Composing and decomposing numbers to 10 Knowledge-Based Study

Study notes

1. What Does It Mean to Compose and Decompose?

   Every whole number up to 10 can be viewed as a whole made of smaller parts.

   • Composing means putting two or more parts together to make a whole number. For example, joining 3 counters and 4 counters makes 7 counters.
   • Decomposing means breaking a whole number apart into smaller parts. For example, separating 7 into 5 and 2.

   Recognizing how numbers are built helps develop strong mental math strategies and prepares you for addition and subtraction.

   Using Number Bonds

   A number bond shows the relationship between a whole number and its parts.

   Consider the number 6. We can decompose 6 into several different pairs of parts:

   • 0 and 6 make 6
   • 1 and 5 make 6
   • 2 and 4 make 6
   • 3 and 3 make 6

   Notice that changing the order of the parts does not change the whole: 4 and 2 make 6, just as 2 and 4 make 6.

   Special Partners for 10

   The number 10 is an essential benchmark in our number system. Learning the pairs that compose 10 is a foundational skill.

   Here are all the two-part combinations that compose 10:

   • 0 and 10
   • 1 and 9
   • 2 and 8
   • 3 and 7
   • 4 and 6
   • 5 and 5

   If you have 7 objects, you know you need exactly 3 more to make a complete group of 10.

   Step-by-Step Practice

   Example 1: Composing a Number

   Problem: What number is composed of 4 and 5?

   Solution: Combine the two parts: count on 5 from 4 (or 4 from 5). Together, 4 and 5 make 9.

   Example 2: Decomposing a Number

   Problem: A group of 8 apples is split into two baskets. The first basket has 3 apples. How many apples are in the second basket?

   Solution: Decompose 8 into 3 and an unknown part. Since 3 and 5 compose 8, the second basket must contain 5 apples.