Mental Computation Strategies for Part-Whole Numbers

Mental strategies used by school students in solving problems involving operations with whole numbers have been documented for some time. There is, however, little information about how students solve fraction, decimal, and percent - or part-whole - number problems mentally. This is despite the fact that there is an increased emphasis on facility with these types of numbers as students move from primary to secondary school. In this study 24 students from grades 3 to 10 participated in individual interviews involving mental computation. This paper will document mental strategies used in operations involving part-whole numbers and relationships. Of particular interest are the links to many of the mental strategies that have been observed with whole numbers. As well, responses will be analysed with respect to their conceptual or instrumental usage. Since many students appear to find part-whole number relationships conceptually challenging, understanding the strategies children use when solving part-whole problems mentally is valuable. This knowledge may help teachers in strengthening students’ understanding about intuitive ideas for part-whole numbers, in providing transitions to written algorithms, and in reinforcing estimation practices that will assist in checking answers obtained in other ways, including by calculator