Older children typically develop number sense through which of the following?

The development of number sense in older children is significantly enhanced through their engagement with operations, basic facts, and algorithms. This represents a structured understanding of numbers and mathematical concepts, where children learn to manipulate numbers and perform calculations systematically.

Operations refer to the basic mathematical processes such as addition, subtraction, multiplication, and division, which are fundamental to developing a grasp of how numbers interact with one another. Basic facts provide the foundational arithmetic knowledge that children need to perform operations quickly and accurately, fostering fluency in mathematics.

Algorithms contribute to children's understanding of how to approach mathematical problems in a logical, step-by-step manner. This methodical approach not only improves their ability to solve problems but also supports their understanding of why certain procedures work, further deepening their number sense.

Experiential learning, physical activities, or verbal reasoning alone may play supportive roles in a child’s mathematical education, but they do not provide the comprehensive framework that operations, basic facts, and algorithms offer in developing a strong number sense. Thus, option B accurately captures the critical components essential for older children to effectively enhance their numerical understanding and proficiency.