Experiences

Geometry

Lupuleasa Daniela

Romania

Vocational School

Maths, ICT

Teaching in class, Laboratory

Direct

Students in the tenth grade had difficulties at geometry. The 8th hours allocated are too less, and this led me to approach in a new manner this chapter. We proposed a scenario to the students:
I want to design a park with:
• A swimming pool in a circle, with center at the point M (8, 3) and radius 5
• Four parallel slides with water. The extremities of the first slide are A (-12, 6), and B (-6, -8). The second has the extremity C (-8, 5); the third has its extremity (-5, 6), and the fourth has a extremity G (-1, 5);
• A tennis table, rectangular with two points P (5, -5) and Q (6, -8).
I will place 12 umbrellas around the pool, at equal distances, the first being positioned to U1 (13, 3).
We will determine:
• The relationship between the coordinates of the circle;
• Vectors and their coordinates
• Equations of lines associated slides and coordinates of the other extremities;
• Intersections of the lines with the axes;
• The angle between the line and the Ox axis;
• Equations of lines that form the rectangle and coordinates of the other peaks;
• The lengths of the sides of the tennis table and its surface;
• Coordinates of points in which the umbrellas will be placed, complex numbers associated with these points;
• An equation that is the solution of complex 12 issues identified above;
• Area of land occupied by water slides;
• Slide lengths.
I offered theoretical support and solution of the proposed model scenarios requiring students to formulate various fields of activity, highlighting a circle, a rectangle, parallel lines, equally spaced points around the circle. Using real life examples, stimulating students to identify examples and solving model proposed contributed to the assimilation and application of specific formulas of analytic geometry, geometric interpretation of complex numbers, the length of a segment of a surface area.