More about points, line segments, lines and rays | Problems, Online Practice, Tests, Worksheets, Quizzes, Assignments | Class 4 | NCERT (CBSE and ICSE)

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Class 4
Geometry
Shapes and spatial understanding
Point, line segment, Line and ray
More about points, line segments, lines and rays

Class 4

1. Roman Numerals

1.1. Basic symbols to write Roman numerals

1.2. Basic rules to form Roman numerals

1.3. Roman numerals upto 100

1.3.1. Write Roman numerals for Hindu-Arabic numerals upto 39

1.3.2. Write Hindu-Arabic numerals for Roman numerals upto 39

1.3.3. Write Roman numerals for Hindu-Arabic numerals upto 100

1.3.4. Write Hindu-Arabic numerals for Roman numerals upto 100

1.3.5. Identify if a given Roman numeral is meaningless for Roman numerals upto 100

1.3.6. Compare Roman numerals upto 100

1.3.7. Do basic arithmetic using Roman numerals upto 100

1.3.8. Miscellaneous questions on Roman numerals

1.3.9. Word Problems on Basic Arithmetic Using Roman Numerals

2. Geometry

2.1. Shapes and spatial understanding

2.1.1. Point, line segment, Line and ray

2.1.1.1. Definition and concept of a point

2.1.1.2. Definition and concept of a line segment

2.1.1.3. Definition and concept of a line

2.1.1.4. Definition and concept of a ray

2.1.1.5. More about points, line segments, lines and rays

2.1.1.7. Draw line segment of a given length

2.1.3. Closed and open figures

2.1.3.1. Closed figures

2.1.3.2. Open figures

2.1.3.3. Difference between closed and open figures

2.1.3.4. Simple closed figures

2.1.4. Polygons

2.1.4.1. Basic definition of a polygon

2.1.4.2. Sides and vertices of a polygon

2.1.4.3. Types of polygons

2.1.5. Triangles

2.1.5.1. Basic definition of a triangle

2.1.6. Quadrilaterals

2.1.6.1. Basic definition of a quadrilateral

2.1.6.2. Adjacent sides of a quadrilateral

2.1.6.3. Diagonals of a quadrilateral

2.1.7. Rectangle

2.1.7.1. Basic definition of a rectangle

2.1.7.2. Rectangle as a special type of a quadrilateral

2.1.8. Square

2.1.8.1. Basic definition of a square

2.1.8.2. Square as a special case of a rectangle

2.1.9. Circle

2.1.9.2. Centre of a circle

2.1.9.3. Radius of a circle

2.1.9.4. Diameter of a circle

2.1.9.5. Identifying centre, radius and diameter of a circle

2.1.9.6. Arc

2.1.9.7. Semi-circle

2.1.9.8. Circumference of a circle

2.1.9.9. Drawing a circle of given radius with compass

2.1.9.10. Chord

2.1.12. Area and perimeter of simple shapes

2.1.12.1. Basic definition of perimeter

2.1.12.2. Perimeter of triangles, rectangles and squares

2.1.12.2.1. Perimeter of a rectangle

2.1.12.2.2. Perimeter of a square

2.1.12.2.3. Find perimeter of triangle

2.1.12.3. Perimeter of simple rectilinear shapes

2.1.12.5. Basic definition of area

2.1.12.6. Area of simple rectilinear shapes using the concept of unit squares

2.1.12.7. Word problems on perimeter and area

3. Numbers

3.1. Number System

3.1.1. Definition of a numeral

3.1.1.2. Indian number system (Hindu-Arabic number system)

3.1.1.2.1. Largest and smallest numbers of 4, 5, 6, and 7 digits

3.1.1.2.2. The ones period, the thousands period, the lakhs period and the crores period

3.1.1.2.3. Number names in the Indian number system for numerals up to 5 digits

3.1.1.2.4. Number names in the Indian number system for numerals up to 7 digits

3.1.1.3. International number system

3.1.1.3.1. Largest and smallest 4, 5, 6, 7, 8 and 9 digit numbers

3.1.1.3.3. Number names in the International number system for numerals up to 6 digits

3.1.1.3.4. Number names in the International number system for numerals up to 9 digits

3.1.1.4. Face value and place value

3.1.1.4.1. Concept: Face Value of a digit in a numeral

3.1.1.4.2. Concept: Place Value of a digit in a numeral

3.1.1.4.3. Questions involving face values and place values of digits in a numeral

3.1.1.4.4. Expanded form of a number

3.1.1.5. Successor and predecessor

3.1.1.5.1. Successor of a number

3.1.1.5.2. Predecessor of a number

3.1.1.7. Comparison of numbers

3.1.1.7.1. Comparision of numbers up to 5 digits

