Tasks for conducting a mathematical battle among 6-7 grades.

1 round (warm-up)

1. The car drove 3 hours at a speed of 60 km per hour and 7 hours at a speed of 80 km per hour. Find average speed car?

2. Half of half is equal to half. Find this number?

3. The mass of 5 apples and 3 pears is the same as the mass of 4 of the same apples and 4 of the same pears. Which is lighter apples or pears?

4. 5 workers will produce 5 parts in 5 days. How many parts will 10 workers make in 10 days?

5. Vovochka collected bugs and spiders in a box - only 8 pieces. How many spiders are in a box if there are 54 legs in total?

Round 2 (tasks for weighing and transfusion)

1. Among 80 coins there is one fake. Find it in four weighings on a balance pan without weights, if it is known that it is lighter than the real one?

2. How to equally divide 8 liters of milk if the milk is in an 8-liter can and there are two empty cans 3L and 5L?

3. There are two hourglass: for 7 min and for 11 min. Porridge should be cooked for 15 minutes. How to cook it by turning the clock over the minimum number of times?

Round 3 (tasks for movement)

1. Two motorists simultaneously left points A and B towards each other. After 7 hours, a distance of 136 km remained between them. Find the distance between A and B if one can cover the entire distance in 10 hours and the other in 12 hours.

2. Having traveled half way, the boat increased its speed by 25% and therefore arrived half an hour earlier. How long did he move?

Round 4 (captains competition)

Three certain wise men entered into an argument: which of the three is more wise? The dispute was resolved by a passer-by who offered them a test of intelligence.

“You see with me,” he said, “five caps: three black and two white. Close your eyes."

With these words, he put on a black cap for each, and hid two white caps in bags.

“You can open your eyes,” said the passerby. “Whoever guesses what color adorns his head, he has the right to consider himself the wisest.”

The wise men sat for a long time, looking at each other ... Finally, one exclaimed.

"I'm wearing black!"

How did he guess?

tasks for the "math battle"

among grades 6-7.

Game rules:

Mathematical battle-competition of two teams in solving problems. Teams receive the conditions of tasks and a certain time for their solution. While the teams are solving problems, any significant clarification of the problems given by one of the teams should be in shortest time communicated to all teams. After the allotted time has elapsed, the actual battle begins, when the teams explain to each other how to solve problems in accordance with the rules.

If one of the teams tells the solution, then the other one acts as an opponent, i.e. looks for errors in it (shortcomings). The speeches of the opponent and the speaker are evaluated in points. If the teams, having discussed the proposed solution, did not solve the problem to the end or did not find errors, then the jury can take some of the points. The team that scores the most points in the end is declared the winner of the fight.

Purpose of the game:

Development of interest in solving complex mathematical problems, ability to work in a team, preparation for participation in city competitions.

Game analysis:

The "math battle" was held as part of the week of Mathematics among 6G (math.) and 7A (gymnasium). The game was held in a friendly atmosphere. Tasks were specially selected for ingenuity that the guys could solve, regardless of the material being studied. The meeting ended with the victory of the 7th class, with a slight margin of 2 points. But this did not upset the 6th grade. on the contrary, they felt their possibilities, and demand revenge. The goal that I set for myself: to arouse interest in solving problems, to feel self-confidence was achieved.

Goals: develop an interest in mathematics, logic and ingenuity, the ability to prove and explain; communicative competence.

Preparing for the lesson: tasks for mathematical combat are recorded on album sheets in three copies: for teams and for the teacher.

The course of the lesson:

• Two teams participate in a mathematical battle. Each team has a captain, who is determined by the team before the start of the battle. The fight consists of two stages. The first stage is solving problems, the second is the battle itself. During the first stage, problem solving can be done jointly by the whole team. Remember that none of the participants in the battle can go to the board more than twice. Therefore, a participant who has solved many problems that have not been solved by others must, during the first stage, tell his teammates about his solutions.
• The second stage begins with the competition of captains. By decision of the team, any member of the team can participate in the competition instead of the captain. The winning team decides which team makes the first challenge. This, like all other team decisions, is announced by the captain.

