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Abstract of the Working Seminar (10-12 years old)
Leonid Shlyapochnik,
The State Budget Educational Institution (SBEI)
"Gymnasium № 1567", Moscow, Russia

In the Working Seminar we refer to tasks, each of which represents certain, not infrequently complicated logical-mathematical scheme and yet allow a clear, relatively simple solution. That is, a solution that is clear for grades of 4-6 of high school.

We use the following sources:
  • lessons from “Entertaining mathematics” for the 5th grade of one of the schools in Dolgoprudny town, Moscow region, Russia;
  • Mathematical Olympiad by prof. S.N.Olehnik (Moscow, 2014-2015,;
  • the popular project Diofant;
  • some tasks of the remarkable mathematician-methodologist Igor Sharygin.
By analyzing these materials the author was amazed by how many of non-standard mathematical models are related to real life!
The names of some of the models and tasks: arithmetical methods of solving text-problems; logical problems; symmetric shapes on a plane; Hamiltonian cycles (without mention of the term); primary concepts of similarity, the ratio of areas and volumes; the concept of the method "by contradiction"; indirect calculation of the least common multiple (LCM); signs of divisibility, etc.
Before the start of solving tasks, participants will be shown the main themes of mathematics in grades of 4-6 of high school. We may say that these methods are specific elements of propedeutics of appropriate mathematical topics that will be covered in high school in future.
It is desirable to perform the presentation of these tasks and their solutions, drawings and diagrams by using computer, projection boards, as well as the blackboard. An analysis of the tasks and their solutions will be made during the seminar.

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