Children develop through a progression as they learn how to add and subtract numbers.  Carpenter, et.al (1999) described this progression using four stages; Direct Modeling, Counting, Derived Facts, and Facts (Visit our Addition Strategies page to watch videos of each of these stages).

Direct Modeling: Children model each piece of the problem.  For example, when solving 5 + 6 they will count 5 items, count 6 items and then count them all starting back at 1.
Counting: Children can "hold" one of the numbers in their head and then count on from there.  For 5 + 6, you might see the child say "5" and then count on their fingers 6 more to get the answer.
Derived Facts: As children develop relationships between numbers they notice that 5 + 5 can help them solve 5 + 6.  Derived Facts is when a child uses facts they know to help them derive facts they do not know.
Facts: This is when children can instantly give the answer.

Unfortunately, too many children are stuck in the Counting stage.  We teach them how to use Doubles Facts and Make a Ten Facts to help them get to the Derived Fact stage, but they still revert back to counting on their fingers!  For kids to be considered fluent with their math facts we need to help them progress up to the Derived Fact and Fact stages.  But how???  Children lack the number sense necessary to see connections between numbers and to use those connections to help them when solving addition and subtraction problems.  To help children we need to spend more time focusing on number relationships.  Van de Walle (2006) described these four relationships that children should have around numbers:

Spatial Relationships: recognizing how many in a set without counting by seeing a visual pattern
One/Two More or Less: knowing which numbers are one/two more or less than any given number
Benchmarks of 5 and 10: how any given number relates to 5 and 10
Part-Part-Whole: ability to conceptualize a number as being made up of two or more parts

With lots of experience playing around with numbers, children start to develop these relationships.  These are not concepts that we can directly teach to a child and expect them to internalize it.  We can't tell a child, "4 is one less than 5" and expect them to just memorize that.  Instead, as they play games, and not just math games, but even just board games and the child rolls a 4 while another player rolls a 5 and the children experience first hand that 4 moves you one less space than the 5, then they will internalize and connect to those relationships.  Numeracy, or number sense, develops from children's experiences with numbers, not direct instruction.  So provide your kids with lots of math help through activities, games, and play.

Looking for a resource for some great activities and games to build number sense and children's fact fluency??  Well, check back or email us, we have a book coming out, Fall 2014, full of lessons which does just that.