"This book is a great choice for teachers as well as students who are interested in either recreational mathematics or in studying interesting number patterns. The activities can easily be used in both middle and secondary mathematics classrooms as enrichment topics. They would also be appropriate for use in math clubs and to challenge advanced learners. I highly recommend this book for anyone who loves exploring interesting properties of numbers." Mathematics Teaching in the Middle School "It is indeed an extremely rare occasion when a book can be used as a reference through such a broad level of math classes. This one is an existence proof." Mathematical Association of America "I recommend this book as a resource for developing lessons that extend students' understanding of the properties and relationships of numbers. The investigations allow students to make conjectures and generalizations about numbers and act as mathematicians." Mathematics Teacher "Many of the provided activities would be suitable for the high-school classroom, and could give students the opportunity to explore certain aspects of mathematics with a degree of independence." Mathematical Gazette This resource volume is an enlargement as well as an update of the previous edition. The book aims to introduce the reader to over 100 different families of positive integers. A brief historical note accompanies the descriptions and examples of several of the families together with a mix of routine exercises and problems as well as some thought provokers to solve. Number Treasury3 especially aims to stimulate further study beyond the scope of the introductory treatment given in the book. The emphasis in Number Treasury3 is on doing not proving. However, the reader is directed to think critically about situations, to provide explanations, to make generalizations, and to formulate conjectures. To engage the reader from the start, the book begins with a set of rich Investigations. These are standalone activities that represent each of the chapters of the book.