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Didactic potential of game Ubongo in teaching mathematics at primary school
Váchová, Michaela ; Slezáková, Jana (advisor) ; Jirotková, Darina (referee)
This diploma thesis seeks the possibilities of using the board game UBONGO in teaching mathematics at elementary school. This thesis focuses on manipulative activities of pupils during the game and its goal is to explore what are pupils learning through the game. The theoretical part describes the basis for the research, thus content of mathematics and geometry curriculum in FEP BE, child's developmental stages in terms of learning, play with emphasis on the board game, lightly examines motivation and is inspired by tasks which are in geometrical environment Parkety and utilize prof. M. Hejný's method. The practical part of the diploma thesis contains the preparation of graded tasks, which are formed from the board game UBONGO in order to implement qualitative research. Didactical potential of the game is verified by performing series of graded tasks, pre-experiment and experiment with elementary school pupils. The course of the experiment is described together with all steps, strategies and findings, which pupils learn through playing the game. At the end of the diploma thesis is an evaluation of the fulfillment of individual objectives. KEYWORDS Planar geometry, 2 D, manipulation, game, Ubongo, motivation, learning, polyomino, polygon, gradation, strategy
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Tiling problems in combinatorics
Dvořáková, Tereza ; Slavík, Antonín (advisor) ; Halas, Zdeněk (referee)
The thesis represents a collection of solved problems concerned with covering planar shapes (mostly rectangles with integer sides) by tiles known as polyominoes (e.g., domi- noes, trominoes, tetrominoes, etc.). In most cases, the goal is to find a tiling or to prove that no such tiling exists. In more difficult problems, the task is to deduce conditions for the rectangle to be tileable by specified polyominoes. The last chapter is devoted to calcu- lating the number of all possible tilings of the specified rectangle.
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Extremal Polyominoes
Steffanová, Veronika ; Valtr, Pavel (advisor) ; Cibulka, Josef (referee)
Title: Extremal Polyominoes Author: Veronika Steffanová Department: Department of Applied Mathematics Supervisor: Doc. RNDr. Pavel Valtr, Dr. Abstract: The thesis is focused on polyominoes and other planar figures consisting of regular polygons, namely polyiamonds and polyhexes. We study the basic geometrical properties: the perimeter, the convex hull and the bounding rectangle/hexagon. We maximise and minimise these parameters and for the fixed size of the polyomino, denoted by n. We compute the extremal values of a chosen parameter and then we try to enumerate all polyominoes of the size n, which has the extremal property. Some of the problems were solved by other authors. We summarise their results. Some of the problems were solved by us, namely the maximal bounding rectan- gle/hexagon and maximal convex hull of polyiamonds. There are still sev- eral topics which remain open. We summarise the literature and offer our observations for the following scientists. Keywords: Polyomino, convex hull, extremal questions, plane 1
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Tiling problems in combinatorics
Dvořáková, Tereza ; Slavík, Antonín (advisor) ; Halas, Zdeněk (referee)
The thesis represents a collection of solved problems concerned with covering planar shapes (mostly rectangles with integer sides) by tiles known as polyominoes (e.g., domi- noes, trominoes, tetrominoes, etc.). In most cases, the goal is to find a tiling or to prove that no such tiling exists. In more difficult problems, the task is to deduce conditions for the rectangle to be tileable by specified polyominoes. The last chapter is devoted to calcu- lating the number of all possible tilings of the specified rectangle.
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