March 16, 2017 Grades 3–4. The time allotted for solving problems is 75 minutes!
Problems worth 3 points
№1. Kanga made 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 the path from the house to the lake with arrows on the diagram. How many arrows did he draw incorrectly?
(A) 3 (B) 4 (C) 5 (D) 7 (E) 10
№3. The number 100 was increased by one and a half times, and the result was reduced by half. 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 composed six three-digit numbers from the numbers 2.5 and 7 (the numbers in each number are different). Then she arranged these numbers in ascending order. What number was the third?
(A) 257 (B) 527 (C) 572 (D) 752 (E) 725
№6. The picture shows three squares divided into cells. On the outer squares, some of the cells are painted over, 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 figures is still visible?
№7. What is the smallest number of white cells in the picture that must be painted so that there are more painted 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 a 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. At the back of this house there is a door and two windows. What does it look like from behind?
№10. It's 2017 now. How many years from now will the next year be that does not have the number 0 in its record?
(A) 100 (B) 95 (C) 94 (D) 84 (E)83
Objectives, assessment worth 4 points
№11. Balls are sold in packs of 5, 10 or 25 pieces each. Anya wants to buy exactly 70 balls. 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 piece of paper and poked a hole in it. Then he unfolded the sheet and saw what is shown in the picture on the left. What might the fold lines look like?
№13. Three turtles sit on the path at the dots A, IN And WITH(see picture). They decided to gather at one point and find the sum of the distances they had traveled. 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 the numbers 1 6 3 1 7 you need to insert two characters + and two signs × so that you get the biggest result. 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 added 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 square in the checkered square. It turned out that in its column this cell is the fourth from the bottom and the fifth from the top. In addition, in its row this cell is the sixth from the left. Which one is she on the right?
(A) second (B) third (C) fourth (D) fifth (E) sixth
№17. From a 4 × 3 rectangle, Fedya cut out two identical figures. What kind of figures could he not produce?
№18. Each of the three boys thought of two numbers from 1 to 10. All six numbers turned out to be different. The sum of Andrey’s numbers is 4, Bory’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 was riding a bicycle along the paths of the park. He entered the park through the gate A. During his walk, he turned right three times, left four times, and turned around once. What gate did he go through?
(A) A (B) B (C) C (D) D (E) the answer depends on the order of turns
Tasks worth 5 points
№21. Several children took part in the race. The number of those who came running before Misha was three times greater than the number of those who came running 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 take part in the race?
(A) 21 (B) 5 (C) 6 (D) 7 (E) 11
№22. Some shaded cells contain one flower. Each white cell contains the number of cells with flowers that have a common side or top with it. How many flowers are hidden?
(A) 4 (B) 5 (C) 6 (D) 7 (E) 11
№23. We will call a three-digit number amazing if among the six digits used to write it and the number following it, 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 picture). What is the largest number of squares that can be colored such 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 string (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 he have done?
№26. A bus leaves from the airport to the bus station every three minutes and takes 1 hour. 2 minutes after the bus departed, a car left the airport and drove 35 minutes to the bus station. How many buses did he overtake?
(A) 12 (B) 11 (C) 10 (D) 8 (E) 7
The international mathematical game-competition "Kangaroo 2017" was held on March 16, 2017. 143,591 students from 2,681 educational institutions of the Republic of Belarus took part in the largest mathematical competition for schoolchildren in the world.
People began to use counting, measurements, and calculations in life from the most ancient times. The origins of mathematical science are usually attributed to Ancient Egypt. In those distant times, knowledge was surrounded by mystery. Education provided access to government service and a prosperous life. Only children of wealthy parents could attend schools. The first schools appeared at the palaces of the pharaohs, and later at temples and large government institutions. The future pharaoh, despite his sacred and divine status, did not have any concessions or privileges in the process of mastering the art of counting, measuring, calculating the areas and volumes of various figures. Every day he was obliged to solve mathematical problems, which the teacher brought him on papyrus (a school notebook of that time), and there was no more important thing until all the problems were solved. This knowledge was necessary for competent management of the great state.
