Mathematical puzzles for schoolchildren. Mathematical puzzles, games and their application in mathematics lessons Complex mathematical puzzles
The more developed a child is at an early age, the easier it will be for him in high school and higher education institutions. Regular classes with preschool children and children in grades 1-2 help develop the ability to comprehend information, remember material, develop perception and thinking. Thanks to these qualities, the child will be able to reason, it will be easy for him to communicate with peers and with teachers.
In order to guide parents in the right direction in terms of when and what to teach their child, there is a wide variety of literature. One of the main directions is mathematical puzzles, which encourage the child to be smart and stimulate theoretical and practical knowledge. One of the sources of knowledge is our website, where math puzzles for children are presented in the form of interesting tasks and games.
Taking into account the different ages of children, on our website Childdevelop you can use math puzzles for schoolchildren in grades 1-2. For preschool children it will be important to download mathematical puzzle games. To understand the essence of logic exercises, the site has similar examples of puzzles for children.
Math puzzles to download and print for free
We offer convenient use of sections with practical tasks, where you can download mathematical puzzles for free. Accessible and quick, thanks to basic knowledge, mathematical puzzles for children and schoolchildren will become the main platform for easy receptivity of information and knowledge in high school.
Acquiring new knowledge through games will not only broaden the child’s horizons, but will also interest him, and soon he himself will ask to “play with him.” You, in turn, try to distribute mathematical puzzles for children from smallest to largest (from preschool age, and then mathematical puzzles for grades 1-2).
There is no point in saying that it is more profitable to use free literature. Today, not every parent will be able to buy books for every developmental period. Therefore, the Childdevelop website makes it possible to use the necessary knowledge absolutely free of charge. Choose for yourself what is better: “cognitive math puzzle to print for free” or buy the same book “math puzzle”?
All puzzles with answers and solutions.
These puzzles are mainly intended for high school age children. Joke problems, riddle problems, comic stories and challenging mathematical problems develop students' curiosity and intelligence. At the same time, children develop intuition, guesswork, and speed of thinking. Children exhibit particular mental activity when achieving a game goal.
Here is an entertaining mathematical material of varying degrees of difficulty. It may also be of interest to adults.
MATH PUZZLES
Squirrel and nuts
A squirrel, stocking up for the winter, came across a large pile of nuts. She worked for three nights, filling her nest with nuts. How many nuts disappeared from the pile if on the first night the squirrel carried away half as many nuts as on both subsequent nights (combined), and on the last night one less nut than on both previous nights?
(For 9 nuts. On the first night - 3, on the second - 2, on the third - 4)
How many cats?
The room has four corners. There is a cat in each corner. Opposite each cat are three cats. There is one cat on each cat's tail. How many cats are there in the room?
(There are only four cats in the room)
Cat and mice
The cat Vaska is sleeping, and in a dream he sees that he is surrounded by twelve gray mice and one white one. Vaska hears a voice in his sleep: “You must eat every thirteenth mouse, counting all the time in one direction, so that the white mouse is eaten last.” Vaska thought: which mouse should I start with?
Help the cat solve the problem.
(You should start counting from the sixth mouse, counting clockwise from the white mouse (not counting it). To determine which mouse to start counting from, draw 12 dots and one cross on the circle and start counting from there. Cross out each dot and cross , when it's his turn. Do this until there is only one dot left. Replace it with a white mouse, and a cross will indicate which gray mouse to start with)
How many are there?
Vanya has as many brothers as sisters, and his sister has half as many sisters as brothers. How many sisters and how many brothers are there in that family?
(3 sisters and 4 brothers)
All my ducks
Vanya watches the ducks swimming in the village pond.
One duck swims in front of two ducks, another duck swims between two ducks, and one duck swims behind two ducks. “We’ve never had so many ducks in our village pond,” Vanya thinks. How many ducks does Vanya see?
(The boy sees 3 ducks in the pond)
Two shepherds
Two shepherds, Ivan and Peter, met. Ivan says to Peter: “Give me one sheep, then I will have exactly twice as many sheep as you!” And Peter answers him: “No! It’s better if you give me one sheep, then we’ll have equal numbers of sheep!”
How many sheep did each person have?
