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