Captains Competition:
A super blitz is held on three questions, the captain who scores two or three points wins. A point can be earned by the captain by answering the question correctly. The first person to answer is the one who quickly raises the signal card (prepared in advance) or his hand.

• A chocolate bar costs 10 rubles and another half a chocolate bar. How much does a chocolate bar cost?
• Hares are sawing logs. They made 10 cuts, how many logs did they get?
• How much earth is in a hole 2 m deep, 2 m wide, 2 m long?

Answers: 20 rubles; 11 logs; not at all.

• The call is made as follows. The captain announces: “We challenge the opponents to task number…”. The other team may or may not accept the challenge. The team that accepted the challenge puts speaker, another command - opponent. After a meeting with the teams, the captains call the opponent and the speaker. The speaker's task is to give a clear and understandable solution to the problem. The task of the opponent is to find errors in the report. During the presentation, the opponent does not have the right to object to the speaker, but may ask him to repeat an unclear place. the main task opponent - to notice all the dubious places and not forget about them until the end of the report. At the end of the report, a discussion takes place between the speaker and the opponent. , during which the opponent asks questions on all obscure places in the report. The discussion ends with the conclusion of the opponent: “I agree with the decision” or “I think that there is no solution, since so-and-so was not explained.”
• After that, the jury (teacher) awards points according to the following rules. Each task is worth a different number of points, as different levels of difficulty. The first and second tasks - 6 points. Third, fourth, fifth and sixth - 8 points. Seventh and eighth - 10 points. Ninth and tenth - 12 points. In the case of an absolutely correct decision, all these points are received by the speaker's team. Points are deducted for errors and inaccuracies. The number of points taken is determined by the proximity of the story to the correct solution. If the errors were found by the opponent, then the opposing team receives up to half of the deducted points. Otherwise, all selected points go to the jury. If the jury decided that the report does not contain a solution to the problem, then the opposing team has the right to tell the correct solution. At the same time, to the points scored for opposing, she can add points for telling the solution to the problem. The team that made an incorrect report puts up an opponent and can earn points on the opposition.
• The team that received the call may refuse to report. In this case, the calling team must prove that it has a solution to the problem. To do this, she exposes the speaker, and the second team - the opponent. If there is no solution and this is proved by the opposing team, then they receive half the points of this problem, and the calling team is obliged to repeat the challenge. This procedure is called call validation. In all other cases, the calls are interleaved.
• During a bout, each team is entitled to six 30-second breaks. Breaks are made in cases where it became necessary to help a standing student at the blackboard or replace him. The decision to take a break is made by the captain.
• The team that has received the right to challenge may refuse it. In this case, until the end of the battle, only their opponents have the right to report, and the team that refused can only oppose. In this case, opposition is carried out according to the usual rules.
• At the end of the fight, the jury calculates the points and determines the winning team. If the gap in the number of points does not exceed 3 points, then a draw is recorded in the battle.
• A team may be penalized up to 6 points for noise, rudeness towards an opponent, failure to comply with the requirements of the jury, etc.

Math Fight Rules

1. Order of battle. Math fight is a competition between two teams in solving mathematical problems. It consists of two parts. First, the teams receive the conditions of the tasks and a certain time for their solution. When solving problems, the team can use any printed literature, non-programmable calculators, but has no right to communicate with anyone except the jury. Also, teams do not have the right to use the Internet, any electronic media and mobile phones. After this time, the actual battle begins, when the teams tell each other how to solve problems.

2. Start of the fight. The fight starts with captains competition. The captain who first solved the proposed task raises his hand and presents the answer. If his answer is correct, he wins, if incorrect, his opponent wins, who is not required to submit his answer. The team that wins the captains' competition decides whether it wants to call the opposing team for a report in the first round or be called.

