Socrates  Comenius 1: 


This term, the pupils of the class V3A solved the tasks from two thematic units:
Circle and cylinder
Ratio
For Socrates project, they chose the second unit  Ratio. They solved together two tasks from the “Mathematical Olympics” that were set last years. They were divided into ten working groups two, three or four at a time and they tried to solve the tasks. They achieved the following results:
solved without help 
solved after a suggestion 
not solved 

Task 1 
1 
4 
5 
Task 2 
4 
5 
1 
Two of the groups were to process the model solution of both tasks. They were as follows:
The father originally decided to bequeathe the money on his two sons in such a way that they had to divide it in the ratio 8 : 7. Then he changed his decision and divided the same sum in the ratio 11 : 9. This way, the value of the inheritance for the older son increased by 925 thalers. What amount did the father bequeathe on both sons together? (Solution)
14 tons of ore were delivered to the smelting works. The pure metal and the alloys were supplied in it in the ratio 2 : 5. In the raw cast obtained by smelting the ore, this ratio changed to 24 : 1 for the benefit of the ore. How many kilos did the cast weigh if the loss of metal during the smelting process made 5 %? (Solution)
The following three tasks were given the pupils to try solving them by themselves at home. Only one pupil brought the solution of all three tasks, the other pupils were not able to solve them or even did not try to.
Kamil reckoned that the numbers of years of his parents are in the ratio 6 : 5 this year. After 12 years, this ratio will change to 8 : 7. Kamil’s mum is younger than his dad. By how many years? (Solution)
Three friends Adam, Bedrich and Cyril live in neighbouring small houses. They decided to supply themselves together with a lawnmower that costs 15000 CZK. As their gardens are of different areas, they contributed to the purchase with different sums: Adam paid 6500 CZK, Bedrich 5500 CZK and Cyril paid the rest. They used the lawnmower together three years. Then Bedøich and Cyril bought their own lawnmowers, while Adam kept the old lawnmower. The friends agreed that during the three years the price had fallen down to 9000 CZK. What amounts of money should Adam pay to Bedrich and Cyril? (Solution)
Two colleagues decided to divide the fee for the shared work in the ratio 2 : 3. After they did so, they went together to dinner for which each of them paid 100 CZK. The remaining sums from the fee were in the ratio 3 : 5. How much was their shared fee? (Solution)