Estimate Sum Or Difference
- Estimating Products of Numbers
- Whole Numbers
- Commutativity Property of Whole Number
- Associativity Property of Whole Numbers
- Distributivity Property of Whole Numbers
- Identity of Addition and Multiplication of Whole Numbers
Introduction to Algebra
Ratio and Proportion
Geometry
Statistics
Information Processing
- Systematic Listing
- Systematic Completion of Lists
Term - 2
Numbers
- Concept of Even and Odd Number
- Prime and Composite Numbers
- Eratosthenes’ Method of Finding Prime Numbers
- Tests for Divisibility of Numbers
- Divisibility by 2
- Divisibility by 3
- Divisibility by 5
- Divisibility by 4
- Divisibility by 6
- Divisibility by 8
- Divisibility by 9
- Divisibility by 10
- Divisibility by 11
- Prime Factorisation
- Factors and Common Factors
- Highest Common Factor (HCF)
- Multiples and Common Multiples
- Lowest Common Multiple
- Relationship between the Numbers and their HCF and LCM
Measurements
- Conversion of Units
- Fundamental Operations on Quantities with Different Units
- Measures of Time
- Conversion of Time
Bill, Profit and Loss
Geometry
- Basic Concepts of Triangles
- Classification of Triangles based on Sides
- Classification of Triangles based on Angles
- Basic Properties of a Triangle
- Triangle Inequality
- Drawing a Perpendicular to a Line
- Construction of Parallel Lines
Information Processing
- Tree Diagram
- Conversion of Tree Diagrams into Numerical Expressions
- Conversion of Algebraic Expressions into Tree Diagrams
Term - 3
Fractions
- Concept of Fraction
- Concept of Equivalent Fractions
- Comparing Fractions
- Addition of Fraction
- Subtraction of Fraction
- Concept of Mixed Fractions
- Multiplication of a Fraction by a Whole Number
- Using Operator 'Of' with Multiplication and Division
- Multiplication of Fraction
- Division of Fractions
- Concept of Proper and Improper Fractions
Integers
Perimeter and Area
- Concept of Perimeter
- Perimeter of a Rectangle
- Perimeter of Squares
- Perimeter of Triangle
- Concept of Area
- Area of Rectangle
- Area of Square
- Area of a Triangle
- Perimeter and Area of Combined Shapes
- Estimate the Area of Irregular Shape Using a Graph Paper
Symmetry
Information Processing
- Iterative Processes
- Iterative Process in Numbers
- Euclid’s Game
- Euclid’s Division Algorithm
- Arranging Things and Putting Them in Order
- Introduction
- Shifting Digits
Notes
Compare Number by Forming Numbers from a Given Digits:
When forming numbers from given digits, we should be careful to see if the conditions under which the numbers are to be formed are satisfied by interchanging positions of digits.
1. Forming Numbers from Digits without repetition:
Suppose, we have four digits 7, 8, 3, 5. Using these digits we want to make different 4-digit numbers in such a way that no digit is repeated in them. Thus, 7835 is allowed, but 7735 is not.
Use the given digits without repetition and make the greatest and smallest 4-digit numbers.
(a) 8357, 3578, 5783, etc. are examples of 4-digit numbers.
The greatest number is 8753 and the smallest is 3578.
2. Forming Numbers from Digits by using any one digit twice:
Make the greatest and the smallest 4-digit numbers by using any one digit twice.
(a) 3, 8, 7
The greatest number is 8873 and the smallest is 3378.
(b) 9, 0, 5
The greatest number is 9950 and the smallest is 5009.
3. Forming Numbers from Digits by using different digits:
Make the greatest and the smallest 4-digit numbers using any four different digits with conditions as given.
(a) Digit 7 is always at one's place
Greatest:
| 9 | 8 | 6 | 7 |
Smallest:
| 1 | 0 | 2 | 7 |
(b) Digit 4 is always at tens place:
Greatest:
| 9 | 8 | 4 | 7 |
Smallest:
| 1 | 0 | 4 | 2 |
(c) Digit 9 is always at hundreds place
Greatest:
| 8 | 9 | 7 | 6 |
Smallest:
| 1 | 9 | 0 | 2 |
(d) Digit 1 is always at thousands place
Greatest:
| 1 | 9 | 8 | 7 |
Smallest:
| 1 | 0 | 2 | 3 |
Notes
Compare Numbers by Shifting Digits:
Changing the position of digits in a number changes the value of the number.
Consider the number 795.
If we exchange the hundredths place digit with the digit at units place, we will get 597 which is smaller than 795.
Similarly, if we exchange the tenths place with the units place, we get 759, which is smaller than 795.