3. Fight order. The fight is made up of several rounds. At the beginning of each round, one of the teams challenges the other team to one of the problems, the solutions of which have not yet been told. The calling team may also refuse further calls (§ 11). The invoked command may accept the call (§ 4) or perform a validation check (§ 9).
The team that made the challenge in the current round becomes the challenged in the next round, except in the case of an incorrect challenge (§ 10), when it is forced to repeat the challenge in the next round.

4. Accepted call. If the challenge was accepted, the called team puts up a speaker, the calling team - an opponent. A team wishing to keep boardwalks (§ 13) may refuse to field an opponent. Then she does not participate in this round. The speaker, with the permission of the jury, can take paper with drawings and calculations. But he has no right to take the text of the decision with him. The speaker tells the solution of the problem; the opponent, by agreement with the speaker, asks him questions either in the course of the presentation or after the report. All calculations, as a rule, are carried out by the speaker on the board and without the use of a calculator. No more than 15 minutes are allotted for the report, no more than 15 minutes for the subsequent discussion of the opponent and the speaker.

5. Rights of speaker and opponent.
During the presentation, the opponent can: ask questions to the speaker with his consent; ask the speaker to repeat any part of the report; allow the speaker not to prove any obvious facts from the point of view of the opponent.
During the discussion, the speaker can: ask the opponent to clarify the issue; refuse to answer the opponent's question, motivating his refusal by the fact that (a) he does not have an answer, (b) he has already answered this question, (c) the question, in his opinion, is not relevant to the task.
During the discussion, the opponent can: ask the speaker to repeat any part of the report; ask the speaker to clarify any of his statements; ask the speaker to prove the formulated non-obvious not well-known statement (the facts included in the school mathematics course are usually considered well-known).
The speaker is not obliged: to state the method of obtaining the answer, if he can prove the correctness and completeness of the answer in another way; compare your solution method with other possible methods.

6.Opponent's Conclusion. When questions are asked and answers are received, the opponent makes a conclusion in one of three forms: (a) "I fully agree with the decision"; (b) "The solution is basically correct, but it has the following shortcomings..."; (c) "The solution is wrong, the fundamental error is as follows...". The opponent should remember that in the end the jury evaluates not his questions, but his conclusion, which must be motivated!
The conclusion on an incorrect decision can be made in the form: "The decision is incorrect, I have a counterexample." In this case, the jury asks the opponent to present a written counterexample without disclosing it to the speaker. If the jury accepts a counterexample, the speaker is given a minute to try to correct the solution. Similar actions are taken at the request of the opponent "The decision is incomplete, not all cases have been considered."
If the opponent agreed with the decision, he and his team no longer participate in this round; further questions to the speaker are asked by the jury. Until the speaker's decision has been refuted, the opponent has no right to tell his decision, even if it is much simpler.

7. Scoring. In each round, 12 points are awarded, which are distributed between the speaker, the opponent and the jury. The speaker for an error-free solution receives 12 points. Otherwise, the jury deducts points from the speaker for the holes contained in the decision. The cost of each hole is estimated by an even number of points. If the speaker patched up the hole after the opponent's question, asked before the end of the report, points from the speaker are not deducted. If the speaker patched up the hole after the opponent's question was asked at the end of the report, the cost of the hole is divided equally between the opponent and the speaker. If the speaker fails to close the hole, the opponent immediately receives half its cost. If the opponent did not notice the hole, and the jury pointed to it with their questions after the conclusion, the jury receives half of the cost of the hole, and the second half goes to the speaker or the jury, depending on whether the speaker managed to close the hole or not.

8. Role reversal. After preliminary scoring, the jury asks the opponent if he would like to present a complete solution to the problem in the case when the opponent has proved that the speaker does not have it, or to close up the remaining holes. If the opponent agrees to a partial or complete change of roles, he temporarily becomes a speaker and tries to earn the second half of the cost of the holes he discovered. A former speaker, while opposing, can himself gain points in half of those that the former opponent is trying to earn as a speaker. Secondary role reversal cannot be performed.

