Although each of these questions can be answered using exact computation, they can be efficiently and confidently answered by the use of mental computation and estimation. In fact, determining exactly what processes are used is often impossible without asking students to describe what they did. Both are appropriate solutions and illustrate that what was treated as a front-end estimation problem by one student was solved by mental computation by another. As students encounter more tedious computations, the efficiency and power of estimation also increase. Experiencing and exploring a variety of estimation strategies are essential.
Students can get the same estimate for a problem using two or more very different strategies.
Different strategies should be illustrated, discussed, and analyzed so that students learn that many different estimation techniques exist. Although no single strategy should be singled out for exclusive use, understanding different strategies will help students make wise decisions about which strategy or strategies are most efficient in a particular situation. Two Instructional Examples Students should be encouraged to make sense of all mathematical problems before attempting to solve them. For example, suppose students are exploring multiplication of decimal numbers. Encourage students to look at each factor and think about its relative size before computing.