3.1.1.7.1.1. Comparision of numbers with different number of digits

3.1.1.7.1.2. Comparision of numbers with same number of digits

3.1.1.7.2. Comparision of numbers up to 7 digits

3.1.1.7.2.1. Comparision of numbers with different number of digits

3.1.1.7.2.2. Comparision of numbers with same number of digits

3.1.1.7.3. Comparision of numbers up to 7 digits (Indian system of numeration)

3.1.1.7.3.1. Comparision of numbers with different number of digits

3.1.1.7.3.2. Comparision of numbers with same number of digits

3.1.1.7.4. Comparision of numbers up to 7 digits (International system of numeration)

3.1.1.7.4.1. Comparision of numbers with different number of digits

3.1.1.7.4.2. Comparision of numbers with same number of digits

3.1.1.7.5. Recognizing the largest and smallest numbers among the given numbers

3.1.1.8. Ascending and descending order

3.1.1.8.1. Arranging numbers of up to 5 digits in ascending order

3.1.1.8.2. Arranging numbers of up to 5 digits in descending order

3.1.1.8.3. Arranging numbers of up to 7 digits in ascending order (Indian system of numeration)

3.1.1.8.4. Arranging numbers of up to 7 digits in descending order (International system of numeration)

3.1.2. Numbers and operations

3.1.2.1. Addition and subtraction

3.1.2.1.1. Addition

3.1.2.1.1.1. Concept of addendum and sum

3.1.2.1.1.2. Addition without carrying

3.1.2.1.1.2.1. Addition of two numbers without carrying

3.1.2.1.1.2.1.1. Addition of two numbers of up to 4 digits without carrying

3.1.2.1.1.2.1.2. Addition of two numbers of up to 6 digits without carrying

3.1.2.1.1.2.2. Addition of up to 4 numbers without carrying

3.1.2.1.1.2.2.1. Addition of up to five numbers of up to 4 digits without carrying

3.1.2.1.1.2.2.2. Addition of up to five numbers of up to 6 digits without carrying

3.1.2.1.1.2.3. Finding the missing digits in column-wise addition of up to 3 numbers (without carrying)

3.1.2.1.1.3. Addition with carrying

3.1.2.1.1.3.1. Addition of two numbers with carrying

3.1.2.1.1.3.1.1. Addition of two numbers of up to 4 digits with carrying

3.1.2.1.1.3.1.2. Addition of two numbers of up to 6 digits with carrying

3.1.2.1.1.3.2. Addition of up to 4 numbers with carrying

3.1.2.1.1.3.2.1. Addition of up to five numbers of up to 4 digits with carrying

3.1.2.1.1.3.2.2. Addition of up to five numbers of up to 6 digits with carrying

3.1.2.1.1.3.3. Finding the missing digits in column-wise addition of up to 3 numbers (with carrying)

3.1.2.1.1.5. Word problems on addition

3.1.2.1.1.5.1. Word problems on addition of two numbers

3.1.2.1.1.5.1.1. Word problems on addition of two numbers of up to 4 digits

3.1.2.1.1.5.1.2. Word problems on addition of two numbers of up to 6 digits

3.1.2.1.1.5.2. Word problems on addition of up to five numbers

3.1.2.1.1.5.2.1. Word problems on addition of up to five numbers (up to 4 digits)

3.1.2.1.1.5.2.2. Word problems on addition of up to five numbers (up to 6 digits)

3.1.2.1.2. Subtraction

3.1.2.1.2.2. Subtraction without borrowing

3.1.2.1.2.2.1. Subtraction of two numbers without borrowing

3.1.2.1.2.2.1.1. Subtraction of two numbers of up to 4 digits without borrowing

3.1.2.1.2.2.1.2. Subtraction of two numbers of up to 6 digits without borrowing

3.1.2.1.2.2.2. Finding missing digits in column-wise subtraction of two numbers (without borrowing)

3.1.2.1.2.3. Subtraction with borrowing

3.1.2.1.2.3.1. Subtraction of two numbers with borrowing

3.1.2.1.2.3.1.1. Subtraction of two numbers of up to 4 digits with borrowing

3.1.2.1.2.3.1.2. Subtraction of two numbers of up to 6 digits with borrowing

3.1.2.1.2.3.2. Finding missing digits in column-wise subtraction of two numbers (with borrowing)

3.1.2.1.2.4. Word problems on subtraction

3.1.2.1.2.4.1. Word problems on subtraction of two numbers

3.1.2.1.2.4.1.1. Word problems on subtraction of two numbers of up to 4 digits

3.1.2.1.2.4.1.2. Word problems on subtraction of two numbers of up to 6 digits

3.1.2.1.2.5. Word problems on subtraction involving up to five numbers

