CLASS -6(Frayer’s Model) ● Prime number ● Composite number ● Line

DEFINITION

A number which has only two factors , 1 and the number itself is called a prime number .

PROPERTIES / CHARACTERISTICS 1. 2. 3. 4.

It is divisible by only 1 and itself . All prime numbers are odd numbers except 2. All prime numbers are natural numbers. 1 is neither a prime nor a composite number.

PRIME NUMBER EXAMPLES

NON-EXAMPLES

3 , 17 , 29 , 37 , 43 etc.

4 , 25 , 30 , 56 , 100 etc.

DEFINITION

A number which has more than two different factors is called a composite number .

PROPERTIES / CHARACTERISTICS 1. It is divisible by more than two numbers. 2. All even numbers are composite numbers except 2. 3. All composite numbers are natural numbers. 4. 1 is neither a prime nor a composite number.

COMPOSITE NUMBER EXAMPLES

NON-EXAMPLES

4 , 25 , 30 , 56 , 100 etc.

3 , 17 , 29 , 37 , 43 etc.

DEFINITION

PROPERTIES / CHARACTERISTICS

A line is a straight path which extends endlessly in both directions .

1. There are no end-point in a line. 2. Length of a line cannot be measured. 3. The symbol of a line is

LINE EXAMPLES

NON-EXAMPLES MN is a ray (not a line ).

AB is a line.

DE is a line segment (not a line ).

CLASS -7(Frayer’s Model ● Rational Number ● Terminating Decimal ● Non Terminating Decimal

DEFINITION

A number which can be expressed in the form of p/q , where p and q are integers and q ≠ 0 is known as a Rational Number.

PROPERTIES / CHARACTERISTICS 1. Fraction with corresponding negative fractions and zero constitute the system of rational numbers . 2. It can be positive or negative. 3. All the integers are rational numbers. 4. The word rational comes from the word 5. ratio. RATIONAL NUMBER

EXAMPLES

NON EXAMPLES

DEFINITION

The rational numbers for which remainder becomes zero after a finite number of steps are known as Terminating decimals.

PROPERTIES / CHARACTERISTICS 1. There are finite number of digits after the decimal point. 2. The denominator of the standard form of the rational number has only 2 and 5 as the prime factors.

Terminating Decimal EXAMPLES

NON EXAMPLES

DEFINITION

The rational numbers for which division process does not terminate are known as non terminating decimals.

PROPERTIES / CHARACTERISTICS 1. There are infinite number of digits after the decimal point. 2. The denominator of the standard form of the rational number has some prime factors other than 2 or 5.

Non-Terminating Decimal EXAMPLES

NON EXAMPLES

CLASS -8(Frayer’s Model) ● ● ● ●

Perfect Square Perfect Cube Direct Variation Inverse Variation

DEFINITION

A given number is called a perfect square or a square number if it is the square of some natural number.

PROPERTIES / CHARACTERISTICS 1. The squares of odd numbers are always odd and the squares of even numbers are always even. 2. The numbers ending with 2,3,7,8 are not perfect squares. 3. The prime factors of a perfect square are always in pairs. PERFECT SQUARE

EXAMPLES 1, 4, 9, 16, 25, 36, 49 , 64 etc.

NON EXAMPLES 2, 3, 5, 6, 7, 8 , 10 , 11, 12 , 13 , 14 , 15 etc.

DEFINITION

An integer ‘n’ is a perfect cube if there is an integer ‘m’ such that n = m x m x m or n =

PROPERTIES / CHARACTERISTICS 1. The cubes of odd numbers are always odd and the cubes of even numbers are always even. 2. The cube of negative number is always negative. 3. The cube of a rational number is equal to the cube of its numerator divided by the cube of its its denominator .

PERFECT CUBE EXAMPLES

NON EXAMPLES

1, 8, 27, 64, 125, 216, 343 , 512 , 27/343 etc.

2, 3, 4, 5, 6, 7, 9, 10 , 11, 12 , 13 , 14 , 15 , 16 , 17 , 100 , 256 etc.

DEFINITION

If two quantities are related in such a way that an increase in one quantity results in a corresponding increase in the other and vice-versa , then such a variation is called direct variation .

PROPERTIES / CHARACTERISTICS 1. x and y are said to be in direct variation if x and y increase or decrease together . 2. x/y remains constant.

DIRECT VARIATION EXAMPLES ● ●

Number of articles and total money to be paid are directly related. Distance covered at uniform speed and time taken are directly related .

NON EXAMPLES ● ●

Speed and time taken are inversely related Time taken to do the work and number of people are inversely related .

DEFINITION

If two quantities are related in such a way that an increase in one causes corresponding decrease in the other and vice-versa , then such a variation is called inverse variation .

PROPERTIES / CHARACTERISTICS 1. x and y are said to be in inverse variation if an increase in x causes corresponding decrease in y (and vice-versa) 2. xy remains constant.

INVERSE VARIATION EXAMPLES ●

●

Number of kids and number of pizza slices each will get are inversely related. Cost of an article and number of articles that can be bought with the given money are Inversely related.

NON EXAMPLES ● ●

Number of words typed and time taken are directly related . Quantity of petrol and distance covered are directly related .