All-Russian kangaroo game. International Mathematical Competition-Game "Kangaroo"

Millions of children in many countries of the world no longer need to be explained what "Kangaroo", is a massive international mathematical contest-game under the motto - " Math for everyone!".

The main goal of the competition is to involve as many children as possible in solving mathematical problems, to show each student that thinking over a problem can be a lively, exciting, and even fun affair. This goal is achieved quite successfully: for example, in 2009 more than 5.5 million children from 46 countries participated in the competition. And the number of participants in the competition in Russia exceeded 1.8 million!

Of course, the name of the competition is associated with distant Australia. But why? After all, mass mathematical competitions have been held in many countries for more than a decade, and Europe, in which the new competition was born, is so far from Australia! The fact is that in the early 80s of the twentieth century, the famous Australian mathematician and teacher Peter Halloran (1931 - 1994) came up with two very significant innovations that significantly changed the traditional school Olympiads. He divided all the problems of the Olympiad into three categories of difficulty, and simple tasks should be accessible to literally every student. And besides, the tasks were offered in the form of a multiple-choice test focused on computer processing of the results. The presence of simple but entertaining questions ensured a wide interest in the competition, and a large number of works.

The new form of competition was so successful that in the mid-80s, about 500,000 Australian schoolchildren participated in it. In 1991, a group of French mathematicians, drawing on the Australian experience, held a similar competition in France. In honor of the Australian colleagues, the competition was named "Kangaroo". To emphasize the entertainingness of the tasks, they began to call it a contest-game. And one more difference - participation in the competition has become paid. The fee is very small, but as a result, the competition ceased to depend on sponsors, and a significant part of the participants began to receive prizes.

In the first year, about 120,000 French schoolchildren took part in this game, and soon the number of participants grew to 600,000. This began the rapid spread of the competition across countries and continents. Now about 40 countries of Europe, Asia and America participate in it, and in Europe it is much easier to list countries that do not participate in the competition than those where it has been held for many years.

In Russia, the Kangaroo competition was first held in 1994 and since then the number of its participants has been growing rapidly. The competition is included in the program "Productive game competitions" of the Institute for Productive Learning under the leadership of Academician of the Russian Academy of Education M.I. Bashmakov and is supported by Russian Academy education, the St. Petersburg Mathematical Society and the Russian State Pedagogical University them. A.I. Herzen. The Kangaroo Plus Testing Technology Center took over the direct organizational work.

In our country, a clear structure of mathematical Olympiads has long been established, covering all regions and accessible to every student interested in mathematics. However, these Olympiads, starting from the regional and ending with the All-Russian, are aimed at highlighting the most capable and gifted from the students who are already passionate about mathematics. The role of such Olympiads in shaping the scientific elite of our country is enormous, but the vast majority of schoolchildren remain aloof from them. After all, the problems that are offered there, as a rule, are designed for those who are already interested in mathematics and are familiar with mathematical ideas and methods that go beyond school curriculum. Therefore, the Kangaroo contest, addressed to the most ordinary schoolchildren, quickly won the sympathy of both children and teachers.

The tasks of the competition are designed so that every student, even those who do not like mathematics, or even are afraid of it, will find interesting and accessible questions for themselves. After all the main objective of this competition is to interest the guys, instill in them confidence in their abilities, and its motto is “Mathematics for everyone”.

Experience has shown that children are happy to solve competition problems that successfully fill the vacuum between standard and often boring examples from a school textbook and difficult, demanding special knowledge and preparation, tasks of city and regional mathematical Olympiads.

Competition "Kangaroo" is an Olympiad for all schoolchildren from grades 3 to 11. The purpose of the competition is to captivate children by solving mathematical problems. The tasks of the competition are very interesting, all participants (both strong and weak in mathematics) find exciting tasks for themselves.

