Elementary school teachers are responsible for constructing the foundation of number sense in youngsters, and so it is recommended that teacher-training programs include an emphasis on number sense to ensure the development of dynamic, productive computation and estimation skills in students. To better prepare preservice elementary school teachers for this challenge, one of the authors' goals while teaching a standard number systems mathematics content course is to implement a thematic emphasis on computational estimation that improves awareness of and proficiency in estimation. They do so through a careful selection of materials and activities focused on estimation and its importance in teaching and in daily life. The authors believe that a continuing, consistent emphasis by mathematics teacher educators on estimation, mental math, and reasonableness of solutions in number systems courses likely will increase preservice teachers' flexibility in working with numbers and will create heightened awareness of estimation's usefulness. Three computational estimation activities for preservice teachers--Newspaper headlines, Fraction kites, and Getting close--are presented. (Contains 2 tables and 3 figures.)