Mathematics with Understanding, Book 1 provides a guide for teaching primary mathematics. This book consists of nine main topics–aims of a modern approach; language of sets; relations and sorting; recording of number and use of different bases; open sentences, number facts and pictorial representation; natural numbers and addition; subtraction; multiplication; and division. In these topics, this text specifically discusses the union and intersection of two sets, Cardinal number of a set, and recording by means of a mapping. The collection of data, fundamental operations for natural numbers, and subtraction algorithm are also deliberated. This compilation likewise covers the Cartesian product of two sets and properties of division. This publication is recommended for math teachers intending to acquire a deeper understanding of the structure behind many mathematical ideas and processes.