The competition was invented by Australian scientist Peter Halloran in the late 80s of the last century. "Kangaroo" quickly gained popularity among schoolchildren in different corners Earth. In 2010, more than 6 million schoolchildren from about fifty countries of the world participated in the competition. The geography of participants is very extensive: European countries, USA, countries Latin America, Canada, Asian countries. The competition has been held in Russia since 1994.

Competition "Kangaroo"

The Kangaroo Competition is an annual competition, it is always held on the third Thursday of March.

Students are asked to solve 30 tasks of three levels of difficulty. Points are awarded for each correctly completed task.

The Kangaroo competition is paid, but its price is not high, in 2012 it was necessary to pay only 43 rubles.

The Russian organizing committee of the competition is located in St. Petersburg. Participants of the competition send all forms with answers to this city. Answers are checked automatically - on the computer.

The results of the "Kangaroo" contest are delivered to schools at the end of April. The winners of the competition receive diplomas, and the rest of the participants receive certificates.

Personal results of the competition can be found out faster - in early April. To do this, you need to use a personal code. The code can be obtained at http://mathkang.ru/

How to Prepare for the Kangaroo Contest

Peterson's textbooks contain problems that were in previous years at the Kangaroo competition.

On the Kangaroo website, you can see problems with answers that were in previous years.

And also for better preparation you can use the books from the series "Library of the Mathematical Club "Kangaroo". These books tell entertaining stories in mathematics in a fascinating way, provide interesting math games. The tasks that were in the past years at the mathematical competition are analyzed, extraordinary ways of solving them are given.

Mathematical club "Kangaroo", issue No. 12 (grades 3-8), St. Petersburg, 2011

I really liked the book, which is called "The Book of Inches, Vershoks and Centimeters." It tells about how units of measurement arose and developed: pie, inches, cables, miles, etc.

Mathematical club "Kangaroo"

Here are a few entertaining stories from this book.

V.I. Dal, a connoisseur of the Russian people, has such a record “what a city, then faith, what a village, then a measure.”

For a long time, in different countries different measures were used. Yes, in ancient China for men and women's clothing various measures have been taken. For men, they used "duan", which was 13.82 meters, and for women they used "pi" - 11.06 meters.

AT Everyday life Measures varied not only across countries, but also across towns and villages. For example, in some Russian villages the measure of duration was the time "until the cauldron of water boils."

Now solve problem #1.

Old clocks lose 20 seconds every hour. The hands are set to 12 o'clock, what time will the clock show in a day?

Task number 2.

In the pirate market, a barrel of rum costs 100 piastres or 800 doubloons. A pistol costs 250 ducats or 100 doubloons. For a parrot, the seller asks for 100 ducats, but how many piastres will that be?

Mathematical club "Kangaroo", children's mathematical calendar, St. Petersburg, 2011

In the Kangaroo Library series, a mathematical calendar is released, in which there is one task for each day. By solving these problems, you will be able to give excellent food to your brain, and at the same time prepare for the next Kangaroo competition.

Mathematical club "Kangaroo"

Ben chose a number, divided it by 7, then added 7 and multiplied the result by 7. It turned out to be 77. What number did he choose?

An experienced trainer washes an elephant in 40 minutes, and his son 2 hours. If they wash the elephants together, how long will it take them to wash three elephants?

Mathematical club "Kangaroo", issue No. 18 (grades 6-8), St. Petersburg, 2010

This edition features combinatorial problems from a branch of mathematics that studies various relationships in finite sets of objects. Combinatorial problems take most in mathematical entertainment: games and puzzles.

Kangaroo Club

Problem number 5.

Count how many ways are there to place a white and a black rook on a chessboard, provided that they do not kill each other?

This is the most difficult task, so I'll give her solution here.

Each rook keeps under attack all the cells of that vertical and that horizontal on which it stands. And she occupies one more cell herself. Therefore, 64-15=49 free cells remain on the board, each of which can be safely placed with a second rook.