(It is clear that Ivan has more sheep. But how much more does he have than Peter? If Ivan gives one sheep not to Peter, but to someone else, will both shepherds have equal numbers of sheep? No, because they have equal shares would only be if Peter received this sheep. This means that if Ivan gives one sheep not to Peter, but to a third party, then he will still have more sheep than Peter, but how much more? It is clear that by one sheep, because if you now add one sheep to Peter's flock, then both will have the same amount. It follows that, as long as Ivan does not give any of his sheep to anyone, he has two more sheep in his flock than Peter. Now Let's start with Peter. As we found, he has two fewer sheep than Ivan. This means that if Peter gives, say, one of his sheep not to Ivan, but to someone else, then Ivan will have three more sheep, than Peter. But let it be Ivan who gets this sheep, and not a third party. It is clear that then he will have four more sheep than Peter has left. But the problem says that Ivan in this case will have exactly twice as many sheep, than Peter's. This means that four is exactly the number of sheep that Peter will have left if he gives one sheep to Ivan, who will have eight sheep. And before the expected return, it means that Ivan had 7, and Peter had 5 sheep)
Camel division
The old man, who had three sons, ordered that after his death they should divide the herd of camels that belonged to him so that the eldest took half of all the camels, the middle - a third and the youngest - a ninth of all camels. The old man died and left 17 camels. The sons began dividing, but it turned out that the number 17 is not divisible by 2, 3, or 9. At a loss as to what to do, the brothers turned to the sage. He came to them on his own camel and divided it according to his will. How did he do it?
(The sage embarked on a trick. He added his camel to the herd for a while, then there were 18 of them. Dividing this number, as stated in the will (the eldest brother received 18 x 1/2 = 9 camels, the middle one 18 x 1/3 = 6 camels , youngest 18 x 1/9 = 2 camels), the sage took his camel back (9 + 6 + 2 + 1 = 18). The secret is that the parts into which the sons were to divide the herd according to the will do not add up amount to 1. Indeed, 1/2 + 1/3 + 1/9 = 17/18)
Pack animals
A mule and a donkey, loaded with sacks, walk side by side. The mule says to the donkey: “I will carry twice as much as you if I take your bag. And if you take my bag, then we will both carry the same amount.”
Zhuravskaya Anastasia
The purpose of this work is to study various mathematical puzzles, their classification and application in mathematics lessons.
Download:
Preview:
Municipal budgetary educational institution "School No. 3"
Competition of design and research works in mathematics
Research project
Mathematical puzzles, games and their application in mathematics lessons
Prepared by:
7th grade student
Zhuravskaya Anastasia
Supervisor:
Babina Marina Sergeevna
Mathematic teacher
g.o. Semenovsky
2017
annotation
The purpose of this work is to study various mathematical puzzles, their classification and application in mathematics lessons.
Tasks:
- Study various examples of intelligence tasks;
2. Consider ways to solve them;
3. Classify tasks by type.
Methods used in this study:
1. Study and synthesis
2. Analysis and synthesis
Why am I interested in this particular topic? It all started with an ordinary puzzle that I recently saw on the Internet.This puzzle has collected tens of thousands of reposts and comments on social networks in less than a month, becoming the subject of attention and controversy of almost half a million people. It is not as simple as it might seem at first glance. But it’s not as complicated as it might seem the second time.
Puzzles as a branch of entertaining mathematics
The puzzle is...The element of play that makes fun math fun can take the form of a puzzle, a competition, a magic trick, a paradox, a fallacy, or a simple math problem with a “secret”—some unexpected or funny twist of thought. Whether all these cases relate to pure or applied mathematics is difficult to decide. On the one hand, entertaining mathematics should certainly be considered pure mathematics without the slightest admixture of utilitarianism. On the other hand, it undoubtedly belongs to applied mathematics, because it meets the eternal human need for play. Probably, such a need underlies even pure mathematics. There is not much difference between the delight of a neophyte who has managed to find the key to a complex puzzle, and the joy of a mathematician who has overcome yet another obstacle on the way to solving a complex scientific problem. Both are engaged in the search for true beauty - that clear, well-defined, mysterious and delightful order that underlies all phenomena. It is not surprising, therefore, that pure mathematics is sometimes difficult to distinguish from entertaining mathematics. Thus, in topology, the problem of four colors remained unsolved until recently, although more than one page was devoted to it in many books on entertaining mathematics.
No one will deny that flexagons are very entertaining toys, however, the analysis of their structure very soon comes up against the need to use the higher sections of group theory, and articles about flexagons can be found on the pages of many purely specialized mathematical journals.
Creative mathematicians are usually not ashamed of their interest in entertaining problems and puzzles. Topology has its origins in Euler's work on the seven bridges of Königsberg. Leibniz spent a lot of time solving a puzzle that has experienced a rebirth under the name “Check your level of development (IQ).” The greatest German mathematician Hilbert proved one of the main theorems in the traditional field of entertaining mathematics - cutting figures. A. Turing, the founder of modern computer theory, examined the game invented by S. Lloyd in 15 in his article on solvable and insoluble problems.
