Practical determination of Pi
For a visually impaired student, the greatest difficulties arise in constructing geometric figures and working with ready-made drawings. Constructive activities can facilitate the learning process.
The number Pi represents the ratio of a circle’s circumference to its diameter.
Let’s look at the key points of a lesson on the practical determination of Pi using string and a ruler.
The visually impaired student should sit at the first desk in the middle row. It’s beneficial to install a magnifying glass above the desk so the child can see and perform the main aspects of the practical work.
Draw a circle with radius R on sturdy cardboard, cut out the resulting circle, and wrap a thin string around it. Measure the length of one complete turn of the string, and divide this number by the length of the circle’s diameter. The result will be a number approximately equal to 3.
The visually impaired student performs this task along with the rest of the class. Working with string and cutting out the circle develops fine motor skills, spatial understanding, and visual-motor coordination. This practical work allows for a leisurely pace. If desired, students can work in pairs or small groups.
Next, students can be offered a plastic cup. In their notebooks, they trace around the rim of the cup, resulting in a circle. Using a ruler, they measure the diameter of the circle. Then, using string, they measure the circumference of the cup. The circumference is divided by the diameter, and the data is entered into a table.
| Circumference | Diameter | Ratio |
To continue the experiment, a plastic bowl is suggested. Flip the bowl over and trace it in the notebook. Then, measure the circumference with the string and the diameter with the ruler. Find the ratio of the circumference to the diameter and enter the data into the table. Similarly, this can be done with a plastic saucer. Any items with a circular cross-section, such as a pot or a jar, are suitable for this practical work. You can also draw and cut out circles of different diameters from cardboard. The ratio of the circumference to the diameter will be an approximate value of Pi.
For more accurate measurements in the experiment, it is recommended to choose circles with larger diameters, up to millimeters. This will allow obtaining the number Pi with two decimal places, i.e., 3.14.
Example of conducting the experiment:
- Take a cup. Measure its circumference: 15 cm. Then measure the diameter of the circle: 4.8 cm. Find the ratio of the circumference to the diameter. 15:4.8=3.125. The result is a value almost equal to Pi.
- Take a pot. The circumference of the pot: 710 mm, diameter: 226 mm. Find the ratio 710:226=3.141592… The result is a value almost equal to Pi.
The accuracy of calculating Pi in this way is not high, so for more accurate results, students can apply Archimedes’ method.
During this practical work, students develop the ability to find cause-and-effect relationships, highlight the main points, generalize, and make conclusions. The ability to engage in dialogue and purposefulness in work is fostered. For a visually impaired student, teamwork is essential.