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Development of mathematical thinking - prevention of schematic Mathematics can not be reduced to the same accounting skills, this leads to blocking of mathematical thinking. S. K. Stein

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From the very beginning of education should focus on intellectual activity and independence of learners. Children should be encouraged to mathematical searching and reasoning, in line with their capabilities.

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Drawing a spiral

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string of numbers: 1, 1, 2, 2, 3, 3, 4, 4,...

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Drawing a spiral string of numbers: 2, 1, 3, 2, 4, 3, 5, 4, 6, 5, 7,...

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Paper cube I

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Paper cube II

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Mesh cube

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Bio - blocks

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front view left side view top view 4 1 2

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Bio - blocks

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Tower of Hanoi (1)

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It consists of three rods, and a number of disks of different sizes which can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top, thus making a conical shape. Tower of Hanoi (2)

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Tower of Hanoi (3)

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Domino-based game

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Picks theorem provides an elegant formula for the area of a simple lattice polygon: a lattice polygon whose boundary consists of a sequence of connected nonintersecting straight-line segments. Pick's theorem Georg Pick (1859-1942)

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Lattice point Lattice point - the point where the two lines intersect forming a grid Picks formula

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where: P - area of a polygon, W - the number of lattice points inside the polygon, B - number of lattice points on the edge of a polygon. Picks formula

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A) B)C) Area of polygon lattice points on the edge B inside lattice points W A B C Picks formula

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Using the Picks formula calculate polygonal areas

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Picks formula

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Fun on the perception How many squares you can get by connecting the dots with sections? 12461246

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Example 1. 21 13 = 2 7 3 2 7 3 Cross-counting method

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Thank you for your attention

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