P. Hein said that, while visiting Einstein, he saw in the owner’s bookcase a whole shelf filled with mathematical toys and puzzles. It is not difficult to understand the interest that all these great minds had in the mathematical game, for creative thinking, which finds reward in such trivial problems, is akin to the type of thinking that leads to mathematical and scientific discovery in general. After all, what is mathematics if not the systematic attempt to find better and better answers to the puzzles that nature poses to us?
The educational value of engaging mathematics is now widely recognized. This is emphasized by magazines intended for mathematics teachers and new textbooks, especially those written from “modern positions.” Thus, even in such a serious book as “Introduction to Finite Mathematics,” the presentation is often enlivened by entertaining problems.
There is hardly a better way to arouse the reader's interest in the material being studied. A mathematics teacher who reprimands students for playing tic-tac-toe in lecture would have to stop to ask himself whether this game is not of more mathematical interest than his lecture. Indeed, an analysis of the game of tic-tac-toe in seminar classes can serve as a good introduction to some areas of modern mathematics.
Examples of puzzles
Puzzles with matches
You need to move only one match in the arithmetic example “8+3-4=0” laid out with matches so that the correct equality is obtained (you can also change the signs and numbers).
Answer: This classic math match puzzle can be solved in several ways. As you may have guessed, the matches need to be moved so that different numbers are obtained.
First way. From the figure eight we move the lower left match to the middle of the zero. It turns out: 9+3-4=8.
Second way. From the number 8 we remove the upper right match and place it on top of the four. As a result, the correct equality is: 6+3-9=0.
Third way. In number 4, we turn the horizontal match vertically and move it to the lower left corner of the four. And again the arithmetic expression is correct: 8+3-11=0.
There are otherscreative
ways to solve this example in mathematics, for example, with a modification of the equal sign 0+3-4 ≠ 0, 8+3-4 > 0, but this already violates the condition.
Rearrange the three matches so that the fish swims in the opposite direction. In other words, you need to rotate the fish 180 degrees.
To solve the problem, we will move the matches that make up the lower part of the tail and body, as well as the lower fin of our fish. Let's move 2 matches up and one to the right, as shown in the diagram. Now the fish swims not to the right, but to the left.
Puzzles – crosswords:
Horizontally: 3. What is the name of the chord passing through the center of the circle? 5. What kind of figure is this, consisting of all points of the plane located at a given distance from a given point? 7. In which triangle are the angles at the base equal? 9. What is the name of a triangle in which all three angles are acute? 10. What is the name of the side of a right triangle that lies opposite the right angle?
Vertically: 1. What is the name of the ray that divides an angle in half? 2. What is used to depict a circle in a drawing? 4. What is the name of a segment connecting two points on a circle? 6. What are two lines in a plane called if they do not intersect? 8. What is the name of a triangle in which one of the angles is obtuse?
Rebuses
A rebus is a riddle, a puzzle consisting of a combination of letters, words, numbers, pictures and punctuation marks. Puzzles promote the development of thinking, train intelligence, logic, intuition, and ingenuity. They help expand your horizons, remember new words and objects. Trains visual memory and spelling. Unlike an ordinary riddle, where only a verbal description in poetry or prose is used, rebuses combine several methods of perception, both verbal and visual.
There are several main types of puzzles:
1. In the form of pictures and illustrations.
2. Word puzzles.
3. Mathematical puzzles.
There are certain rules for solving puzzles.
1. A comma at the very beginning of a word indicates that you need to remove the first letter in this word, and a comma at the end means that you need to remove the last letter in the word. Two commas - remove two letters. In the word mosquito we remove the last two letters AP, in the word iron we remove the first letter U and the last letter G.
2. Crossed out numbers indicate that the letters standing in this place are removed. In the word five we remove the second and third letters, that is, YAT. If letters are crossed out, they are also removed from the word.
3. Numbers that are not crossed out indicate that the letters in places 2 and 3 must be swapped. In the word iron, the letters T and Y are swapped YUT. Now we read the word in full.
This picture encrypts the word PERPENDICULAR.
4. If the picture is upside down, then the word guessed using the picture is read from right to left. The word read is not turnip, but aper. The first letter A is removed. In the word stump, the last letter b is removed. The word whale is read backwards. In the word chair, the first two letters ST are removed. The names of all objects depicted in the rebus are read only in the nominative case.
5.An “arrow” or an “equals” sign indicates that one letter must be replaced by another. In our case, in the word tick, the letter T must be replaced with the letter D. Now the word can be read in full.
The word EAST is encrypted in this picture.
6.Letters, words or pictures can be depicted inside other letters, above other letters, under and behind them. Then prepositions are added: IN, ON, ABOVE, UNDER, FOR. Our letter O contains the number STO, so it turns out B-O-STO-K.
The word MAP is encrypted in this picture.
