Definition to join two or more numbers (quantities) to get one number (called sum or total)
Fact families A fact family is a group of related facts using the same numbers. One example would be 4 + 3 = 7, 3 + 4 = 7, 7 – 3 = 4, and 7 – 4 = 3. Fact families are a very powerful tool for mastering facts; once you know one fact in a family, you can work out the other facts in the same family. Fact families are also useful for solving problems with missing addends, such as 4 + __ = 7.
Properties of Numbers Commutative 

Property for Addition

 If a and b are numbers, then a + b = b + a

When adding a group of 3 boys and a group of 5 boys, the sum is the same whether 3 is added to 5 or 5 is added to 3.

Associative 

Property for Addition

If a and b and c are numbers, then (a + b) + c = a + (b + c)

When adding groups of apples, the sum is the same no matter the order in which the groups are added.
  Cancellation 

Property for Addition

If a, b and c are numbers, and if a + b = a + c, then b = c

If the result obtained when group B is added to group A is the same as the result obtained when group C is added to group A, then group B is equal to group C.

     
Terminology 4 + 8 = 12
addend   addend   sum