Today, mathematicians all over the world are making efforts to popularize this science. "Math for everyone!" - this is the motto of the international association “Kangaroos Without Borders” (KSF - Le Kangourou sans Frontieres), which today includes 81 countries.
On March 16, children from different countries tried their hand at solving problems prepared by the best teachers and instructors and approved at the annual conference of KSF participating countries. It is pleasant to note that in terms of the number of problems selected for assignments at six age levels, the group of Belarusian mathematicians came out on top.
In our country, 143,591 students solved problems that day, which is 6,759 more than the previous competition. An increase in the number of participants occurred in all regions, with the exception of the Grodno region. The largest number of students participating in this intellectual competition are registered in the capital. The number of participants by region is shown in the diagram:
“Kangaroo” tasks are developed for six age groups: for 1-2, 3-4, 5-6, 7-8, 9-10 and 11 grades. The distribution of participants according to classes is as follows:
Let us remind you that according to the rules of the competition, all problems in the task are conditionally divided into three levels of difficulty: simple, each of which is worth 3 points; more complex problems, the solution of which sometimes requires a good knowledge of the school mathematics curriculum (estimated at 4 points); complex, non-standard tasks, for the solution of which you need to show ingenuity, the ability to reason, and analyze (estimated at 5 points). The success of completing tasks is reflected in the following diagrams.
Information about the success of the task for grades 1-2, which the youngest participants worked on:
The success of completing the same task by 2nd grade students:
When analyzing the results of this task, it is surprising that, in percentage terms, first-graders coped more successfully than second-graders with solving 8 problems (a third of the task out of 24 problems), and another 8 problems (another third of the task) were solved equally successfully. Only with problems Nos. 1, 5, 6, 8, 11, 12, 13 and 19 did second-graders, who study mathematics a year longer, cope more successfully than first-graders.
Percentage of correctly solved assignment problems for grades 3-4 by third graders:
The success of completing the same task by 4th grade students:
In this task, fourth-graders confirmed a higher level of knowledge compared to third-graders, completing all tasks more successfully in percentage terms.
Statistical data on the completion of assignments for grades 5-6 by 5th grade students:
Success in completing the same task by 6th grade students:
In this task, sixth-graders also confirmed that they had acquired knowledge over the year, completing the task more successfully than fifth-graders. Only problems No. 7, 29 and 30 were solved equally successfully in percentage terms; in the rest, the percentage of correct answers for sixth-graders was higher than for fifth-graders.
Data on the success of assignments for grades 7-8 by 7th grade students:
Data on the completion of the same task by participants - 8th grade students:
A comparative analysis of the success of completing the task shows that the percentage of correctly solved problems is higher among older children, only problem No. 28 was completed more successfully by seventh-graders, and problems No. 23, 24, 25 and 29 were solved equally successfully by children from different parallels.
Information about the success of the assignment for grades 9-10, which ninth-graders worked on:
Success in completing the same task by 10th grade students:
The comparative analysis of the success of completing the task is similar to the previous ones: in solving only one problem No. 30, the younger children turned out to be more successful. Ninth and tenth graders showed the same percentage of correct answers to problems Nos. 5, 12, 16, 24, 25, 27 and 29.
Information about the success of the assignment by 11th grade students:
The following diagram characterizes the level of difficulty of tasks in general. She introduces the average scores for the country for each parallel:
We remind participants and organizers of the competition that the results are preliminary for a month. 1 month after posting on the website, the preliminary results of the competition are declared final and are not subject to any changes.