7.The numbers under the picture indicate that from this word you need to take the letters located in places numbered 7,2,4,3,8 and compose them in the order in which the numbers are located. In the word cheesecake you need to take the letters 7-K, 2-A, 4-P, 3-T, 8-A. You can read the word.
Let's try to solve a few puzzles in the field of mathematics.
PROOF
Examples of puzzles:
Hypotenuse
Median
Chord
Puzzles with weights
Diamonds and scales
The box contains 242 diamonds, one of which is of natural origin, the rest are copies made in a laboratory (artificial). The masses of artificial diamonds are the same, the mass of natural diamonds is slightly less. Come up with a system of actions to isolate a natural diamond using five weighings on a cup scale without weights or balances.
Answer
We place 81 diamonds on the scales. This weighing selects 81 or 80 diamonds. The second time we place 27 diamonds from the selected group on the scales. This weighing selects 27 or 26 diamonds. The third time we place 9 diamonds from the selected group on the scales. So we select 9 or 8 diamonds. The fourth time we put 3 diamonds on the scales, and 3 or 2 diamonds stand out. Finally, for the fifth time, we put one diamond on the scale and determine which one is natural.
Math games
Math games
All the above puzzles keep our interest alive in the classroom. But most of all I like it when our lesson takes the form of a game. Our teacher often uses games in lessons on generalizing and systematizing knowledge. Then repeating everything is easy and simple, the class is divided into teams, we compete, and get grades. There are no indifferent people in such lessons.
Often at the beginning of the lesson we repeat previously studied material in the form of “Our own game”. Any student can choose a question from the table for a certain score. If a student does not answer, the right to answer passes to another student. The collected points are summed up and you can get a grade for repetition.
In the form of a fairy tale game, we reinforced actions with decimal fractions in the 6th grade. We practice examples and prepare for the test.
Conclusion
This project was written based on my own experience. Personally, I find it more interesting in class when we not only learn something new and practice this knowledge by solving all sorts of problems, but also have the opportunity to play, compete, and show that I can complete the task faster and better than anyone else.
Also, entertaining mathematics develops thinking, trains intelligence, logic, intuition, and ingenuity.
List of studied literature
1. Gardner Martin "Math Puzzles and Fun"
2. B.A.Kordemsky. Mathematical savvy. Moscow. State publishing house of technical and theoretical literature. 1957
3. “Extracurricular work in mathematics”, Alkhova Z.N., Makeeva A.V., Saratov: “Lyceum”, 2002
4. “Tasks for ingenuity” Sharygin I.F., Shevkin A.V., Moscow “Enlightenment” 2003
6. http://riddle-middle.ru/zagadki/s_podvohom/
7. http://www.toybytoy.com/game/Puzzle
8. http://puzzlepedia.ru/100.html
9. http://www.e-crossword.ru
Puzzles for schoolchildren with solutions and answers.
Mathematical problems vary in complexity, so start solving them with your child in kindergarten. Mathematical puzzles are almost always popular with children, so you won’t need to force your child to study. We will try to tell you about the benefits that mathematical puzzles bring to children, and what kind of puzzles can be offered to schoolchildren of a certain age to solve.
Why do we need math puzzles for children?
Mathematics is considered the most difficult science, which can cause a student a lot of problems while studying. But without ordinary mental arithmetic skills and various mathematical techniques, it is simply impossible to live normally in the future.
Long and rather complex mathematical classes, especially from 1st to 4th grades, tire children and do not give them the opportunity to properly assimilate the information they hear. If you want to prevent this from happening to your child, encourage him to study mathematics in a playful way, for example, in the form of mathematical puzzles or rebuses.
Many modern schoolchildren love to have fun with computer games or communicate on social networks with classmates in their leisure time. However, today there are those children who do not spend their own time on such toys, but give preference to the development of logic and intelligence.
Currently, the Internet is filled with a variety of sites where you can easily find logical riddles and puzzles. They are intended not only to waste your own time, but also to provide useful, and most importantly, entertaining entertainment. Many parents have already been able to appreciate the benefits of mathematical puzzles, charades, puzzles, and puzzles, since thanks to them their children were able to develop much faster.
Thanks to mathematical puzzles and problems, the child begins to reason more correctly much faster. His mind and logic are formed.
The advantage of math puzzles is that they are not considered ordinary math problems. From the first meeting, they interest children with their original presentation, arouse in children the desire to quickly find the solution to this or that puzzle.
If you and your child begin to regularly find solutions to mathematical puzzles, your child will very soon begin to solve more complex problems without problems, which he could not solve before. Get your child interested in ordinary mathematics, and mathematical puzzles will help you with this.
Mathematical puzzles and riddles are riddles of varying degrees of difficulty, composed using graphic elements. Solving such puzzles is very exciting. In addition, older children with great pleasure can independently compose mathematical puzzles for friends and classmates, which will allow them to better train their own mind and intellect, plus develop logic.