9. Validation consists in the fact that the called command refuses to tell the solution of the problem, but instead checks whether the calling command has solved it. In this case, the calling team will nominate a speaker, and the called team will nominate an opponent. If the calling team immediately admits that they do not have a solution, then the called team receives 6 points. The speaker and the opponent in this case are not appointed and the exits to the board are not counted. During validation, role reversal cannot be performed. If, when checking the correctness, the opponent proved that the speaker does not have a solution, then he receives at least 4 points.

10. The order of the next call when checking the correctness and. If the call is recognized as correct (the calling team presented a solution, or the opponent could not prove that the speaker did not have a solution), then the next call is made by the called team. If the challenge is recognized as incorrect (the calling team immediately admitted that it did not have a solution, or the opponent managed to prove that the speaker did not have a solution), then the calling team again makes the next call.

11. Rejection of calls. Starting from a certain round, one of the teams may refuse further challenges. In this case, the opponents can nominate speakers for any tasks not previously considered, and the team that refused the challenge nominates opponents. Once the calls have been abandoned, role reversal can no longer be performed.

12. Time-out. Communication between the speaker and the team is allowed only during the 30-second break taken by the team. Opponents at this time can also confer, spending all 30 seconds of the break. A team may take no more than six 30-second breaks per fight. If the opponent proceeded to issue a conclusion, his team within 10 seconds can withdraw the words of the opponent and take a timeout. If after the conclusion of the opponent within 10 seconds there was no withdrawal, then the conclusion of the opponent is considered made and it can no longer be changed.

13. Number of exits to the board. Each player is allowed to come to the board (whether as an opponent or speaker) no more than two times per battle, regardless of the number of team members participating in this battle. If desired, the team may not put the opponent in the round, thus saving the number of exits.

14. Substitution order. The team can replace its speaker at any time, which is equivalent to using two breaks. When replacing, the exit is counted for both participants.

15. 10 minute breaks. Team captains have the right to ask the jury for a 10-minute break during the fight (approximately every two hours). A break may only be granted between rounds. In this case, the calling team, before the break, makes a call in writing and hands it over to the jury, which announces the call after the end of the break.

16. End of the fight. The battle ends when all the problems have been considered or when one of the teams has refused the challenge, and the other team has refused to tell the solutions to the remaining problems.

17. Determination of the winner. The team with the most points is considered the winner of the battle. With a difference of no more than 3 points, the fight is considered to have ended in a draw (except in special cases).

18. General rules behavior I. During the fight, the team communicates with the jury only through the captain; if the captain is at the board - through his deputy. The speaker and the opponent address each other only in a respectful manner, on "you". If these rules are violated, the team is first warned, and then punished with penalty points.

19.Jury. The jury is the supreme interpreter of the rules of the fight. The decisions of the jury are binding on the teams. The jury can remove the opponent's question, stop the report or opposition if they are delayed. The jury keeps the protocol of the fight on the board. If one of the teams does not agree with the decision made by the jury on the problem, it has the right to immediately demand an analysis of the situation with the participation of the senior in the league. After the start of the next round, the score of the previous round can no longer be changed.

Math fight

Math fightis a competition between two teams in solving mathematical problems.

Matboy is an emerging form of extracurricular work in mathematics. She has actively entered the practice of the school in the last 10-15 years.

Matboys can be organized as tournaments intraclass , school-wide, or as city or district, when combined teams of schools or districts compete.

Matboys are always held in the form of competitions, the results of which are evaluated by the jury. Matboys are a very exciting and emotional form of mathematical competition, teams should always feel the support of their fans. Tasks in matboys can be designed to be completed within a certain period of time, sometimes a team is given a week to complete the task. However, matboys with express tasks are especially interesting, which are completed in a matter of minutes and are immediately evaluated by the jury.

