Estimation should be a routine part not only of mathematics lessons, but of the entire school day. Children should be regularly engaged in estimating both quantities and the results of operations. After children have had several chances to make estimates about numbers like these, they should defend their estimates by giving some rationale for thinking they are close to the actual number. These discussions can be invaluable in helping them develop good number sense. Technology plays an important role in number sense at these grade levels.
Calculators can be wonderful exploration tools when examining new relationships.
Many insights about the relationships between fractions and decimals, for instance, can be achieved by simply dividing the numerators of fractions by their denominators. Generalizations about what kinds of fractions produce what kinds of decimals start to flow very freely in such open-ended explorations. Computer software also creates environments in which students manipulate decimal models on-screen and explore fraction and decimal relationships. The cumulative progress indicators for grade 8 appear below in boldface type. Each indicator is followed by activities which illustrate how it can be addressed in the classroom in grades 5 and 6.