Rectangular numbers
Definition: A rectangular number is one that can be represented in a rectangular dot pattern                          
Ex: Represent the following in a rectangular dot pattern
a)5, b)15
Solution:
a)5 is not possible because it is a prime number
b)6     or
                  

Square pattern
Definition: A square number is one which can be represented in a square dot form.
Ex: represent 4 and 6 in a square dot pattern
Solution: 4    6 cannot be represented because it is not a squared number
    

Triangular numbers
Definition: A triangular number is one the can be represented in a triangular dot pattern
Ex: represent 3 and 6 in a triangular dot pattern
Solution:    

Addition of numbers using dot patterns
Ex: combine and name the structure formed by the following
a)     +    = 9 =         Square

b)     +    = 4 =     Square

Odd and even numbers
Definition:
An even number is a number that can be represented in 2 rows or 2 columns on dot patterns. For example, 8 is an even number and can be reprensented as shown below
        2 columns

2 rows

Therefore, an even number is a number that is divisible by 2

An odd number is a number that cannot be divisible by 2 meaning they cannot be represented in 2 rows or 2 columns dot patterns. For example, 9, an odd number can be represented as follows