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![Page 1: Development of mathematical thinking - prevention of schematic Mathematics can not be reduced to the same accounting skills, this leads to blocking of.](https://reader034.fdocuments.us/reader034/viewer/2022051819/5517a9f55503460e6e8b6048/html5/thumbnails/1.jpg)
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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Drawing a spiral
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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Bio - blocks
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Bio - blocks
front view
left side view
top view
4
12
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Bio - blocks
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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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Pick’s 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
Pick‘s formula
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1
P W B 12
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.
Pick‘s formula
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A)
B) C)
Area of polygon
lattice points on the edge B
inside lattice points W
A
B
C
Pick‘s formula
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Pick‘s formula
Using the Pick‘s formula calculate polygonal areas
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Using the Pick‘s formula calculate polygonal areas
Pick‘s formula
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Fun on the perception
How many squares you can get by connecting the dots with sections?
1
2
4
6
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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