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This textbook is designed to aid teachers by putting the teaching of arithmetic on a rational basis. The text has four main purposes: To present a pedagogical development of elementary mathematics as both a tool for use and as an elementary science; to use subject-matter representing real conditions; to present mathematics--its wide range and variety of uses in common affairs--to pupils to build number sense; to provide training in attacking common problems arithmetically and some power to analyze quantitative problems. Each teacher should select such topics and problems as have a particular interest for their school.