STANDARD ALGORITHMS IN THE COMMON CORE STATE STANDARDS

This article discusses standard algorithms for multidigit addition, subtraction, multiplication, and division. It clarifies that the Common Core State Standards state that students are to develop, discuss, and use efficient, accurate, and generalizable methods in the first year in which a multidigit computation is introduced so students may use a standard algorithm from that early year. Standard algorithms rely on decomposing numbers written in base-ten notation into base-ten units. The properties of operations then allow any multi-digit computation to be reduced to a collection of single-digit computations. These single-digit computations sometimes require the composition or decomposition of a base-ten unit. There are multiple standard algorithms for any computation; these are just variations in the written method. Criteria for variations that should be taught in classrooms are discussed. The best method for multidigit addition writes the new groups on the line below the problem. The best method for multidigit subtraction does all needed ungrouping first and then subtracts everywhere; this can be done from the left or from the right. Best methods for multidigit multiplication and division are discussed. Common methods that are often taken to be “the standard algorithm” for an operation are described and shown to be problematic because they elicit errors or make it difficult to understand the place values involved. Math drawings that show place value and support student sense making are used throughout the article to enable teachers to use such drawings in the classroom and teach computation meaningfully.