Tasks from the Lesson to Develop Hearing and Logic

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This material is suitable for children of any school age. These approaches will be useful for those who teach or want to teach mathematics to a visually impaired child.

An individual (adult or child) with full or partial vision loss compensates for the lack of visual cues with auditory sensations. The importance of hearing increases with the complete or partial loss of visual functions. A blind person needs to gather and process information from multiple sources: hearing, touch, and air movements. Children need to develop the ability to rely on auditory perception and the intact senses (smell, touch, taste) that provide accurate information about the world around them.

In my lessons, I strive to diversify the tasks as much as possible to give children the opportunity to develop their hearing. This is beneficial not only for visually impaired children but also for sighted students. Along with the development of hearing, abstract thinking is enhanced, and children verbally build logical chains.

Task #1: Seven old women are heading to Rome. Each of them has 7 mules, each mule carries 7 bags, each bag contains 7 loaves of bread, each loaf has 7 knives, and each knife has 7 sheaths. What is the total number of all the listed items?

In the educational process, the teacher’s speech plays a crucial role. It should be clear, precise, and expressive. Emphasis is placed on key points: 7 old women, 7 mules, 7 bags, 7 loaves, 7 knives, 7 sheaths. The task condition is not written down but is always spoken aloud. The solution to the problem is also verbalized.


  1. 7×7=49 mules for all the old women.
  2. 49×7=34349×7=343 bags for all the old women.
  3. 343×7=2401343×7=2401 loaves of bread for all the old women.
  4. 2401×7=168072401×7=16807 knives for all the old women.
  5. 16807×7=11764916807×7=117649 sheaths for all the old women.

The total number of all listed items (old women, mules, bags, loaves of bread, knives, and sheaths) is: 7 + 49 + 343 + 2401 + 16807 +117649 = 137256. Answer: 137256

Task #2: In summer, paramecia reproduce asexually by splitting in half. How many paramecia will there be after 2 divisions, 3 divisions, and 10 divisions?


Each division doubles the number of existing paramecia. So, after the first division, there will be two paramecia. After the second division:

2×2=4 paramecia

After the third division:

4×2=8 paramecia

After the fourth division:

8×2=16 paramecia

Continuing this pattern, after the tenth division, we will have:

210=1024 paramecia

Task #3: The Legend of Chess

According to the legend, chess was invented by a wise man named Sassa. He presented his invention to the ruler of the country and taught him how to play. The ruler liked the game so much that he decided to reward the wise man and asked him what he wanted. The wise man asked for grain based on the following scheme: for the first square of the chessboard, the ruler should give him one grain of wheat, for the second square — two grains, for the third — four grains, and so on, doubling the number of grains on each subsequent square. The ruler, not being a mathematician, laughed and immediately agreed, instructing his treasurer to calculate the amount of grain needed and give the reward. However, a week later, the treasurer still could not calculate the amount needed. When the ruler asked for the reason for the delay, the treasurer showed him the calculations and said that it was impossible to pay the amount unless they dried up the seas and oceans and sowed all the space with wheat.


1 + 2 + 4 + 8 + 16 + 32 + 64 + … – This is a geometric progression with the first term equal to 1 and a common ratio of 2. The number of terms is equal to the number of squares on the chessboard, which is 64. We find that it is necessary to give two to the power of sixty-four.

Enhancing auditory sensitivity in the case of vision impairment occurs due to the more active functioning of the auditory analyzer, which is driven by intensive training.