A variety of contexts are necessary for children to develop an understanding of the meanings of the operations such as addition and subtraction. These contexts often arise from real-life experiences in which they are simply joining sets, taking away or separating from a set, or comparing sets. These contexts might include conversations, such as “How many books do we have all together?” or “How many cookies are left if I eat two?” or “I have three more candies than you do.” Although young children first compute using objects and manipulatives, they gradually shift to performing computations mentally or using paper and pencil to record their thinking. Therefore, computation and estimation instruction in the early grades revolves around modeling, discussing, and recording a variety of problem situations. This approach helps students transition from the concrete to the representation to the symbolic in order to develop meaning for the operations and how they relate to each other.
In grades K–3, computation and estimation instruction focuses on
· relating the mathematical language and symbolism of operations to problem situations;
· understanding different meanings of addition and subtraction of whole numbers and the relation between the two operations;
· developing proficiency with basic addition, subtraction, multiplication, division and related facts;
· gaining facility in manipulating whole numbers to add and subtract and in understanding the effects of the operations on whole numbers;
· developing and using strategies and algorithms to solve problems and choosing an appropriate method for the situation;
· choosing, from mental computation, estimation, paper and pencil, and calculators, an appropriate way to compute;
· recognizing whether numerical solutions are reasonable;
· experiencing situations that lead to multiplication and division, such as equal groupings of objects and sharing equally; and
· performing initial operations with fractions.
Virginia Mathematics Standards of Learning
Computation & Estimation
k.6 The student will model adding and subtracting whole numbers, using up to 10 concrete objects.