How to Teach Composing and Decomposing Numbers
To build a solid number sense, kids will learn about composing and decomposing numbers as early as kindergarten, and practice these critical skills in first grade, second grade, and beyond. I’m here to explain the difference between the two, and show different ways to build the students’ understanding of these early math concepts.
What is Composing vs. Decomposing Numbers
Decomposing and composing numbers, in short, is the ability to break apart a given number and put it back together again. In other words, it’s learning how to parts make a whole. If you have young children, or teach elementary school, you may know this as “part, part, whole”. Let’s look a little closer at what this means, and how you can teach it to kids.
Composing numbers is the ability to put two parts together to make a whole. For example, kids will put together sets of objects, of smaller numbers, to make a complete set.
Decomposing numbers is the ability to break down numbers into their sub-parts.
7 Different Ways to Teach Decomposing Numbers
Learning how to decompose and compose numbers looks different in each grade. However, here on Little Learning Corner, I share tips and resources for early childhood, specializing in Kinder, grade one, and grade two. Therefore, let’s look at some tips to teach decomposing numbers in the younger grades. If you’re looking for teaching strategies for the older kids, check out Time for Learning Middle School Math.
- Model, model, model: I can’t stress this enough. When you teach numbers, talk about them as much as possible. Instead of saying this is number 7, you could say “This is 7. There are different ways we can make the number 7, such as 1 and 6, 2 and 5, 3 and 4, 5 and 2, 6 and 1, or 7 and 0.”
- Math Talks: Something special happens when you sit down and do math talks, or number talks, with kids. I have created math talks for kindergarten, first grade, and second grade to increase engagement and promote independent thinkers. When you do a math talk about numbers, the kids express their thinking in a no judgement environment. The kids learn to explain their reasoning, while also learning from others’ processing.
- Provide a variety of tools and materials: To teach decomposing numbers, have a variety of manipulatives, visuals, and recording sheets for the kids to work through the process. It’s also important to encourage young children to use pictures, fingers, or objects to work through and build their understanding.
- Play games: Learning math through games builds problem solving skills, allows them to practice strategy in an informal setting, and allows kids to discuss strategies with their peers. There are fun games listed below.
- Extend Calendar time: After talking about the weather and days of the week, you will likely do an activity to count the days of school. Use that time to talk about the number. For example, if you just added a sticker for day 64, talk about what 64 means, and the place value of each digit. (i.e. 6 groups of 10 and 4 days left over)
- Small group and whole group: Do a combination of small group and whole group lessons when teaching how to compose and decompose numbers. Typically, when teaching kindergarten, I would introduce the skill to the whole class, reteach and refine to a small group, then allow the other students to work in centers – allowing them time to explore and practice on their own or with peers.
- Create and display an anchor chart: When you create a math anchor chart WITH the kids, it becomes meaningful. Work together to create an anchor chart for decomposing numbers, and hang it in a location where they can early reference it when they need support.
Use colorful post it notes to make anchor charts for numbers through 10. When using post-it-notes, you can remove one of the colors and ask the kids to create a number sentence and find the missing number. For example, on the anchor chart below, the kids would say “4+_=10, and the missing number is 6.”
7 Teaching Resources for Decomposing Numbers
1. Decomposing Numbers to 10 Dot Cards
With 30 dot cards included, these colorful tens-frame decomposing cards represent the numbers 1-10 with 3 different dot arrangements. Dots are red and yellow to match the standard counter manipulatives used in classroom.
2. Number Bonds
In most kindergarten, first grade, and second grade classrooms, you will see kids working with number bonds.
Number bonds are visual tools used to teach composing and decomposing numbers. They are also a great way to introduce fact families and missing number concepts.
Here is an example of how to show the number 10 using a number bond. This number bond mat was included in one of my Kindergarten Crate subscription boxes. If you want to try a box, use code CORNER to get 10% off.
The number ten was randomly selected from a set of themed number cards.
You can also find a collection of number bond materials on amazon, such as:
3. Place Value Games
- Dino-Math Track game board for place value, addition, and subtraction
- Place Value Safari
- Magnetic Base Ten blocks for place value demonstration
- Free Place Value printable game
4. I Have, Who Has Ten’s Frames Numbers to 20
I Have…Who Has (Superheroes) is a fun, chain-reaction, math game to practice number recognition and composing numbers to 20. This kindergarten and first grade math game can be played as a whole group or with small groups in math stations.
Students quickly learn the pattern of this game, and get excited to call out their card. “I have _____, Who has____?” – counting how many in the tens frames at the top, then reading the next number the bottom of the card, next to the colorful superhero.
Kids can’t argue who goes first, and you don’t have to make that decision! A starting card, and ending card are included. Grab “I Have, Who Has?” HERE.
5. Free Part-Part-Whole Games
- Free Part, Part, Whole (Numbers to 5)
- Free Part-Part-Whole Mini Unit
- Free Math Olympics Shake and Spill printable. Shake and spill games work best with double sided counters. The kids put a set number of counters in the cup, shake it, then spill them out. When they are spilled, the kids can see how to decompose the whole number using smaller numbers.
6. Puzzles
Puzzles, even if they aren’t counting puzzles, show how the concept of part-part-whole. When you put the parts of a puzzle together, you get a whole picture. Here are a few puzzles to teach this concept:
- The Learning Journey math puzzle
- Really Good Stuff Kites and Tails Puzzle for Decomposing numbers to 10
- Pattern blocks
7. My Tens-Frame Book
Practice composing and decomposing ten numbers, or numbers 10-20, then have the kids record their work in this “My Ten’s Frame Book“.
The kids will use cut and paste counters available, or use other materials such as dotters or stickers, in combination with the tens-frames to build the number shown. Then, on each page, they have to write the numeral in expanded form, showing the place value for the tens place and ones place.
Assessing Composing and Decomposing Numbers
Now that you’ve learned the difference between composing and decomposing, along with teaching strategies and resources, let’s talk a little about assessments.
When checking the students’ understanding, you want to do so using multiple assessments. For example, you will want to observe and take notes as they manipulate objects, play games, and participate in math talks when learning to decompose numbers. You can also check their progress by looking over completed work samples, such as the tens-frame book shown above.
If you are looking for a formal assessment, you can track their progress on a point-based rubric. Here are examples of kindergarten and first grade math rubrics that can be used to document the kids’ progress in math.
I hope you’ve found everything you need to help you feel confident in teaching composing and decomposing numbers in the early childhood years.
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