Overview As indicated in the K-12 Overview, the widespread availability of computing and calculating technology has given us the opportunity to significantly reconceive the role of computation and numerical operations in our fifth and sixth grade mathematics programs. Some skills are less important while others, such as estimation, mental computation, and understanding the meanings of the standard arithmetic operations, all play a more significant role than ever in the everyday life of a mathematically literate adult. A sample unit on fractions for the sixth-grade level can be found in Chapter 17 of this Framework. Much research in the past decade has focused on students' understandings of operations with large whole numbers and work with fractions and decimals. Each of these areas requires students to restructure their simple conceptions of number that were adequate for understanding whole number addition and subtraction.
Multiplication requires students to think about different meanings for the two factors.
It tells how many groups one has of a size specified by the second factor. Thus, students need different understandings of the roles of the two numbers in the operation of multiplication than their earlier understandings of addition, in which both addends meant the same thing. A similar restructuring is necessary for dealing appropriately with operations involving fractions and decimals. In earlier grades, students thought about 5 or 498 as numbers that represented that many things . The understood unit, one, is the number which was used to count a group of objects.