If the puzzles are presented in the form of complex riddles, children have to “rack their brains” a little in order to find the right solution. During this exciting and educational activity, your child will develop non-standard solutions. In the future, this skill will be useful for your child to find possible ways out of various situations.
And most importantly, math problems and puzzles will give your child a lot of positive mood. If he solves such puzzles with friends or with you, he will be able to further socialize and strengthen relationships.
Now let's figure out how to solve mathematical puzzles correctly. Colorful pictures depicting certain objects, numbers, signs and letters constantly arouse “mad” interest in children. But such pictures, as a rule, seem to them to be pure chaos. And all because children do not know how to solve puzzles correctly.
Accordingly, they think that such pictures do not make sense. But this can be easily corrected if you carefully study the main rules for solving these puzzles:
- The names of the pictures that are encrypted are presented in the nominative case only. When you look at a picture of an object, think about what name this image might have. Accordingly, if you see an eye in the picture, then perhaps “eye” will be encrypted in the picture. Never settle on one answer.
- If the picture shows a comma, This means that from a given word it is necessary to remove a specific letter or several at the same time. Everything will depend on where the comma is located: before the image or after it.
- Often in puzzles of this kind there are letters that are underlined. This is very easy to solve. You guess the word in the picture, and then remove the letters that are underlined. If the picture shows underlined numbers, then you need to remove the letters that correspond to the serial number. If there are numbers and letters next to the image that is not underlined, then you need to leave only these letters.
- If the picture has a value B = P, then you need to replace the letters “B” with the letter “P”. If you see this equality 2 = O, then replace the second letter in the word with “O”. There may also be an arrow in the picture, for example, from the first letter to the third, then they just need to be replaced with each other.
- There are pictures that shown upside down. Then read the word from the end.
- There are mathematical puzzles in which there are fraction. They are easy to decipher: you need to insert the preposition “on”. If there is a “2” in the denominator, it means “gender”. In some cases, you may notice that there is a syllable or letter in the inner part of the letter. It is interpreted as follows: for example, if there is “Yes” inside the letter “O”, then this picture means “Water”.
There are other rules that will help you learn to solve complex puzzles or numerical puzzles. But the child should get acquainted with them after he learns to solve simple problems.
Spend your free time with your children more often. Solve puzzles with them, teach them to find solutions to these puzzles, as this has a positive effect on the brain activity of the developing organism.
Mathematical puzzles with answers for 1st grade children: photo, solution, description
If your child starts solving logic problems from the 1st grade, he will quickly develop intelligence, thinking, and the ability to draw correct conclusions and perform analysis. It is this approach to increasing mathematical capabilities that has the greatest positive side for the formation of correct thinking in children.
We all know that a program compiled for school, as a rule, only involves teaching children to solve certain types of problems. Scientists argue that it is more important that a first-grader, from the very first steps of school, be able to learn to think well and reason correctly. They also confirmed that non-standard problems, which need to be solved using ingenuity and a little thinking, very often put those children who are excellent students at school in a difficult situation.
We offer you a large number of mathematical puzzles for schoolchildren. Solve them together with your children, find the right solutions together, relax so that the child finds it interesting.
Numbers that are the same are indicated in the picture by the same elements. Different numbers are different.
The first rebus (see the original source) Think together, what number did the magician decide to turn into a snake?
Solution:
In the first example, the snake and turtle can hide the following pairs of numbers: 0 – 4 or 1 – 3. Now add these numbers. In the first case you will get 4, in the second – also 4.
In the second example of the rebus, only the second combination of numbers is suitable, since if you subtract 2 from 3 you get 1.
Answer: a unit is hidden behind the snake.
Solution:
In the word “bone”, replace “O” with “I”, and remove the last letter altogether. In the second word, replace “I” with “A”.
Combine these two words.
Answer:
Brush.
Solution:
The picture shows a watering can. Before this word put “K”, and remove the last two “K” and “A”.
Answer:
Fourth puzzle:
Solution:
The picture shows a cloud. Place an “R” in front of this word and remove the first letter “T”.
Answer:
Mathematical puzzles with answers for 2nd grade children: photo, solution, description
In 2nd grade the program is more difficult than in 1st grade. The learning process becomes more labor-intensive, so you need to help your child.
Of course, studying is necessary, but the student cannot be overloaded. The curriculum given at school and homework will be enough. There are some schoolchildren who do great at school, but when they come home, they begin to refuse to do their homework.
But you know that children definitely need to repeat the material they have covered at school, learn something new, pick up words that are new to them, develop their own thinking, and so on. Perhaps you think that your child in the 2nd grade has already become more mature, you begin to give him a lot of new information in the form of additional lessons, and then you wonder why your efforts do not produce positive results.
