How Decomposing Numbers Helps Students with Common Core Math
In Common Core math, first grade students need to begin thinking about the properties of numbers more deeply. One important property of all numbers is that they can be decomposed.
When you decompose a number, it means that you take the number apart. You can do it in many ways; for example, you can think of 8 as 4 + 4, or as 3 + 5, or as 9 – 1, and so on.
Being able to decompose numbers is important for two reasons:

People who excel in math and science tend to be able to decompose numbers in many ways.

Even if you aren’t going into a math or science career, your ability to do computations in your head (as you go about your daily life surrounded by numbers) is greatly enhanced by being able to decompose numbers.
The good news here is that this skill can be taught through practice. If you aren’t good at it now, you can be in a few weeks. If your child is struggling with it now, he can improve in short order by practicing a little bit every day.
Students who quickly recall memorized facts are impressive, but students who can decompose numbers — even if they take longer to reconstruct a given number fact — often achieve at higher levels.
Taking numbers apart and putting them back together is directly useful in addition and subtraction of larger numbers later on. For example, in second grade, students can think of 97 + 8 as 100 + 5 if they’re used to decomposing 8 (and 100). These skills also apply in algebra and later mathematics.
You can practice with your child anytime you have a small number of objects and a few spare moments. Put eight things in two piles (maybe you keep three and give him five). Count yours; have your child count his. Then change the number in each pile. In a minute or so, the two of you will have practiced all of the ways to decompose 8 (or 9 or 12 or . . .). You can go one step further by recording your decompositions as “3 and 5” or “3 + 5” and comparing all the expressions you got for decomposing 8 (or 9, or 12, or . . .).