3.1.2.1.2.5.1. Word problems on subtraction involving up to five numbers of up to 4 digits

3.1.2.1.2.5.2. Word problems on subtraction involving up to five numbers of up to 6 digits

3.1.2.1.2.5.3. Framing simple word problems on subtraction

3.1.2.1.3. Mixed operations: Word problems with a mix of addition and subtraction of up to 5 numbers

3.1.2.1.3.1. Word problems with a mix of addition and subtraction of up to five numbers of up to 4 digits

3.1.2.1.3.2. Word problems with a mix of addition and subtraction of up to five numbers of up to 6 digits

3.1.2.2. Multiplication and division

3.1.2.2.1. Multiplication

3.1.2.2.1.1. Understanding what is multiplication

3.1.2.2.1.3. Properties of multiplication

3.1.2.2.1.3.3. Multiplicative property of 1

3.1.2.2.1.3.4. Multiplicative property of 0

3.1.2.2.1.5. Multiplication of a number by 10, 100, 1000 etc.

3.1.2.2.1.8. Multiplication of two, three, and four digit numbers using the standard (column) method.

3.1.2.2.1.8.3. Multiplication of a four digit number by a two digit number using standard method

3.1.2.2.1.8.5. Multiplication of a four digit number by a three digit number using standard method

3.1.2.2.1.9. Word problems on multiplication

3.1.2.2.1.9.1. Simple word problems on multiplication involving two digit numbers

3.1.2.2.1.9.2. Simple word problems on multiplication involving three digit numbers

3.1.2.2.1.9.3. Simple word problems on multiplication involving four digit numbers

3.1.2.2.1.9.4. Simple word problems involving multiplication and addition for numbers up to four digits

3.1.2.2.1.9.5. More word problems on multiplication

3.1.2.2.1.10. Miscellaneous problems on multiplication

3.1.2.2.2. Division

3.1.2.2.2.1. Meaning of division, dividend, divisor, quotient and remainder

3.1.2.2.2.2. Properties of division

3.1.2.2.2.2.1. Division of a number by 1

3.1.2.2.2.2.2. Division of a number by itself

3.1.2.2.2.3. Division by 10, 100 and 1000

3.1.2.2.2.8. Division of two numbers using standard method (no remainder)

3.1.2.2.2.8.1. Division by a number up to 9

3.1.2.2.2.8.2. Division by a number up to 19

3.1.2.2.2.9. Division using standard method (with remainder)

3.1.2.2.2.9.1. Division by a number up to 9

3.1.2.2.2.9.2. Division by a number up to 19

3.1.2.2.2.9.3. Division by a number up to 49

3.1.2.2.2.9.4. Division by a number up to 99

3.1.2.2.3. Word problems on division (No remainder)

3.1.2.2.3.1. Word problems involving division of two and three digit numbers by one and two digit numbers

3.1.2.2.3.2. Solve word problems involving division of up to five digit numbers by one and two digit numbers

3.1.2.2.4. Word problems on division (With remainder)

3.1.2.2.4.1. Word problems involving division of two and three digit numbers by one and two digit numbers

3.1.2.2.4.2. Word problems involving division of up to five digit numbers by one and two digit numbers

3.1.2.3. Mixed Operations: Word problems involving a mix of addition, subtraction, multiplication and division

3.1.2.5. Estimation

3.1.2.5.1. Estimating sums of given numbers

3.1.2.5.3. Estimating products of given numbers

3.1.3. Fractional numbers (Fractions)

3.1.3.1. Basic meaning of fractions

3.1.3.1.1. Understanding fraction as part of a whole

3.1.3.1.1.1. Identifying half, one fourth and three-fourths of a whole

3.1.3.1.1.2. Identifying the symbols, 1/2, 1/4, 3/4

3.1.3.1.1.4. Identifying a fraction as part of a whole

3.1.3.2. Equivalent fractions

3.1.3.2.2. Writing fractions equivalent to a given fraction

3.1.3.3. Comparison of fractions

3.1.3.3.1. Comparision of fractions having same denominator

3.1.3.3.2. Comparision of fractions having same numerator

3.1.3.3.3. Comparision of fractions having different numerator and denominator

3.1.3.4. Like and unlike fractions

3.1.3.4.1. Understanding and identifying like and unlike fractions

3.1.3.4.2. Addition and subtraction of like fractions

3.1.3.4.2.1. Addition of like fractions

3.1.3.4.2.2. Subtraction of like fractions

3.1.3.4.2.3. Word problems on addition of like fractions

3.1.3.4.2.4. Word problems on subtraction of like fractions

