# Finding Squares of one digit

### Objective

• Finding squares of a number by repeated multiplication.
• Defining the meaning of square number/perfect square.
• Recognizing the relationship between the square of a positive and negative integer.
• Recalling the square numbers from 1 to 10.

40 min

### Materials:

Beads (or any other object), sheet, pencil.

### Prerequisites/Instructions

1. The children should be familiar with counting of objects.
2. They should know the multiplication/product of numbers.

### Process

Team 1

Initially the teacher gives a set of beads to three different group of students and ask each group to count the number of beads.

Each group starts to count the number and comes up with their answers as 3 beads in each group.

Now the teacher instruct to check the number of beads in all the groups. Therefore all the group found 3 in number.

The teacher ask all the three group to tell the total number of beads found with them and the students answers it as 9 beads.

The teacher instruct to write in the multiplication form with the help of the numbers obtained,Each group writes in the form of 3 x 3=9 beads.

The teacher asks what can you observe in the above multiplication,The students answers repetition of number 3 twice.

Team 2

Similarly the teacher gives some beads to six different groups and tell each each group to count the number of beads and check whether all the groups have same in number.

The children counts the number of beads in their group and finds in other groups also, they found that there were 6 beads among six groups.

Now the teacher instructs them to write it in the form of multiplication and children come up with the answers as 6x6=36 beads.

Teacher asks what do u observe with this, the students answers it as 6 is repeated twice.

Therefore the activity can be done with different number of beads and different group of students

Hence the teacher helps out the students with different number of beads where the students figures it out that the same number is multiplied by itself. The teacher ask the students what do we tell when the same number is multiplied by itself.

The teacher concludes that the product of a number by itself is called as the square of the number or perfect square.

In general, if we consider a natural number m can be expressed as n^2,where n is also a natural number, then m is a square number.

symbolically the square is represented as refer the link

for example 7*7=7^2=49,therefore 0,1,4,9,16,25......... are perfect squares.

What about the numbers which comes in between the two square numbers?

If we observe the numbers 5^2=25 and 6^2=36 there comes many natural numbers between 25 and 36 but we can notice that there is no natural number between 5 and 6 so,the numbers which comes in between two perfect squares or square numbers are called non perfect squares.

How to find square of a negative numbers?

Finding square of a negative number

• As we have already learnt how to find a square of a natural number,suppose if there is any integer -2.

How do we find its square?

Do we have the square of negative integers also?

• To answer all these questions let us recall the square of a natural number
• consider 3^2,we can write 3^2 as 3x3 which is 9
• similarly let us take any negative integer such as (-4)^2,
• We can write this as (-4)x(-4), when we use the rules of multiplication of two negative integers the product becomes positive such that [- x - =+]then the square also becomes positive.
• similarly lets consider one more integer (-9)^2,this can be written as (-9)x(-9) which is equal to 81. From this we can conclude that "the square of any negative integer will always be a positive integer"

### Evaluation

1. The repeating of the same number twice is called as ___________.
2. What is the square of the number 6?
3. Name the operation used to find the square of a number?
4. The product obtained is 16 then how many beads are supposed to be taken?
5. Name the perfect square between 20 and 30?
6. Do 0 has its square number?
7. What is the square of (-8)?
8. The square of an integer will be a ___________ integer.
9. The square of 5^2 and (-5)^2 is _____.
10. Define perfect square with the help of an activity?