The fact is that your baby gets tired at school, he wants to play a little and have a good rest. A game, for example, mathematical puzzles, will help him with this. There are a large number of such puzzles. But there are parents who make the mistake of choosing an entertaining puzzle that is not age appropriate.
Don't do this either. Carefully study the options for mathematical puzzles that we offer you. They are intended specifically for 2nd grade students.
Solution:
The picture shows a key. Remove the last two letters of this word. And at the end of the word itself put “YK”.
Answer:
Solution:
The picture shows an umbrella. Remove the last two letters from the word. Place a “U” in front of the word and a “R” at the end.
Answer:
Solution:
The picture shows a leaf. Instead of the letter "L" put the letter "A".
Answer:
Mathematical puzzles with answers for 3rd grade children: photo, solution, description
Puzzles that are intended for 3rd grade schoolchildren can be divided into several types. It all depends on the discipline in the school to which these puzzles belong. They can also be divided according to difficulty level.
Teachers have repeatedly proven that mathematical puzzles help students learn the learning process more effectively. They claim that thanks to such puzzles, the child begins to think well and develops creative ability. Math puzzles also help improve your mood in order to study new subjects.
It is very difficult to identify those puzzles that are suitable for a 3rd grade student. We would like to offer you some options that you can solve with your child.
Solution:
The picture shows a rhombus. Remove the last two letters "M" and "B". Put a “K” in front of the word and a “T” at the end.
Answer:
Solution:
The picture shows a house. Remove the first letter "D". Place the letter “L” in front of the word.
Answer:
Solution:
The picture shows an upside down house. This means that the word must be read from the end. Add the letter “A” to the end of the word.
Answer:
Fourth puzzle:
The fourth puzzle Solution:
This version of the mathematical puzzle depicts letters and numbers. You need to do the following: instead of the number 100, write in letters, and then connect all the letters.
Answer:
Mathematical puzzles with answers for 4th grade children: photo, solution, description
Schoolchildren in the 4th grade are already beginning to become familiar with spatial concepts. Children study superficial geometric figures and their simple properties, and gradually begin to make simple drawings, using primitive measuring instruments. It is during this period of time that children begin to form the basis for future learning.
Schoolchildren move on to a more complex science, which will very soon be divided into a couple of courses: the first course is algebra, the second is geometry. Often, in order for students to have a little rest from a difficult lesson, teachers use additional tasks, for example, mathematical puzzles and rebuses. We offer you some of them that you may be able to solve with your child.
Solution:
In the picture you see the word and an image of the object “knife”. Instead of the number 100, write the word “hundred”. Remove the first letter from the front of the word “knife”. Connect all the letters.
Answer:
Solution:
The picture shows a mushroom. Remove the first letter from the front of the word. Instead of the letter "I" put the letter "Y". Place “KA” at the end of the word.
Answer:
Solution:
The picture shows a leaf and a goose. In the first word, swap the letters as shown in the picture. In the second word, remove the first three letters. Then try to read what you got.
Answer:
Mathematical puzzles with answers for 5th grade children: photo, solution, description
For students who have already reached the 5th grade and above, there are their own complicated mathematical puzzles. Children must work seriously on them to find the correct answer. If this does not happen, the problems simply will not interest the children and then they will not be useful.
For fifth graders we offer you the following puzzles:
Solution:
The picture shows a wasp and a shot. Since we have a fraction here, the solution is this: under the letter “H” there is a wasp. Subtract the last letter from the word “wasp”. And then fold it under + n + os (the last letter is already missing).
Answer:
Solution:
The combination “FOR” is in the letter “A”. The solution is: in + a + for.
Answer:
Mathematical puzzles with answers for 6th grade children: photo, solution, description
In 6th grade, children are already becoming adults. This means that math puzzles also need to be more difficult.
Solution:
The picture shows an upside down mushroom and a wasp. Proceed as follows: read the word “mushroom” backwards. In the same word, replace the letter “G” with the letter “K”. Subtract the first two letters from the word “wasp”. Fold the remaining letters.
Answer:
Solution:
Here, to find a solution, the child will have to think a little. Don't tell him the answer right away. Let your student think about the answer himself, and you listen to what kind of solution he will offer you.
Answer:
Mathematical puzzles with answers for 7th grade children: photo, solution, description
As a rule, in the 7th grade, children begin algebra and geometry. They are already familiar with many geometric figures, their thinking is better developed than that of primary school students. This means that these children need math puzzles with a high degree of difficulty.
The picture shows a combination of letters and numbers. Instead of the number 100, write the word “hundred”. Now connect all the letters. You'll actually have to think a little.