The experience of mateboys will help the participants in the future: the ability to make a scientific report, to listen and understand the work of another, to ask clear questions on the merits - all this will be useful at seminars and conferences, for reviewing books and articles, for joint scientific work. And one more thing: students from different schools get to know each other at matboys, create a new social circle. And the last thing: after a successful matchup, the taste for good work wakes up, I want to perform again, but as it should, taking into account all the mistakes. Therefore, it is sometimes more useful for teams to lose than to win.

Matboys originated in Leningrad and were invented by Joseph Yakovlevich Verebeichik around 1965. The first matboys were held within the walls of school No. 30, where Iosif Yakovlevich worked as a mathematics teacher and led circles. After many years, matboys began to be held in different cities, but some discrepancies in the rules arose. With great difficulty, thanks to the summer mathematical schools in Kirov, where Moscow, Leningrad and Kirov teachers met, long disputes succeeded in overcoming these differences.

Signs:

The presence of rules of communication in the conditions of the competition;

Availability common purpose commands;

Limited time and its distribution by stages of the competition;

Objectivity of evaluation of results;

A clear system of organization;

Entertaining wording of tasks, tasks.

Characteristic:

Target:

• Development of cognitive interest in the subject.
• Generalization and systematization of knowledge: in matboy, tasks are used mainly for logic and ingenuity. As well as tasks on the topics: drawing up equations and solving them; Polynomials and arithmetic operations on them; Solution of systems of equations with two unknowns.
• To develop the ability of group members to interact with each other.
• Score the most points.

Preparing for the lesson:

The tasks for the mathematical battle are written down on album sheets in four copies: for the teams, the jury and the teacher. The protocol of the fight for the jury. Black box "with a surprise" (see captains' competition)

Rules:

Two teams (7 people each) participate in the mathematical battle. Each team has a captain, who is determined by the team before the start of the battle. The fight consists of two stages.

The first stage is solving problems, the second is the battle itself. During the first stage, problem solving can be done jointly by the whole team. Remember that none of the participants in the battle can go to the board more than twice. Therefore, a participant who has solved many problems that have not been solved by others must, during the first stage, tell his teammates about his solutions.

The second stage begins with the competition of captains. (According to the decision of the team, any member of the team can participate in the competition instead of the captain). The winning team decides which team makes the first challenge. This, like all other team decisions, is announced by the captain.

▪ The call is made as follows. The captain announces:. The other team may or may not accept the challenge. The team that accepted the challenge puts up a speaker, the other team - an opponent. After a meeting with the teams, the captains name the opponent and the speaker. The task of the speaker is to give a clear and understandable solution to the problem. The task of the opponent is to find errors in the report. During the presentation, the opponent does not have the right to object to the speaker, but may ask him to repeat an unclear place. The main task of the opponent is to notice all the dubious places and not forget about them until the end of the report. At the end of the report, a discussion takes place between the speaker and the opponent, during which the opponent asks questions about all the unclear places in the report. The discussion ends with the opponent's conclusion:I agree with the decision ("disagree"", explanation).

▪ After that, the jury (teacher) awards points. Each task is worth 12 points. Points are deducted for errors and inaccuracies. The number of points taken is determined by the proximity of the story to the correct solution. If the errors were found by the opponent, then the opposing team receives up to half of the deducted points. Otherwise, all selected points go to the jury.

▪ The team that received the call may refuse to report. In this case, the calling team must prove that it has a solution to the problem. To do this, she exposes the speaker, and the second team - the opponent.

▪ During a bout, each team is entitled to six 30-second breaks. Breaks are made in cases where it became necessary to help a standing student at the blackboard or replace him. The decision to take a break is made by the captain.

▪ If the captain is at the board, he leaves for himself the deputy, who at that time acts as the captain. The names of the captain and deputy are communicated to the jury before the start of solving problems. During the solution of tasks, the main duty of the captain is to coordinate the actions of the team members so that the available forces solve as many tasks as possible. The captain finds out in advance who will be the speaker or opponent for a particular task and determines the entire tactics of the team in the upcoming battle.

