Özet:

Geometry is one of the sub-learning areas of mathematics and meaningful geometry learning includes reasoning methods such as generalizing, classifying, and inferring. Therefore, it improves students' mathematical thinking skills, increases their ability to support their thoughts with mathematical arguments, and positively affects their mathematics achievement in general. The aim of this study is to prepare an instructional activity for teaching geometry to gifted students in accordance with the 5th level they have reached in Van Hiele geometry learning levels. While preparing this teaching activity, the decomposition technique in the Pythagorean Proof Application in the study "Application of the Pythagorean Relation Expressed for Square to Other Regular Polygons and Circle" by Aslaner and İlhan (2018) was used. In the activity, the table is filled in by fulfilling the steps of disassembly and assembly in accordance with the instructions given, and a mathematical relationship is asked to be found between the polygons formed. The Expand Polygon activity can be used as an activity in the support education mathematics activities of gifted students and in the mathematics applications courses of middle school and high school students from the 7th grade onwards to improve students' reasoning and spatial skills.

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