Now it remains to note that for the first (for example, white) rook, we can choose any of the 64 squares of the board, and for the second (black) - any of the 49 squares, which after that will remain free and will not be under attack. This means that we can apply the multiplication rule: total options for the required arrangement is 64*49=3136.

When solving this problem, it helps that the very condition of the problem (everything happens on a chessboard) helps to visualize possible options relative position figures. If the conditions of conception are not so clear, you should try to make them clear.

I hope you enjoyed getting to know math competition"Kangaroo" .

The Kangaroo competition has been held since 1994. It originated in Australia at the initiative of the famous Australian mathematician and teacher Peter Halloran. The competition is designed for the most ordinary schoolchildren and therefore quickly won the sympathy of both children and teachers. The tasks of the competition are designed so that each student finds interesting and accessible questions for himself. After all, the main goal of this competition is to interest the children, instill in them confidence in their abilities, and the motto is “Mathematics for everyone”.

Now about 5 million schoolchildren around the world participate in it. In Russia, the number of participants exceeded 1.6 million people. In the Udmurt Republic, 15-25 thousand schoolchildren participate in Kangaroo every year.

In Udmurtia, the competition is held by the Center educational technologies"Another School"

If you are in another region of the Russian Federation, please contact the central organizing committee of the competition - mathkang.ru

Competition procedure

The competition is held in a test form in one stage without any preliminary selection. The competition is held at the school. Participants are given tasks containing 30 tasks, where each task is accompanied by five possible answers.

All work is given 1 hour 15 minutes of pure time. Then the answer forms are submitted and sent to the Organizing Committee for centralized verification and processing.

After verification, each school that took part in the competition receives a final report indicating the points received and the place of each student in general list. All participants are given certificates, and the winners in parallel receive diplomas and prizes, the best ones are invited to math camps.

Documents for organizers

Technical documentation:

Instructions for conducting a competition for teachers.

The form of the list of participants in the competition "KANGAROO" for school organizers.

Form of Notification of the informed consent of the participants of the competition (their legal representatives) to the processing of personal data (to be filled in by the school). Their filling is necessary due to the fact that the personal data of the contest participants are automatically processed using computer technology.

For organizers who wish to additionally secure themselves for the validity of collecting the fee from the participants, we offer the form of the Minutes of the meeting of the parent community, by the decision of which the powers of the school organizer will also be confirmed by the parents. This is especially true for those who plan to act as an individual.

March 16, 2017 Grades 3-4 The time allotted for solving problems is 75 minutes!

Tasks worth 3 points

№1. Kenga made up five addition examples. What is the largest amount?

(A) 2+0+1+7 (B) 2+0+17 (C) 20+17 (D) 20+1+7 (E) 201+7

№2. Yarik marked with arrows on the diagram the path from the house to the lake. How many arrows did he draw wrong?

(A) 3 (B) 4 (C) 5 (D) 7 (E) 10

№3. The number 100 is multiplied by 1.5 times, and the result is halved. What happened?

(A) 150 (B) 100 (C) 75 (D) 50 (E) 25

№4. The picture on the left shows beads. Which picture shows the same beads?

№5. Zhenya made six three-digit numbers from the numbers 2.5 and 7 (the numbers in each number are different). She then arranged the numbers in ascending order. What is the third number?

(A) 257 (B) 527 (C) 572 (D) 752 (D) 725

№6. The figure shows three squares divided into cells. On the extreme squares, some of the cells are shaded, and the rest are transparent. Both of these squares were superimposed on the middle square so that their upper left corners coincided. Which of the figurines is visible?

№7. What is the most small number white cells in the figure should be painted over so that there are more shaded cells than white ones?

(A) 1 (B) 2 (C) 3 (D) 4 (E)5

№8. Masha drew 30 geometric shapes in this order: triangle, circle, square, rhombus, then again triangle, circle, square, rhombus and so on. How many triangles did Masha draw?