We draw the attention of all participants, parents and teachers that independent and honest work on the task is the main requirement for the organizers and participants of the competition game. The Organizing Committee regrets that, based on the results of the work of the disqualification commission, cases of violation of the rules of the competition game were once again discovered in certain educational institutions and by individual participants. Fortunately, this year there have been slightly fewer such violations, but elementary schools still continue to suffer from this. Some teachers, in an effort to “help” their students, often cause tears of little participants and justified complaints from their parents. After all, the tasks are designed in such a way that even the most prepared guys rarely complete them completely within the allotted time. Over the many years of Kangaroo, even the winners of international mathematics Olympiads did not always complete them completely in 75 minutes. How can one comment, for example, on the fact that first-graders, who, according to the teachers themselves, are not yet fully trained to read and write, perform the same tasks better than second-graders, as evidenced not only by the analysis of the answers, but also by higher national average. Or this fact: with a number of participants of about 21,000, in parallel 3rd grades across the country, 19 children showed the highest possible result. Of these, from only one institution, 8 participants - third graders - scored 120 maximum possible points. It’s time to send all other teachers to the teacher of these kids at this school for experience. These and other facts indicate that not all teachers and organizers fully understand their responsibility for organizing and conducting not only this, but also other competitions. We are full of confidence that the majority of participants and organizers are honest and conscientious in their participation and organization of our games-competitions.
The organizing committee congratulates all participants in the Kangaroo 2017 game-competition. Each participant will receive a prize “for everyone”. Students who show the best results in their area and in their educational institution will be rewarded with additional prizes. We express our gratitude to the organizers and coordinators of the competition game in districts (cities) and educational institutions, who took a responsible approach to organizing and conducting the competition.
We wish all participants of the competition success in studying mathematics and other disciplines!
Based on the results of the Kangaroo competition, each school should receive the following package:
- Final report, which contains the following information for each participant: the number of points he scored, a complete list of the answers he chose (indicating correct and incorrect ones), place in school (in a given parallel), place in territory (settlement or region), place by region (subject of the Russian Federation), as well as the percentage of participants in the Russian parallel list who scored fewer points (the “Percentage” column in the school report). In addition, the report contains some statistical data about the competition: the number of participants in the school, in the territory, in the region and in Russia as a whole (data are provided for each parallel separately).
- Certificates for each participant in the competition (the school receives certificate forms based on the number of submitted works and a program for automatically filling out certificates). If the school does not have the opportunity to use this program, the certificates are filled out manually by the teacher.
- Certificates of school winners, which are awarded to participants who take first place in their school in their parallel (provided that there is more than one participant in the parallel).
- Certificate to the school organizer of the competition, certificate to the educational institution from the Russian organizing committee "Kangaroo", confirming that the school took part in the next competition. In addition, the school receives letters of gratitude for teachers who actively participated in the competition.
- Prize for each participant: a sticker on a notebook for students in grades 3-10 and an envelope with postcards for second graders.
- Gifts for the best participants (at least one gift for each parallel). Regional organizing committees are responsible for awarding the results of the competition, and they can choose prizes from the assortment developed by the Russian organizing committee, or they can take advantage of other opportunities. Therefore, the prizes awarded to participants in different regions may vary. In addition, we must remember that in most regions the competition does not have sponsors, and all costs associated with it are covered exclusively by registration fees of participants. Accordingly, the vast majority of prizes are some small souvenirs or toys with the symbols of the competition, but there should be a lot of these prizes and they should reach every school.
The international mathematical game-competition "Kangaroo 2017" was held on March 16, 2017. 143,591 students from 2,681 educational institutions of the Republic of Belarus took part in the largest mathematical competition for schoolchildren in the world.
People began to use counting, measurements, and calculations in life from the most ancient times. The origins of mathematical science are usually attributed to Ancient Egypt. In those distant times, knowledge was surrounded by mystery. Education provided access to government service and a prosperous life. Only children of wealthy parents could attend schools. The first schools appeared at the palaces of the pharaohs, and later at temples and large government institutions. The future pharaoh, despite his sacred and divine status, did not have any concessions or privileges in the process of mastering the art of counting, measuring, calculating the areas and volumes of various figures. Every day he was obliged to solve mathematical problems, which the teacher brought him on papyrus (a school notebook of that time), and there was no more important thing until all the problems were solved. This knowledge was necessary for competent management of the great state.