▪ The team that has received the right to challenge may refuse it. In this case, until the end of the battle, only their opponents have the right to report, and the team that refused can only oppose. In this case, opposition is carried out according to the usual rules.

▪ The jury is the supreme interpreter of the rules of combat. In cases not provided for by the rules, it makes a decision at its own discretion. The decisions of the jury are binding on the teams.

▪ At the end of the fight, the jury calculates the points and determines the winning team. If the gap in the number of points does not exceed 3 points, then a draw is recorded in the battle.

▪ A team may be penalized up to 6 points for noise, being rude to an opponent, etc.

Math Battle Protocol

call no.	task number			Who called whom			Jury
		Surname	Number of points.		Surname	Number of points.	Number of points.	Notes, not accuracy
Total:

Sample:

call no.	task number	Name of the 1st team		Who called whom	Team II name		Jury
		Surname	Number of points.		Surname	Number of points.	Number of points.	Notes, not accuracy
								Team I broke the silence

What class is the math battle for?

Math fight for 7th grade

Course of the competition: Epigraph: “The subject of mathematics is so serious that it is useful not to miss

chance to make it entertaining»

(Pascal)

I invite two teams to conduct the fight: the “team name” team and the “team name” team.

(To the teams) Please receive your assignments. Within 15-30 minutes you should complete it.

Now let's start the math fight. I'm calling the team captains.

"Captain Contest"

Task: You need to guess what is in the black box, while using as few clues as possible.

Hints:

1. The oldest item has been lying in the ground for 2000 years.
2. Under the ashes of Pompeii, archaeologists have discovered many such objects made of bronze. In our country, this was first discovered during excavations in Nizhny Novgorod.
3. For many hundreds of years, the design of this object has not changed, it was so perfect.
4. In Ancient Greece, the ability to use this subject was considered the height of perfection, and the ability to solve problems with its help was a sign of a high position in society and a great mind.
5. This item is indispensable in architecture and construction.
6. It is necessary to transfer dimensions from one drawing to another, to build equal angles.
7. Riddle: “Two legs conspired

Make arcs and circles

Additional competition for captains:Who will quickly name 5 mathematical terms starting with the letter "P":

1. The unit of measure for angles.
2. Segment in a circle.
3. Type of number.
4. Flat quadrilateral.
5. Equations that have the same solutions.

The team captain "team name" won.

You have the floor, captain. (“We challenge rivals to task number…”.)

Team "team name", are you up for the challenge? (Yes)

What questions or additions will the jury have?

Dear jury, please put your marks in the fight protocol.

The word is given to the team "team name"

Team "team name", are you up for the challenge?

Please nominate a speaker and an opponent.

For now, our esteemed jury is counting the results, I invite the teams to the stage ...

To sum up the results of the mathematical battle, the floor is presented to the chairman of the jury...

So, in today's mathematical battle, the team "team name" won with a score of: ...

The team "team name" is given the title"The Wisest of the Wise",

Team "team name" -"The smartest of the smartest."

Thanks to the teams, please take your seats.

Task list

1. A chocolate costs 10 rubles and another half a chocolate. How much does a chocolate bar cost?
2. The man says:I lived 44 years, 44 months, 44 weeks and 44 days". How old is he?
3. The car meter showed 12921 km. After 2 hours, a number appeared on the counter again, which was read the same in both directions. At what speed was the car traveling?
4. Letter designations were first introduced by the French mathematician François Viet (1540-1603). Before that, they used cumbersome verbal formulations. Try to write down in modern symbolism such an example: “The square and the number 21 are equal to 10 roots. Find roots».
5. How old is grandma?

Vasya came to his friend Kolya.

Why weren't you with us yesterday? Kolya asked. “Yesterday my grandmother celebrated her birthday.

I didn't know, Vasya said. - How old is your grandmother?

Kolya answered intricately: “My grandmother says that in her life there was no such occasion that her birthday did not cope. Yesterday she celebrated this day for the fifteenth time. So think about how old my grandmother is.

