So what does that have to do with math you might ask. I'd say a lot. Think about the ultimate goal of math instruction--students with strong skills and flexibility with numbers. I would say one of the key factors in reaching that goal is helping our students learn to compose and decompose numbers. It's a skill that starts in Kindergarten and follows students throughout their mathematical career, and it's something that should be present in your classroom on a daily basis.
Composing and decomposing numbers is getting a lot of press these days with the adoption of the Common Core State Standards (CCSS). Consider the following examples:
A Kindergarten student uses number bracelets to find all the combinations for a given number. This is actually the foundation for learning basic facts, but it goes beyond that. Say the student is now presented larger numbers, like 8 + 5. They know that a combination for 5 is 3 and 2. They also know that a combination for 10 is 8 and 2. They can now solve it by decomposing the 5 into 3 and 2, adding the 2 to the 8 to make 10, and then adding the remaining 3 to get 13. Now that's mental gymnastics.
In a 1st grade class, a student uses her knowledge of number combinations to solve 8 = ? +3, modeling the problem with counters.
A 2nd grade class is working on place value and writing numbers in expanded form (235=200 + 30 + 5). We don't typically refer to it as decomposing the number, but that's really what it is. I wrote a post last week about the importance of showing students that numbers can be decomposed in more than one way. Students need to understand that 235 is also 100 + 130 +5. That's the basis for understanding subtraction with regrouping.
A 3rd grade class is working on multiplication facts. A student is trying to master the fact 7 x 6. He realizes he can decompose the 6 into 3 + 3 and then he knows that 7 x 6 is just twice 7 x 3 (a fact he happens to know).
In the 4th grade classroom down the hall, students use an area model to solve 12 x 13, leading to a deeper understanding of the multiplication process.
And in yet another classroom, a 5th grade student decomposes 11/7 into 7/7 and 4/7 to change it to the mixed number 1 4/7.
Strong, flexible mathematicians. Go for the gold!