3.1.3.7. Proper and improper fractions

3.1.3.7.1. Understanding proper fractions

3.1.3.7.2. Understanding improper fractions

3.1.3.7.3. Differentiating between the proper and improper fractions

3.1.3.8. Mixed fractions (Mixed numbers)

3.1.3.8.1. Meaning of mixed fractions

3.1.3.8.2. Conversion of mixed fractions to improper fractions

3.1.3.8.3. Conversion of improper fractions to mixed fraction

3.1.3.9. Simplest form of a fraction

3.1.3.9.2. Conversion of given fractions into simplest/lowest form

3.1.3.10. Word problems on fractions

3.1.4. Factors and multiples

3.1.4.1. Factors

3.1.4.1.1. Basic definition of a factor

3.1.4.1.3. HCF: Highest Common Factor (or GCD: Greatest Common Divisor)

3.1.4.1.3.2. Finding HCF/GCD of small numbers (smaller than 100) by heuristic method

3.1.4.2. Multiples

3.1.4.2.1. Basic definition of a multiple

3.1.4.2.2. Basic properties of multiples

3.1.4.2.2.1. Property of multiples: Every non-zero number has unlimited number of multiples

3.1.4.2.2.2. Property of multiples: Every number is a multiple of 1

3.1.4.2.2.6. Property of multiples: The first multiple of a number is the number itself

3.1.4.2.3. LCM; Least common multiple

3.1.4.2.3.2. Finding LCM of small numbers by heuristic method (For LCMs less than or equal to 100)

3.1.4.3. Appreciating factors and multiples

3.1.4.4. Appreciating LCM (Least common multiple) and HCF (highest common factor)

3.1.4.4.1. Properties of LCM and HCF of two numbers

3.1.4.4.2. Miscellaneous questions on LCM and HCF

3.1.4.4.3. Word problems on LCM and HCF

3.1.4.4.3.1. Word problems on LCM

3.1.4.5. Prime and composite numbers

3.1.4.5.1. Basic definition of prime numbers

3.1.4.5.2. Identifying all prime numbers upto 100

3.1.4.7. Even and odd numbers

3.1.4.7.1. Basic definition of even numbers

3.1.4.7.2. Basic definition of odd numbers

3.1.4.7.3. Appreciating even and odd numbers

3.1.4.8. Tests of divisibility

3.1.4.8.1. Test divisibility by 2

3.1.4.8.2. Test divisibility by 3

3.1.4.8.3. Test divisibility by 4

3.1.4.8.4. Test divisibility by 5

3.1.4.8.5. Test divisibility by 6

3.1.4.8.6. Test divisibility by 9

3.1.4.8.7. Test divisibility by 10

3.1.5. Decimals

3.1.5.6. Writing fractional numbers as decimals

3.1.5.7. Writing decimals as fractional numbers

3.1.5.9. Identifying place values of digits in a decimal number

3.1.5.10. Writing decimal numbers in expanded form (sum of decimal fractions)

3.1.5.11. Writing expanded form of decimals (as sum of decimal fractions) in short form

3.1.5.12. Comparision of decimal numbers

3.1.5.13. Conversion of decimals to improper fractions

3.1.5.14. Conversion of decimals to mixed fractions

3.2. Word problems on addition of decimals

3.3. Word problems on subtraction of decimals

4. Money

4.1. Understanding the concept of currency

4.3. Converting rupees to paise

4.4. Converting 'rupees and paise' into paise

4.5. Converting an amount expressed in figures into paise

4.6. Converting an amount given in paise into rupees and paise

5. Measurement

5.1. Length

5.1.3. Conversion from one unit of length to another

5.1.3.1. Conversion from higher to lower units of length

5.1.3.1.1. Converting kilometres into metres

5.1.3.1.2. Converting metres into decimetres

5.1.3.1.3. Converting metres into centimetres

5.1.3.1.4. Converting centimetres into millimetres

5.1.3.2. Conversion from mixed units to lower units of length

5.1.3.2.1. Converting 'kilometres and metres' to metres

5.1.3.2.2. Converting 'metres and decimetres' to decimetres

5.1.3.2.3. Converting 'metres and centimetres' to centimetres

5.1.3.2.4. Converting 'centimetres and millimetres' into millimetres

5.1.3.2.5. Converting lengths in 'kilometres, hectometres, decametres and metres' into metres

5.1.3.3. Conversion from lower to higher units of length

5.1.3.3.1. Converting millimetres into centimetres

5.1.3.3.2. Converting centimetres into metres

5.1.3.3.3. Converting metres into kilometres

5.1.3.3.4. Expressing metres as 'kilometres and metres'

5.1.3.3.5. Converting millimetres into metres and centimetres

