## Addition Facts Through 12

As children begin adding three numbers, they learn to look for facts they already know. This strategy is possible because of the Associative Property of Addition and the Commutative Property of Addition.

Associative Property of Addition
When numbers are added, the addends can be grouped in different ways without changing the sum.

With numbers, this can be shown as (2 + 3) + 4 = 2 + (3 + 4).
With variables, this can be shown as (a + b) + c = a + (b + c).

Commutative Property of Addition
When numbers are added, the order of the addends can be changed without changing the sum.

With numbers, this can be shown as 2 + 3 = 3 + 2.
With variables, this can be shown as a + b = b + a.

Children are also introduced to the missing addend concept through exercises such as 8 + = 11 and through relating addition and subtraction with fact families. As we pointed out in earlier chapters, if a, b, and c are whole numbers with ab and ca, then a fact family can be shown as follows.

a + b = c
b + a = c
c − a = b
c − b = a

Teaching Model 15.6: Add Three Numbers