Pouring Tasks
This material is suitable for children of any school age. It helps develop auditory perception through solving mathematical tasks, training auditory memory, and enhancing logical and mathematical thinking.
The role of hearing in the life and activities of visually impaired children is much greater than for those with normal vision. Increased auditory sensitivity arises through intensive training. Teaching mathematics to visually impaired children aims not only to solve general educational tasks but also to address specific needs.
Pouring tasks are mathematical puzzles where one is required to divide a liquid in a certain ratio or measure out a portion of it using other containers. The following actions are allowed in pouring tasks: completely filling one of the containers, pouring liquid from one container to another, or emptying a container. The solution must indicate the sequence of steps needed to achieve the desired measurement. Each pouring task can be solved in two ways: by starting with the larger container or by starting with the smaller container.
Task #1
There are two containers with capacities of 3 liters and 5 liters. How can you measure exactly 4 liters of water using these containers and a water tap?
Solution (presented as a table):
| Step | 1 | 2 | 3 | 4 | 5 | 6 |
| 5 liters | 5 | 2 | 2 | – | 5 | 4 |
| 3 liters | – | 3 | – | 2 | 2 | 3 |
Result: After the pouring steps, we have exactly 4 liters of water.
Task #2
A 10-liter canister is filled with milk. You need to pour exactly 5 liters into a 7-liter canister, using a third container that holds 3 liters.
Solution (presented as a table):
| Step | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 10 liters | 3 | 3 | 6 | 6 | 9 | 9 | 2 | 2 |
| 5 liters | 7 | 4 | 4 | 1 | 1 | – | 7 | 5 |
| 3 liters | – | 3 | – | 3 | – | 1 | 1 | 3 |
Result: After these steps, 5 liters of milk are poured into the 7-liter canister.
Task #3
In his youth, the famous French mathematician Siméon Poisson (1781-1840) was given a task. His interest in this task led him to pursue a lifelong passion for mathematics. Here is the task: Someone has 12 pints of wine and wants to pour out exactly half of it, but they don’t have a 6-pint container. However, they do have two other containers: one holds 8 pints and the other holds 5 pints. How can they measure exactly 6 pints using the 8-pint container?
Solution (presented as a table):
| Step | ||||||||
| 12 pints | 12 | 4 | 4 | 9 | 9 | 1 | 1 | 6 |
| 8 pints | – | 8 | 3 | 3 | – | 8 | 6 | 6 |
| 5 pints | – | – | 5 | – | 3 | 3 | 5 | – |