The picture shows the number 7, the letter “K” and a mouth. Write “7” with the word “seven” and subtract the last two letters from it. The mouth is shown upside down. This means you need to read it backwards from the end.
The picture shows a pen with a meter. The comma indicates that you need to remove the last letter from the word “feather”. Everything is very simple. Connect the letters that remain from the word “feather” with the letter “I” and the word “meter”.
Video: Rebus with answers for schoolchildren
A brick weighs 1 kilogram plus half its own weight.
How much does a brick weigh?
Fly
Two trains located at a distance of 200 km are moving towards each other at a speed of 50 km/h each. A fly starts from one of the trains and flies towards the other at a speed of 75 km/h. Having reached another train, the fly turns around and flies back to the first one. So it flies back and forth until two trains collide and the insect dies.
How far did the fly fly?
There are two ways to solve this problem, one is simple, the other is difficult.
The hard way to solve the problem: calculate each section of the path. It is much easier to solve the problem if you simply calculate the distance that a fly can fly in 2 hours (it is after two hours that the trains will collide) at a constant speed of 75 km/h.
She will fly 150 km.
Trains
A freight train leaves Boston for New York, moving at a speed of 60 km/h. After 30 minutes, a passenger train leaves New York for Boston, moving at a speed of 80 km/h.
Which train will be closest to New York at the time of the meeting? (Ask schoolchildren for help - they will probably cope with the problem faster.)
When the trains meet, they will both be approximately the same distance from New York.
A train leaving New York will be closer to New York by about the same distance as one train length, because the trains are traveling in the opposite direction. Well, that is, if by the word “meet” you mean “they will meet”, and not “they will cross at the very moment when one of the trains is aligned with all of its cars with the cars of the second train.”
average speed
I drove half the way to the city, located 60 km away, at an average speed of 30 km/h.
At what speed should I drive the rest of the way so that the overall average speed of the entire trip is 60 km/h?
Wire over the equator
The circumference of the Earth is approximately 40,000 km. If you stretch a wire over the equator around the Earth so that the length of the wire is only 10 meters (0.01 km) longer than the circumference of the Earth, will a flea be able to crawl under this wire? Mouse? Human?
Let's compare the initial perimeter with the length of the wire. The original perimeter is 2πr (two radii times Pi), while the length of the wire is 2π(new r) (two new radii times Pi). The difference between them is approximately 1.6 m.
A short person can easily walk under such a wire at full height, but taller people will have to bend in single file.
Diophantus
Little is known about the life of one Greek mathematician from Alexandria, who is called the founder of algebra. He is believed to have lived in the 3rd century AD. According to stories, the following epitaph was carved on his tombstone:
“Diophantus’s childhood took 1/6 of his life; Diophantus spent 1/12 of his life growing a beard; another 1/7 of Diophantus’s life passed before he got married. 5 years after the wedding, Diophantus had a son, who lived only half the years that his father lived. And 4 years after the death of his son, Diophantus died.”
How many years did Diophantus live?
Ahmes Papyrus
In 1858, Scottish collector Henry Rhind acquired an ancient Egyptian papyrus signed with the name "Ahmes". This papyrus scroll, 33 cm wide and 5.25 meters long, is a copy of an even older mathematical manual dating back to the time of Pharaoh Amenemhat III. Here is one problem from this oldest of mathematical collections:
One hundred measures of grain must be divided among five workers so that the second receives as much more than the first, as much as the third more than the second, and as much as the fourth more than the third, and as much as the fifth more than the fourth. How many measures of grain should each person receive if the first and second workers together receive seven times less grain than the other three workers?
To solve the problem, let's create two equalities. 5w + 10d = 100; 7*(2w + d) = 3w + 9d, where w is the amount of grain for the first worker, d is the difference in the amount of grain between the two (next in order) workers. Answer: the first worker 10/6 measures of grain, the second worker 65/6 measures of grain, the third worker 120/6 (20) measures of grain, the fourth worker 175/6 measures of grain, the fifth worker 230/6 measures of grain.
How long until midnight?
In two hours until midnight there will be half as much time left as there would be in an hour.
What time is it now?
Clock hands
At noon, the hour, minute and second hands of the clock coincide at one point on the dial. In a little more than an hour and five minutes, the hour and minute hands will coincide again. Find, to the nearest millisecond, the time when they coincide.
What angle will the second hand make with them at this time?
This problem can be solved in several ways, but I like the following one, the simplest one, the most. This situation (when the hour and minute hands coincide) is repeated 11 times every 12 hours. It is not difficult to guess that the 1/11 mark of the dial circumference is at 1:05:27.273, that is, the second hand will be at 27.273 seconds.
The angle between the hour and second hands in this case will be 131 degrees.
