Mathematics Olympiad (5th grade)

Tasks for the school tour of the Olympiad for students of grades 5 of secondary secondary school. For the school Olympiad, tasks were selected within the framework of the state educational standard, an emphasis was placed on interesting, diverse tasks of a creative nature that would be both instructive and practical. Tasks contribute to the disclosure of the creative potential of students, expanding their horizons, developing interest in the study of the subject and identifying gifted, creatively thinking schoolchildren and students with non-standard thinking.

Option 1

1. 1. Instead of stars, put the numbers so that the addition is done correctly:

73*8
+ **46*
9*36
97125

1. The square consists of 9 equal squares. How many squares are there?
   
2. Three identical watermelons should be divided equally between 4 children. How do you do this with the fewest cuts?
3. From town to village, the distance between which is 32 km, left the cyclist at a speed of 12 km / h. From the village to the city at the same time with him came a pedestrian at a speed of 4 km / h. Which one will be farther out of town in 2 hours?
4. In order to kill 40-year-old Snake Gorynych, Koschei Immortal came up with the idea to accustom him to smoking. He calculated that if Snake Gorynych smokes 17 cigarettes every day for a year, he will die in 5 years, and if 16, then in 10 years. How long will Snake Gorynych live if he does not smoke?

Option 2

1. Write down all the natural numbers divisible by 2 lying on the numerical beam between 1992 and 2007.
2. Cut the rectangle into 3 triangles so that only 1 is rectangular.
3. How to use a 7-liter bucket and a 3-liter can to pour exactly 5 liters of water into a pan?
4. The older brother walks from home to school for 30 minutes, and the younger one for 40 minutes. After how many minutes will the older brother catch up with the younger one if he left 5 minutes earlier?
5. From 12345678910111213...5657585960, cross out 100 digits so that the remaining number is the largest.

Literature used:

1. Farkov A.V. Extracurricular work in mathematics. Grades 5-11. M. Iris Press, 2006
2. Rusanov V. N. Mathematical Olympiads of Junior Schoolchildren. - M. "Education", 1990.
3. Subject weeks at school. Mathematics. L.V. Goncharova. - Volgograd. "Teacher," 2002.
4. Nagibin F.F., Kanin W.S. Mathematical box. - M. "Education", 1988.
5. Shevkin A.V. School Olympiad in mathematics. Challenges and solutions. — M. “Russian word”, 2004.

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