Activity W2.3
The number 9 can be written as 9 = 3 × 3.
So, it is a square number.
This activity will make the students aware about such special
numbers called square numbers.
Material required:
Grid sheet/graph paper/Math notebook (used
in foundational stage),
coloured sketch pens,
square numbers cards
and box.
Preliminaries
Prepare number cards (of square of numbers from 1 to 8 and a
few non-square numbers)
The number of cards will be equal to total number of students in the class.
There can be multiple cards with the same square number.
Procedure
One grid sheet or graph paper or page of a Math notebook may be given to every student.
All the students may be provided opportunity to present their work in front of the whole class.
Put all the number cards in a box.
One student comes and picks a number card from the box and reads the number on it loudly.
Colour or cross the number of boxes on the sheet equal to the number written on the chosen card.
For example, if the number on the number card is 9, then 9 boxes should be coloured in the grid.
Example Number Picked: Let’s assume the card shows 9.
The following process should be adopted for doing this:
Fill or cross the adjacent boxes equally in horizontal and vertical manner (sample has been shown as under).
Fill the boxes with different colours.
There is a possibility that students may not get equal number of filled or crossed squares horizontally and vertically for some numbers.
Now they may observe and tell about the shape formed and write its name.
The teacher may ask questions to the presenters.
Some sample
questions are as follows:
1. How many rows are coloured? Write in your notebook.
ANSWER:
3 rows are coloured.
2. How many columns are coloured? Write in your notebook.
ANSWER:
3 columns are coloured.
3.Count the number of boxes coloured in total.
ANSWER:
Total boxes coloured = 9.
4. Is there any relationship between the number of rows and
columns, are coloured and the total number of boxes?
ANSWER:
Yes!
The total number of boxes = Number of Rows × Number of Columns
Here: 3 × 3 = 9.
5. If yes, then what is that relationship?
ANSWER:
The relationship is that both rows and columns have the same number, and their multiplication gives the total number —
This is the square of a number.
6. What pattern have you observed in this relationship?
ANSWER:
When the number of rows and columns are the same, the total is always a square number (e.g., 1, 4, 9, 16, 25...).
7. What is the name of shape formed by the coloured boxes?
ANSWER:
The shape is called a Square.
8. What is the difference between shapes of the coloured boxes
for numbers 16, 4, 25, 9 36 and of 8, 10, 15, 12, 30?
ANSWER:
For 16, 4, 25, 9, 36:
The shape is always a perfect square (equal rows and columns).
For 8, 10, 15, 12, 30:
You cannot form a perfect square because these numbers are not square numbers — the rows and columns cannot be equal.
Extension Question:
How does the area of a square and square numbers relate?
→ The area of a square = side × side.
If the side is a whole number, the area is always a square number!
After discussion on above questions, teacher will conclude the
class by introducing square numbers relating to the concept of
multiplication.
For example:
1 × 1 = 1
2 × 2 = 4
3 × 3 = 9
4 × 4 = 16
5 × 5 = 25
6 × 6 =36
And so on.
Teacher may discuss how the square number and the 2D square
shapes are related to each other.
Extended Learning and Exploration
Try the same process of filling colours in boxes for some other
random numbers like 10, 15, 12, 20, etc.
Is it possible to make the
shape of square with these number of boxes?
Answer:
→ No, it is not possible!
Because a perfect square shape always has equal rows and columns — and for numbers like 10, 15, 12, 20 there’s no whole number that can multiply by itself to reach these totals.
For example:
-
√10 ≈ 3.16 (not a whole number)
-
√15 ≈ 3.87 (not a whole number)
-
√12 ≈ 3.46 (not a whole number)
-
√20 ≈ 4.47 (not a whole number)
So these cannot form a square-shaped pattern on the grid.
Students may be motivated to extend their learning by knowing
the need of square numbers in mathematics.
Discuss on how does the area of a square and the square numbers
are related?
Real-Life Connection:
Tiles on a floor, windows, chessboards, and fields often show square patterns — so this helps students link math with the world around them!
Participation of Special Children
Special children will also be able to do this activity, if the teacher
pairs them with a peer buddy.
Some concrete objects like same size marbles or bindi can be
given to the children with visual impairment so that they can
count them and arrange in square shape