5.1.4. Solves problems involving length and distances.

5.1.4.2. Word problems on addition and subtraction of length measurements

5.1.4.2.1. Word problems involving addition of length measurements

5.1.4.2.2. Word problems involving subtraction of length measurements

5.1.4.2.3. Word problems involving both addition and subtraction of length measurements

5.1.4.3. Word problems on multiplication and division of length measurements

5.1.4.3.1. Word problems involving multiplication of length measurements

5.1.4.3.2. Word problems involving division of length measurements

5.1.4.3.3. Word problems involving both multiplication and division of length measurements

5.2. Weight/Mass

5.2.5. Conversion from one unit of weight/mass to another

5.2.5.1. Conversion from higher to lower units of mass/weight

5.2.5.1.1. Converting kilograms into grams

5.2.5.1.2. Converting 'kilograms and grams' into grams

5.2.5.1.3. Converting grams into milligrams

5.2.5.1.4. Converting 'grams and milligrams' into milligrams

5.2.5.1.5. Converting 'kilograms, hectograms, decagrams, grams' into grams

5.2.5.2. Conversion from lower to higher units of mass/weight

5.2.5.2.1. Converting grams into kilograms

5.2.5.2.2. Converting grams into 'kilograms and grams'

5.2.5.2.3. Converting milligrams into 'grams and milligrams'

5.2.6. Problems involving weight/mass

5.2.6.1. Determining sums and differences of weights

5.2.6.1.3. Subtraction of weights/mass in one unit

5.3. Volume

5.3.4. Conversion from one of volume/capacity to another

5.3.4.1. Conversion from higher to lower units of volume

5.3.4.1.1. Converting kilolitres to litres

5.3.4.1.2. Converting 'kilolitres and litres' to litres

5.3.4.1.3. Converting litres to millilitres

5.3.4.1.4. Converting 'litres and millilitres' to millilitres

5.3.4.1.5. Converting 'kilolitres, hectolitres, decalitres, and litres' to litres

5.3.4.2. Conversion from lower to higher units of volume

5.3.4.2.1. Converting litres into kilolitres

5.3.4.2.2. Converting litres into 'kilolitres and litres'

5.3.4.2.3. Converting millilitres into litres

5.3.4.2.4. Converting millilitres into 'litres and millilitres'

5.4. Time and Calendar

5.4.1. Time

5.4.1.1. Time in a clock

5.4.1.1.2. Reading clock time to the nearest hours and minutes

5.4.1.2. Expressing time using the terms A.M. and P.M.

5.4.1.5. Conversion from one unit of time to another

5.4.1.5.1. Conversion of days into hours

5.4.1.5.2. Conversion of hours into minutes

5.4.1.5.3. Conversion of hours into seconds

5.4.1.5.5. Conversion of hours into days

5.4.1.6. The 24-hour clock time

5.4.1.6.1. Conversion from 24-hour clock time to 12-hour clock time

5.4.1.6.2. Conversion from 12-hour clock time to 24-hour clock time

5.4.1.7. Addition and subtraction of time

5.4.1.7.1. Addition of time

5.4.1.7.2. Subtraction of time

5.4.1.8. Word problems on time

5.4.1.8.1. Word problems on addition and subtraction of time

5.5. Miscellaneous word problems on time

6. Unitary method

6.3. Word problems using unitary method involving both multiplication and division

7. Data Handling

7.1. Data

7.1.1. Basic definition of data

7.2. Pictographs

7.2.1. Basic definition of pictographs

7.2.2. Representing given data as a pictograph

7.3. Bar graphs

7.3.2. Representing data in the form of bar graphs

8. Patterns

8.1. Number patterns

8.1.5. Identifying patterns in multiplication and division

8.1.6. Finding missing terms in given number pattern

8.2. Symmetry

8.2.1. Understanding the concept of symmetrical and asymmetrical figures

8.2.3. Identifying symmetry in common shapes and objects

8.2.3.1. Identifying symmetry in English capital letters

8.2.3.2. Identifying symmetry in common objects around us

8.2.3.4. Identifying symmetry in simple geometric figures

8.2.3.6. Symmetry in circles

9. Logical Reasoning

9.1. General logical reasoning

9.2. Cubes and Dice

9.3. Venn Diagrams

Class 4 NCERT (CBSE and ICSE) More about points, line segments, lines and rays

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