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Problems for 5th grade

Kvant 1970, No. 5p. 64Tag DQ71

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64

In the new trial textbook on mathematics for the 5th grade *) (after revisions it will become the main one when the fifth grade switches to new programs, that is, from the 1970-1971 school year) there is a section “Problems of increased difficulty.” In this and subsequent issues of the course we will place part of these tasks. They will probably seem interesting and not too simple to those readers «Kvant» who have been fifth-graders for a long time. For the “section” it asks you to answer the following question: the first task in this section is numbered 1213, the last one is 1294; How many problems are there in this section? (Of course, the answer “81 problems” is incorrect). Those who are interested in the tasks are asked to write us reviews.

  1. A vessel with a capacity of 10 liters is filled with kerosene. From this vessel you need to pour 5 liters into a seven-liter vessel, use an auxiliary empty vessel with a capacity of 3 liters (divisions are not indicated on the vessels). How to do this?

  2. The alarm clock is 4 minutes behind. per hour About an hour and a half ago, the alarm clock was set accurately. This is the hour on the clock showing the exact

  • N. Ya. Vilenkin, K. I. Neshkov, S. I. Shvartsburg, A. D. Semushin, A. S. Chesnokov, T. F. Neaeva, edited by A. I. Markushevich, “Matematika”, 5th grade, “Enlightenment”, 1969.

The time is exactly 12. In how many minutes will the alarm clock also show 12 o’clock?

  1. Yura and Sasha were supposed to meet at 8 o’clock in the morning. Yura thinks that his watch is 25 minutes fast, although in reality it is 10 minutes behind. And Sasha thinks that his watch is 10 minutes behind, although in fact it is 5 minutes ahead. What time will each of the friends be at the meeting place if they try to arrive 5 minutes before the appointed time?

  2. Restore numbers replaced by asterisks:

  • ***** 8
  1. Out of 8 coins, one is counterfeit (lighter). How to identify a counterfeit coin by two weighers on a scale with two cups without mushrooms, identify the counterfeit coin and determine whether it is lighter or heavier than intended.