## Monday, July 9, 2012

### Composing and Decomposing Numbers

In less than a month, they eyes of the world will be focused on the Summer Olympic games in London.  I don't know about you, but one of my favorite 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.  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!

1. I will definitely be using number bracelets in my class this year! Such a great lesson for the little ones!
Amy

1. Yes, and the kids love them. Get a class set made this summer!

2. I spend tons of time in my first grade classroom on composing and decomposing numbers. That deep understanding of number relationships really is a foundational building block! (I just posted about this a few days ago, too!)
I love your blog and have gotten so many wonderful ideas and resources from you. Thank you so much for getting the word out about the importance of number sense!

~Nikki
Teaching in Progress

1. I just checked out your blog, Nikki, and that was a GREAT post!

Here's the link for others who might like to visit: What's Your Magic Number?

3. I feel that I have benefited greatly from your posts. You have awesome ideas and I am so excited to implement many of them in my classroom this year! Thanks

1. You're so welcome! Don't you love the anticipation of a new school year?

4. I definitely agree with the importance of composing & decomposing numbers!! There's always a few that have a lot of difficulty with this & it's so important to provide them with many opportunities to practice. Great post! :)
Lisa
Learning Is Something to Treasure

1. Thanks, Lisa. And when we see kiddos in the upper elementary grades who have been struggling their whole elementary career, it's probably because they don't have that foundation. :(

5. Have you tried Ken-Ken with your students? It also forces students to decompose/compose numbers in order to solve the puzzle and figure out which numbers go together. It takes a lot of modeling to get them started, but my students really enjoy it. Here is the link for their site.

http://www.kenken.com/misc/classroom

1. Ooh, very Sudoku-ish. I just gave it a try, and I like it! What grade do you use it with?

6. thank you for your wonderful ideas. Last year I have started to compose and decompose using the 4 corners. This year I am going to use these braceletes.

7. Your blog is excellent. It is helping me teach my math students in a more hands-on way. Thank you so much. If you can recommend any resources for teaching fifth-graders how to decompose numbers and multiply, it would be appreciated.

8. I've used SO many of your ideas so far this year (2 weeks) I made rekenreks, I played several games to make ten, I made the pipe cleaner circles with the beads, etc. I have SO MUCH stuff and the kids love using them... thank you! Much more fun than the worksheets my teammates are using to meet the same objectives.
:)

1. Mary Anne,
I am so happy to hear that both you and your kiddos are enjoying math so much! It won't be long before your teammates will be knocking on your door for ideas. :)

9. We use Math Expressions in our district and our parents are totally puzzled by how we teach multidigit multiplication and "long" division. We teach using the decomposing method and all our kiddos get it!! Now we just have to retrain the parents!!

1. Absolutely, Fran! That's often the biggest challenge. Ha ha. :)