The "Building a System of Tens Casebook" was developed as the key resource for participants' Developing Mathematical Ideas seminar experience. The thirty cases, written by teachers describing real situations and actual student thinking in their classrooms, provide the basis of each session's investigation of specific mathematical concepts and teaching strategies. By reading and discussing the cases under the guidance of the facilitator, participants are actively engaged in their own learning enterprise and will: (1) learn to recognize the key mathematical ideas with which your students are grappling; (2) consider the types of classroom settings and teaching strategies that support the development of student understanding; (3) become aware of how core mathematical ideas develop across the grades; (4) work on mathematical concepts and gain better understanding of mathematical content; and (5) discover how to continue learning about children and mathematics. The casebook is composed of eight chapters: the first seven consist of classroom cases from kindergarten through grade 8; chapter 8 is an essay providing an overview of the research related to the situations described in the first seven chapters. The chapters are as follows: (1) Students' addition and subtraction strategies; (2) The base-ten structure of numbers; (3) Making sense of addition and subtraction algorithms; (4) Multiplication of multidigit numbers; (5) Division with multidigit numbers; (6) Place-value representation of numbers less than 1; (7) Multiplying and dividing with decimals; and (8) Highlights of related research. [For part 2 "Number and Operations, Part 2: Making Meaning for Operations. Casebook," see ED594600. For part 3 "Number and Operations, Part 3: Reasoning Algebraically about Operations. Casebook," see ED592077.]