1. Let's say I took 100 rubles from my mother. Went to the store and lost them. Met a friend. I took 50 rubles from her. I bought 2 chocolates for 10. I have 30 rubles left. I gave them to my mother. And I owed 70. And my friend 50. Total 120. Plus I have 2 chocolates. Total 140! Where is 10 rubles?
2. Three friends: Ivan, Peter and Alexey came to the market with their wives: Maria, Ekaterina and Anna. Who is married to whom, we do not know. It is required to find out on the basis of the following data: each of these six people paid for each purchased item as many rubles as the number of items he bought. Each man spent 48 rubles. more than his wife. In addition, Ivan bought 9 items more than Ekaterina, and Peter bought 7 items more than Maria.
3. Fill in the cells so that the sum of any three adjacent cells is 20:

1. A tourist goes on a hike from A to B and back, and completes the whole journey in 3 hours and 41 minutes. The road from A to B goes first uphill, then on level ground, and then downhill. How long does the road pass through a flat place, if the speed of a tourist is 4 km/h when going uphill, 5 km/h on level ground, and 6 km/h when going down the mountain, and the distance AB is 9 km?
2. The number ends with the number 9. If you discard that number and add the first number to the resulting number, you get 306,216. Find this number.

Answers:

Captains Competition: Compass

Additional competition of captains:radian, radius, rational, rhombus, equivalent.

Problem solutions:

1. Answer: 20 rubles . X / 2 + 10 \u003d X, where X is the price of a chocolate bar.
2. Answer: 48 years old 44 months = 3 years and 8 months.

44 weeks = 9 months

44 days = 1.5 months

44 years + 3 years and 8 months. + 9 months + 1.5 months = 48 years and 6.5 months.

1. Answer: 55 km/h (105 km/h).

13031-12921=110 (km)

110:2 = 55 (km/h)

or

13131-12921=210 (km)

210:2=105 (km)

1. Grandma - 60 years old She was born on February 29th. Thus, she celebrated her birthday once every 4 years.
2. You need to add not chocolates, but 30 rubles, which they gave away. Chocolates don't count anymore. 30 rub. already given away, the remaining 20 went on account of the debt.

Took: 100 + 50 = 150 rubles.

Should: 150-30 = 120 rubles.

Spending 100+20=120

After all the losses and expenses, 150-120 \u003d 30 remained - I gave them to my mother, and she owed 70 rubles to her. and 50 - to a friend, total 120 rubles. (compare with the 2nd line).

If his wife bought at items, then she paidrub. So we have, or (x-y)(x+y)=48. Numbers x,y- positive. This is possible when x-y and x+y are even, and x+y>x-y.

Decomposing 48 into factors, we get: 48=2*24=4*12=6*8 or

Solving these equations, we get:

Looking for those meanings x and y , the difference of which is 9, we find that Ivan bought 13 items, Ekaterina - 4. In the same way, Peter bought 8 items, Maria - 1.

Thus, we get pairs:

1. The numbers between which there are two cells must match.

The difference is only in the third number: 4

Answer:

1. Let x be the length of the path along the flat place of the SD, then AC + DV = 9-x.

A tourist passes sections AS and DV twice, once uphill at a speed of 4 km / h, the other

downhill at a speed of 6 km/h.

On this path he will spend

The path on level ground will takeBecause for the whole way there and back, the tourist will need 3 hours. 41 min., then

|*60

15(9th)+10(9th)+12*2x=221

135-15x+90-10x+24x=221

X=-4

Answer: x = 4 km.

1. Answer: 278 379

Tasks for fans:

Puzzles:

I do not look like a penny,

Doesn't look like ruby.

I am round, but not a fool,

With a hole, but not a donut.

(zero)

I'm not an oval and not a circle,

I am a friend of the triangle

I am the brother of the rectangle

After all, my name is...

(square)

Squirrel dried mushrooms,

There were 25 whites

Yes, 5 more oilers,

7 mushrooms and 2 chanterelles,

Very red-haired sisters.