Today, mathematicians all over the world are making efforts to popularize this science. "Math for everyone!" - this is the motto of the international association “Kangaroos Without Borders” (KSF - Le Kangourou sans Frontieres), which today includes 81 countries.
On March 16, children from different countries tried their hand at solving problems prepared by the best teachers and instructors and approved at the annual conference of KSF participating countries. It is pleasant to note that in terms of the number of problems selected for assignments at six age levels, the group of Belarusian mathematicians came out on top.
In our country, 143,591 students solved problems that day, which is 6,759 more than the previous competition. An increase in the number of participants occurred in all regions, with the exception of the Grodno region. The largest number of students participating in this intellectual competition are registered in the capital. The number of participants by region is shown in the diagram:
“Kangaroo” tasks are developed for six age groups: for 1-2, 3-4, 5-6, 7-8, 9-10 and 11 grades. The distribution of participants according to classes is as follows:
Let us remind you that according to the rules of the competition, all problems in the task are conditionally divided into three levels of difficulty: simple, each of which is worth 3 points; more complex problems, the solution of which sometimes requires a good knowledge of the school mathematics curriculum (estimated at 4 points); complex, non-standard tasks, for the solution of which you need to show ingenuity, the ability to reason, and analyze (estimated at 5 points). The success of completing tasks is reflected in the following diagrams.
Information about the success of the task for grades 1-2, which the youngest participants worked on:
The success of completing the same task by 2nd grade students:
When analyzing the results of this task, it is surprising that, in percentage terms, first-graders coped more successfully than second-graders with solving 8 problems (a third of the task out of 24 problems), and another 8 problems (another third of the task) were solved equally successfully. Only with problems Nos. 1, 5, 6, 8, 11, 12, 13 and 19 did second-graders, who study mathematics a year longer, cope more successfully than first-graders.
Percentage of correctly solved assignment problems for grades 3-4 by third graders:
The success of completing the same task by 4th grade students:
In this task, fourth-graders confirmed a higher level of knowledge compared to third-graders, completing all tasks more successfully in percentage terms.
Statistical data on the completion of assignments for grades 5-6 by 5th grade students:
Success in completing the same task by 6th grade students:
In this task, sixth-graders also confirmed that they had acquired knowledge over the year, completing the task more successfully than fifth-graders. Only problems No. 7, 29 and 30 were solved equally successfully in percentage terms; in the rest, the percentage of correct answers for sixth-graders was higher than for fifth-graders.
Data on the success of assignments for grades 7-8 by 7th grade students:
Data on the completion of the same task by participants - 8th grade students:
A comparative analysis of the success of completing the task shows that the percentage of correctly solved problems is higher among older children, only problem No. 28 was completed more successfully by seventh-graders, and problems No. 23, 24, 25 and 29 were solved equally successfully by children from different parallels.
Information about the success of the assignment for grades 9-10, which ninth-graders worked on:
Success in completing the same task by 10th grade students:
The comparative analysis of the success of completing the task is similar to the previous ones: in solving only one problem No. 30, the younger children turned out to be more successful. Ninth and tenth graders showed the same percentage of correct answers to problems Nos. 5, 12, 16, 24, 25, 27 and 29.
Information about the success of the assignment by 11th grade students:
The following diagram characterizes the level of difficulty of tasks in general. She introduces the average scores for the country for each parallel:
We remind participants and organizers of the competition that the results are preliminary for a month. 1 month after posting on the website, the preliminary results of the competition are declared final and are not subject to any changes.
