As a young girl, I briefly took gymnastics lessons. Anybody else? I have to admit that I was not very flexible—I couldn’t do a smooth backward roll to save my life! That said, one of my favorite Olympic events is the gymnastics competition. Every four years, I’m blown away by the strength and flexibility of these athletes. It is truly awe-inspiring.
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. 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 became part of our instructional vocabulary after the Common Core State Standards for Mathematics (CCSSM) were adopted in 2010. 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 2 and 3. They also know that 8 and 2 makes 10. They can now solve it by decomposing the 5 into 2 and 3, adding the 2 to the 8 to make 10, and then adding the remaining 3 to get 13. Now that’s mental gymnastics. And trust me, the time it takes a child to do this is a lot less than the time it takes me to explain it!
In a 1st-grade class, a student uses their 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 (135 = 100 + 30 + 5). We don’t typically refer to it as decomposing the number, but that’s really what it is. Check out this post I wrote about the importance of showing students that numbers can be decomposed in more than one way and grab a little freebie. Students need to understand that 135 absolutely can be represented as 100 + 30 + 5, but it can also be decomposed into 130 + 5 or 100 + 20 + 15. 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 6 x 7. They realize they can decompose the 6 into 3 + 3 and then knows that 6 x 7 is just twice 3 x 7 (a fact they happen 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!