Computational Strategies

Operational sense allows students to make sense of addition, subtraction, multiplication, and division, and to use these operations meaningfully in problem-solving situations. Students who possess a strong understanding of the operations see the relationships among them and develop flexible strategies for computing with numbers.

As students move from the Primary to Intermediate grades:

• students’ effectiveness in using operations depends on counting strategies, combining and partitioning numbers, and a sense of place value
• students learn the patterns of basic operations by learning effective counting strategies and working with various tools and representations
• students begin to understand that groups of equal size can be combined to form a quantity (a fundamental concept in multiplication)
• students explore relationships to help with learning the basic facts and to help in problem solving
• development of operational sense, especially related to multiplication and division, becomes a focus of instruction
• it is important for teachers to provide meaningful contexts, to help students develop an understanding of the operations, and to connect new concepts about the operations to what they already understand
• students demonstrate operational sense when they can work flexibly with a variety of computational strategies, including those of their own devising
• efficiency in using the operations and in performing computations depends on an understanding of part-whole relationship