Pool
There are four pipes leading to the pool, through which the speed of filling the pool can be controlled through taps. By opening the first tap, you can fill the pool in 2 days, the second in 3 days, the third in 4 days and the fourth in 6 hours.
How long will it take to fill the pool by opening all four taps at the same time?
Since there are 24 hours in a day, the first tap will fill 1/48 of the pool in an hour, the second tap will fill 1/72, the third tap will fill 1/96, and the fourth will fill the pool 1/6. From here we get: (6+4+3+48) / 288 = 61/288. The pool will fill in 288/61 hours, that is, in 4 hours, 43 minutes and approximately 17 seconds.
Moving through the desert
A military vehicle with an important message must cross the desert. However, a full gas tank only lasts half the way. A military base has several of these vehicles at its disposal, and gasoline can be pumped from one tank to another. They cannot use any canisters or cables.
How to deliver a message without abandoning a single vehicle in the desert? (For clarity, try to play out the situation with toy cars.)
In total, you will need 4 cars, including the one containing the valuable message (the one that will reach the middle of the desert). In order for her to cross the desert and reach her destination, she will need to refill the gas tank at the neck halfway. The path from the military base (where the cars and gasoline are) to the middle of the desert can be roughly divided into three parts. Each of the three auxiliary cars, in short “dashes” between conventional marks and the base, will be able to drain a third of the gas tank into another auxiliary car, located closer to the main car, on each trip.
Over several back-and-forth trips, the auxiliary vehicles will eventually be able to fully refuel the main vehicle so that it can continue its journey through the second half of the desert.
Air tour
On one distant planet there is only one airport, located at the Seven Pole. The airport has 3 aircraft and an unlimited amount of fuel at its disposal. The plane's tank is enough to reach the South Pole. Airplanes have the ability to refuel (pump fuel from one to another) while in flight.
How can a plane fly around the planet so that all planes return to the airport?
Magic belt
The magic belt that grants the owner's wishes decreases by half in length and 3 times in width after each wish is fulfilled. After three wishes were fulfilled, the area of the front side became 4 cm2.
What was the original length of the belt if its original width was 9 cm?
Baldville
All residents of the city of Baldville have a different amount of hair on their heads. There is not a single resident who has exactly 518 hairs on his head. The population of the city exceeds the number of hairs on the head of any of the inhabitants of Baldville.
What is the maximum possible population of the city of Baldville?
Unfaithful wives
An anthropologist studying a tribe in a remote corner of the Amazon jungle discovered a strange custom. When the husband found out that his wife was cheating, he had to publicly execute her at midnight that same day. All the inhabitants of the tribe, except her husband, always knew about any woman cheating on her husband. But no one ever told the husband about his wife’s infidelities, because it was contrary to the code of honor. The same code of honor did not allow wives to notify the wife whose husband was unfaithful to her. Otherwise, she would have shot her husband that same evening. On the day of his departure, the anthropologist called all the representatives of the tribe and announced: “I know that in this tribe there are unfaithful wives.” And on the ninth day all the unfaithful husbands were executed.
How many unfaithful husbands have there been?
If we take the number of unfaithful husbands as the number “n”, then the number of unfaithful husbands known to each wife of an unfaithful husband is “n-1” (because everyone knows exactly about everything - you only have to guess about the fidelity of your own husband). Now let's build the following logical chain.
Let's assume that the number of unfaithful husbands is one. Then all but one of the wives knows that among the residents there is one unfaithful husband, while the wife of this unfaithful husband is sure that all husbands are faithful to their wives. As soon as she hears that there is at least one unfaithful husband among the residents, she will immediately understand that it can only be her husband, so that same evening she will shoot him without hesitation.
Now imagine that among the residents there are two unfaithful husbands. Each wife of such unfaithful husbands is sure that there is only one unfaithful husband among the residents, so she waits for one of the wives to shoot her husband. But that evening no one shot anyone, and this can only mean one thing: her OWN husband is ALSO unfaithful to her and is the SECOND unfaithful husband in the tribe. The first wife of the first unfaithful husband comes to exactly the same conclusions (she also expected one of the wives to shoot her husband). Thus, both offended wives realize on the very first evening that their husbands are cheating on them, and the next evening (the second day) they shoot both husbands.
Following this logic, it is not difficult to guess that “n” number of unfaithful husbands will be shot on “n” evening.
1 = 2
Find the error in the math calculations:
X=2
x(x-1) = 2(x-1)
x2 -x = 2x-2
x2 -2x = x-2
x(x-2) = x-2
x = 1
Connect 9 dots with four straight lines without lifting your hand or tracing the lines.
Motto
In my youth I discovered that my big toe would eventually make a hole in my sock. So I stopped wearing socks.Albert Einstein
