The basics of patterns in whole numbers begins with shapes made of dots.
The shapes we take are 1) line 2) triangle 3)square 4) rectangle.
Every number should be arranged in the following shapes.
Every number can be arranged as a line :
The number 2 is shown as . .
The number 3 is shown as . . .
And so on.
Some numbers show as a square using dots.
The number 4 is shown as . .
9 -----------> . . .
. . .
. . .
The number 6 can be written in the form of rectangle.
The number 6 is shown as . . .
. . .
Some numbers can be shown by two rectangles.
Let us take an example of 12
1) Firstly, we can arrange the dots either by 3 x 4. That means 3 rows and 4 columns.
2) Secondly, we can arrange the dots by 2 x 6. That means 2 rows and 6 column.
Some numbers can also be arranged as triangles, such numbers are called triangular numbers.
For example :
Noe that the triangle should have two equal sides. The number of dots in the rows starting from the bottom row should be like 4,3,2,1. The top row should always have one dot. Example : Draw a triangular number diagram for 9 and 12.
Patterns in numbers Example : 1
1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4= 9876
Observe the above pattern and write the next two steps. Example : 2
9 x 3= 27
90 x 3 = 270
900 x 3 = 2700
Observer the above pattern and Write the next two steps.
1) Which numbers can be shown only as a line? Also draw the diagram using dots.
2) Which of the following numbers shown as squares?
a) 6 b) 5 c) 8 d) 10
3) Draw the rectangles using dots. Mention the number of dots used for making the rectangles.
4) Write the 1st five numbers that can be drawn as a triangle. Also draw the diagram.
5) The numbers that can be shown by two rectangles. Give at least three examples.