Who has an answer?

How many mushrooms were there?

(39)

1. Hares are sawing logs. They made 10 cuts. How many churboks turned out? (eleven)
2. What does the word "darkness" mean in mathematics? (a lot of)
3. Zero's rival? (cross)
4. How many kids did a large goat have? (7)
5. Triangular scarf? (scarf)
6. Who changes clothes 4 times a year? (Earth)
7. A disappearing variety of disciples? (excellent students)

Exercise: Name mathematical terms with the letter P:

1. Hundredth of a number (percentage)
2. Graph of a quadratic function (parabola)
3. Mutual position of two straight lines (parallel)
4. The sum of the lengths of all sides of a polygon (perimeter)
5. A line segment that forms a right angle with a given line (perpendicular)
6. Sign to indicate action (plus)
7. Geometric transformation (rotation)
8. Planar quadrilateral (parallelogram)

Crossword

Horizontally:

1. A ray that bisects an angle. 4. Triangle element. 5, 6, 7. Types of a triangle (at the corners). 11. ancient mathematician. 12. Part of the line. 15. 16. A line segment that connects the vertex of a triangle with the midpoint of the opposite side.

Vertical: 2. The apex of the triangle. 3. figure in geometry. 8. Triangle element. 9. View of a triangle (on the sides). 10. A segment in a triangle. 13. A triangle with two equal sides. 14. Side of a right triangle. 17. Triangle element.

The game.

I will tell you a story

In half a dozen phrases,

I'll just say the word "three" -

Get your prize now!

Once we caught a pike

Gutted, and inside three

Small fish were seen

And not one, but whole ... two.

Dreaming boy tempered

Become an Olympic champion

Look three, at the start do not hee three,

And wait for the command “one, two, ... march!”

When you want to remember poetry

They do not bison until late at night,

And repeat them to yourself

1. Bisector.

4. Party.

5. Rectangular.

6. Acute-angled.

7. Obtuse.

11. Pythagoras.

12. Cut.

15. Hypotenuse.

16. Median.

2. Point.

3. Triangle.

8. Top.

9. Equilateral.

10. Height.

13. Isosceles.

14. Leg.

17. Angle.

When developing a mathematical battle, the following was used

Literature:

1. Ignatiev, E.I. In the realm of ingenuity [Text]. / ed. M.K. Potapov with textological processing by Yu.V. Nesterenko. - M.: Nauka, 1978. - 192 p.

The book contains tasks of an entertaining nature, with varying degrees of difficulty. As a rule, problems are solved with the involvement of minimal information from arithmetic and geometry, but they require quick wits and the ability to think logically. The book contains both tasks accessible to children and tasks of interest to adults.

1. Journal "Mathematics at School". - 1990. - No. 4. An article called "Math Fight" was used. It describes in detail what Matboy is, the rules of mathematical combat, and sample tasks.

1. Karp, A.P. I give lessons in mathematics [Text]: A book for the teacher: From work experience. - M.: Enlightenment, 1992. - 191 p.

The book contains methodological developments some lessons, samples of k / r., materials for mathematical competitions (olympiads, matboy) and other competitions. The book will assist the teacher in working with students who are interested in mathematics.

1. From the book of Kovalenko V.G. Didactic games at the lessons of mathematics [Text]: A book for the teacher. – M.: Enlightenment, 1990. – 96 p.

some tasks were taken for relay competitions.

1. V.A. Gusev, A.I. Orlov, A.L. Rosenthal "extracurricular work in mathematics in grades 6-8". M: Education, 1984-285 p.

1. Kordemsky B.Ya. "To captivate schoolchildren with mathematics: (material for classroom and extracurricular activities). M: Education, 1981-112s.

This book is a kind of manual containing auxiliary materials for fostering a passion for mathematics. The author selected interesting and valuable arguments of scientists, presented original entertaining tasks for mathematical games and mathematical battles.