A colorful bouquet of various contributions to modeling in mathematics education: From GPS, how calculators compute sine values, modeling in economic contexts, to data and randomness, and much more. The contributions have been developed for concrete use in mathematics classes. They demonstrate to students the significance of mathematics in solving real-world problems from many areas of life. Within the series "Real-World Connections in Mathematics Education," this first volume titled "New Materials for a Reality-Based Mathematics Education" is now being published by Springer Spektrum, produced by ISTRON, a long-established group of educators from schools and universities, as well as individuals involved in teacher training, who actively dedicate themselves to this goal as experts in application-oriented mathematics education.