We draw the attention of all participants, parents and teachers that independent and honest work on the task is the main requirement for the organizers and participants of the competition game. The Organizing Committee regrets that, based on the results of the work of the disqualification commission, cases of violation of the rules of the competition game were once again discovered in certain educational institutions and by individual participants. Fortunately, this year there have been slightly fewer such violations, but elementary schools still continue to suffer from this. Some teachers, in an effort to “help” their students, often cause tears of little participants and justified complaints from their parents. After all, the tasks are designed in such a way that even the most prepared guys rarely complete them completely within the allotted time. Over the many years of Kangaroo, even the winners of international mathematics Olympiads did not always complete them completely in 75 minutes. How can one comment, for example, on the fact that first-graders, who, according to the teachers themselves, are not yet fully trained to read and write, perform the same tasks better than second-graders, as evidenced not only by the analysis of the answers, but also by higher national average. Or this fact: with a number of participants of about 21,000, in parallel 3rd grades across the country, 19 children showed the highest possible result. Of these, from only one institution, 8 participants - third graders - scored 120 maximum possible points. It’s time to send all other teachers to the teacher of these kids at this school for experience. These and other facts indicate that not all teachers and organizers fully understand their responsibility for organizing and conducting not only this, but also other competitions. We are full of confidence that the majority of participants and organizers are honest and conscientious in their participation and organization of our games-competitions.
The organizing committee congratulates all participants in the Kangaroo 2017 game-competition. Each participant will receive a prize “for everyone”. Students who show the best results in their area and in their educational institution will be rewarded with additional prizes. We express our gratitude to the organizers and coordinators of the competition game in districts (cities) and educational institutions, who took a responsible approach to organizing and conducting the competition.
We wish all participants of the competition success in studying mathematics and other disciplines!
The international mathematical competition "Kangaroo" in Belarusian schools was scheduled for March 16, but according to parents who contacted the editorial office of Rebenok.BY, in some institutions it was held the day before, which is unacceptable according to the rules of the competition
Photo source: website
Within a few hours, photos of assignments for first and third grade appeared on the Internet.
According to the information of the applicants, the first graders at the capital's school No. 110 and the third graders of the 39th gymnasium in Minsk solved the Kangaroo task a day earlier than scheduled. While reviewing the assignments with their children, parents noticed that tomorrow’s date was written on the form with the assignments.
Katerina, mother of a third grader:
It turns out that some of the schoolchildren who wrote the competition on March 16 knew the tasks in advance. The children found themselves in unequal conditions.
Director of the NGO "Belarusian Competition Association", which organizes a mathematical competition in Belarus, Gennady Vladimirovich Nekhai commented on the current situation in the following way:
I already had a signal that the competition was held at school 110 earlier, and I talked with the organizer. The organizer explained that these were just training sessions on old tasks. This is always done to prepare children for the competition.
We checked the tasks that appeared on the Internet. They were posted by Ukrainian and Russian participants.
The competition is international and is held simultaneously in all countries. Since the competition is international, the main set of tasks is common. But countries can change some of the tasks at their discretion, as, for example, their Russian colleagues regularly do. But some of them will still match.
Gennady Vladimirovich said that the Belarusian Association immediately informed colleagues in St. Petersburg and Lvov about the information leak.
You understand that there is a human factor everywhere. Some people don’t like to lose and are ready to win by any means necessary.
We have a short description of the rules before each task. And the main stated requirement is honest and independent work. This year the case will be publicized at the General Assembly. This is a disaster for the international association.
For now, I took the word of the organizer at school 110, but everything is so serious that we need to figure it out.
Now, according to Gennady Nekhai, the association is waiting for information from parents about what specific tasks were offered to the children. If the fact of holding the competition ahead of schedule is confirmed, Belarus may be excluded from among its participants.
But Belarus was among the first participating countries and we were always held up as an example,” noted Gennady Nekhai with regret. - This is a scandal of international proportions. Therefore, we would be grateful for any information on this matter.”
