Sylwia and the children are not just having fun playing musical hoops. They are engaged in a math experience about composing and decomposing the number 6. Sylwia used a game and real-life problems to make this big math idea meaningful for the children.

What Is Number Composition and Decomposition?

Composing a number is putting together two numbers (two parts) to make a larger number (whole), like joining 2 and 4 to make 6. To decompose a number is to break that number (whole) into parts to make smaller numbers. For example, the number 5 can be decomposed as 5 and 0; 4 and 1; 3 and 2.

Activities such as the one in the opening vignette foster an understanding of quantity and of the relationship between numbers, and they lay the foundation for more complex math concepts to come. Number composition is different from addition or subtraction in that we are asking children to grasp the structure of a number. What makes up 5? What are different ways 5 can be split up? As young children think about and model this with concrete objects, they are learning to see the underlying patterns in the number system and to develop number sense.

As children develop their skills to compose and decompose numbers quickly and accurately, they can begin solving number problems in various contexts. For example, a child might be asked to set the snack table for seven children, but only have four cups in their stack. If they can fluidly decompose 7, they can quickly figure out how many cups are missing. Later, children will use what they know about number composition to help them do addition and subtraction.

Foundations of Number Composition and Decomposition

Children have the most success with number composition and decomposition activities when they have the beginnings of some foundational skills. For example, it is helpful when children have begun to

• know the verbal number sequence (be able to count from 1 to 10 aloud)
• count objects with one-to-one correspondence (numbers correspond with specific quantities)
• identify the quantity of objects in a set and know that the last number counted tells how many (cardinality)
• understand that numbers higher in the number sequence are greater than those earlier in the sequence (magnitudes)

These skills may not develop in the same sequence or at the same rate for all children, so games like Sylwia’s are perfect for utilizing and building upon several of the skills at once.

Introducing Number Composition to Children

Here are tips you can use when introducing number composition and decomposition to the children in your classroom:

• Start small. Counting and manipulating smaller numbers, like numbers 1 through 5, are easier for early math learners. Check for children’s understanding of the fundamental skills noted above. Later, challenge them with larger numbers.
• Use concrete objects. Use objects such as fingers or toys to represent quantity. You can use both hands to represent numbers under 10, then borrow a child’s or coteacher’s hand for larger numbers. The use of concrete objects supports dual language learners as well because they are able to make connections to numbers and quantities by manipulating materials without depending so heavily on language.
• Use identical objects. When possible, use objects that all look the same, like identical, one-inch blue cubes, in number composition activities. This is especially helpful early in the development of number composition, as children may be distracted by objects that have different features.

With the above strategies in mind, the following are activities you can do with children to practice number composition and decomposition:

• Practice during daily routines. Find opportunities to compose and decompose numbers across the day during children’s routine activities. During snack time, prompt children to find different ways to group their blueberries, pretzels, or cookies.
• Tell a story. You can mathematize many of the stories you tell children. Having a story behind a problem helps children connect to and make sense of the number operation. For example, after reading 10 Little Rubber Ducks, by Eric Carle, give children a mat that has been divided into two sections using tape. One half of the mat represents a pond, and the other half represents grass. Encourage children to create stories about the 10 ducks and find as many combinations of 10 as possible. For dual language learners in your classroom, use the Spanish translation of this book alongside the English version. During the activity, translate key phrases for them as you go, such as “diez patitos de goma.”

In Sum

Get inspired when children not only understand something new about their mathematical worlds, but also when they choose to use this new knowledge in their play! You can build upon children’s capacity for number composition and decomposition through engaging games and stories and authentic and meaningful experiences. With your help, children can come to see math as fun and as a useful tool to use every day.

Photographs: courtesy Sylwia Lech.
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