Classical Averages in Arithmetic and Geometry

The seventh book in the series "School Mathematical Circles" is dedicated to classical averages, most of which were known since ancient times, and the applications of their properties in solving arithmetic, algebraic, and geometric problems. Special attention is given to the interrelationship of various averages and the establishment of interdisciplinary connections between some topics of school algebra and geometry courses. The book is intended for students in grades 5-11. It includes the development of ten lessons for the mathematical circle with detailed examples of varying difficulty, problems for independent solution, and methodological guidelines for the teacher.
A large list of additional problems of varying difficulty levels is also provided. For ease of use, the concluding part of the book is made in the form of handout materials. The book is addressed to school mathematics teachers and leaders of mathematical circles.