Year 7 Interactive Maths - Second Edition

## Patterns

Patterns often occur in science and mathematics, and they are formed by groups of shapes, objects, diagrams or numbers.  Patterns are a part of daily life and are very useful in mathematics as they can help us to solve some problems.

## Square Numbers

A square number is a number that can be arranged in a square pattern. The patterns of the first three square numbers are depicted below.

The first square number, 1, is shown as a square containing a single dot.  There is 1 row containing 1 dot.

So, there is 1 × 1 = 1 dot in this square number.

The second square number, 4, is shown as a
square with 2 dots in each side.  It is clear that there are 2 rows each containing 2 dots.

So, there are 2 × 2 = 4 dots in this square number.

The third square number, 9, is shown as a square with 3 dots in each side.  It is clear that there are 3 rows each containing 3 dots.

So, there are 3 × 3 = 9 dots in this square number.

From the above discussion, we find that the following numbers are all squares.

Following the pattern above, we can find any particular square number.

E.g.  The fourth square number will form a square with 4 rows each containing 4 dots.
So, there are 4 × 4 = 16 dots in the square.

Likewise, the fifth square number will form a square with 5 rows each containing 5 dots.
So, there are 5 × 5 = 25 dots in the square.

Note that 52 is often read as '5 to the power 2' and 2 is called the index (or power).

## Index Form

If a number is written with an index, then it is said to be in index form.

E.g.  36 can be written as 62 .

#### Example 1

Write the tenth square number.

##### Solution:

The tenth square number will form a square with 10 rows each containing 10 dots.

#### Example 2

Write down a number between 50 and 100 that is both odd and square.

##### Solution:

We find that 81 is between 50 and 100, and it is both an odd and square number.
So, the required number is 81.

#### Example 3

Write 20 × 20 in index form.

#### Example 4

Write 122 in words.

##### Solution:

122 in words is 'twelve squared'.