In solving 8 + 5, how does the student's work demonstrate integration of addition skills?

• A. By applying associative and commutative properties.
• B. By decomposing and composing numbers into place-value components.
• C. By using inverse operations to confirm their solution.
• D. By applying fractional representations.

Answer: (B)

The correct answer highlights that by decomposing and composing numbers into place-value components, the student is demonstrating a deep understanding of addition. This method involves breaking down the numbers involved in the addition to simplify the calculation. For example, a student might break the number 5 into 2 and 3, allowing them to first add 8 + 2 to get 10, and then add 10 + 3 to reach the final answer of 13. This approach reinforces their understanding of how numbers can be manipulated and combined, strengthening their foundational skills in addition.

In contrast, while the associative and commutative properties play important roles in addition, they are not the primary focus in the context of solving the specific problem of 8 + 5. The use of inverse operations, such as subtraction to check the answer, is also a valuable skill but not directly related to the integration of basic addition skills in this particular instance. Lastly, applying fractional representations is not relevant when considering the addition of whole numbers like 8 and 5. Thus, the focus on decomposing and composing numbers is the best reflection of integrating addition skills.