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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
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.
Drawing a spiral
Drawing a spiral
string of numbers: 1, 1, 2, 2, 3, 3, 4, 4, ...
Drawing a spiral
string of numbers: 2, 1, 3, 2, 4, 3, 5, 4, 6, 5, 7, ...
Paper cube I
Paper cube II
Mesh cube
Bio - blocks
Bio - blocks
Bio - blocks
front view
left side view
top view
4
12
Bio - blocks
Bio - blocks
Tower of Hanoi (1)
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)
Tower of Hanoi (3)
Domino-based game
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)
Lattice point
Lattice point - the point where the two lines intersect forming a grid
Pick‘s formula
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
A)
B) C)
Area of polygon
lattice points on the edge B
inside lattice points W
A
B
C
Pick‘s formula
Pick‘s formula
Using the Pick‘s formula calculate polygonal areas
Using the Pick‘s formula calculate polygonal areas
Pick‘s formula
Fun on the perception
How many squares you can get by connecting the dots with sections?
1
2
4
6
Example 1. 21 13 = 2 7 3
2
7
3
Cross-counting method
Thank you for your attention