(A) 5 (B) 6 (C) 7 (D) 8 (E)9

№9. From the front, the house looks like the picture on the left. Behind this house there is a door and two windows. What does he look like from behind?

№10. It's 2017 now. In how many years will the next year be without the digit 0?

(A) 100 (B) 95 (C) 94 (D) 84 (E)83

Tasks, evaluating 4 points

№11. Balls are sold in packs of 5, 10 or 25 pieces each. Anya wants to buy exactly 70 balloons. What is the smallest number of packages she will have to buy?

(A) 3 (B) 4 (C) 5 (D) 6 (E) 7

№12. Misha folded a square sheet of paper and poked a hole in it. Then he unfolded the sheet and saw what is shown in the figure on the left. What might the fold lines look like?

№13. Three turtles are sitting on a path in dots A, AT and With(see picture). They decided to gather at one point and find the sum of their distances. What is the smallest amount they could get?

(A) 8 m (B) 10 m (C) 12 m (D) 13 m (E) 18 m

№14. Between numbers 1 6 3 1 7 two characters must be inserted + and two characters × so that you get the best results. What is it equal to?

(A) 16 (B) 18 (C) 26 (D) 28 (E) 126

№15. The strip in the figure is made up of 10 squares with a side of 1. How many of the same squares must be attached to it on the right so that the perimeter of the strip becomes twice as large?

(A) 9 (B) 10 (C) 11 (D) 12 (E) 20

№16. Sasha marked a cell in the checkered square. It turned out that in its column this cell is fourth from the bottom and fifth from the top. In addition, in its line, this cell is the sixth from the left. Which one is right?

(A) second (B) third (C) fourth (D) fifth (E) sixth

№17. Fedya cut out two identical figures from a 4 × 3 rectangle. What kind of figurine could he not get?

№18. Each of the three boys guessed two numbers from 1 to 10. All six numbers turned out to be different. Andrey's sum of numbers is 4, Borya's is 7, Vitya's is 10. Then one of Vitya's numbers is

(A) 1 (B) 2 (C) 3 (D) 5 (E)6

№19. Numbers are placed in the cells of a 4 × 4 square. Sonya found a 2 × 2 square in which the sum of the numbers is the largest. What is this amount?

(A) 11 (B) 12 (C) 13 (D) 14 (E) 15

№20. Dima rode a bicycle along the paths of the park. He entered the park at the gate BUT. During the walk, he turned right three times, left four times and turned around once. Through which gate did he leave?

(A) A (B) B (C) C (D) D (E) the answer depends on the order of rotations

Tasks worth 5 points

№21. Several children took part in the run. The number of Misha who came running before three times more number those who ran after him. And the number of those who came running before Sasha is two times less than the number of those who came running after her. How many children could participate in the race?

(A) 21 (B) 5 (C) 6 (D) 7 (E) 11

№22. In some of the filled cells, one flower is hidden. Each white cell contains the number of cells with flowers that have a common side or vertex with it. How many flowers are hidden?

(A) 4 (B) 5 (C) 6 (D) 7 (E) 11

№23. three digit number we call it surprising if among the six digits that it and the number following it are written, there are exactly three ones and exactly one nine. How many amazing numbers are there?

(A) 0 (B) 1 (C) 2 (D) 3 (E) 4

№24. Each face of the cube is divided into nine squares (see figure). What is the most big number squares can be colored so that no two colored squares have a common side?

(A) 16 (B) 18 (C) 20 (D) 22 (E) 30

№25. A stack of cards with holes is strung on a thread (see picture on the left). Each card is white on one side and shaded on the other. Vasya laid out the cards on the table. What could have happened to him?

№26. From the airport to the bus station every three minutes there is a bus that travels 1 hour. 2 minutes after the departure of the bus, a car left the airport and drove to the bus station for 35 minutes. How many buses did he overtake?

(A) 12 (B) 11 (C) 10 (D) 8 (E) 7