The length of this chain is more than 5 jobs. How to determine the size of the chain: a few simple tricks
Today, the number of workers and technicians is only in the tens, and the number of robots is in the thousands; The simplest robots, including those that recognize images, are assembled by our schoolchildren using LEGO DACTA construction sets. It all starts with chains of chains. (By the way, bags also appeared in works on artificial intelligence in the 60s.) Comments on problems 26–35 of Part 1 Problem 26. Definition problem. The only difficulty here is the new table format. However, the table is so simple and "transparent" that most likely there will be no difficulties. Answer: Chains G EZH I N P Length of the chain 7 0 11 3 5 7 Problem 27. Answer: awake, jumper, talker, braggart. Task 28. The task of understanding new definitions. Children should learn that X is a chain, which, as they are used to, has a beginning, an end, and beads that maintain a strict order. There is only one difference from those chains with which the guys worked before: each bead of the X chain is itself a chain of beads. That is why we call the new object a "chain of chains". As much as this name is natural from the point of view of formal logic, it is unusual from the point of view of colloquial language. In Russian, as you know, it is customary to avoid the repetition of words with the same root in one sentence. Therefore, structures similar to our chain of chains are trying to be called a phrase of two different words. For example, it is customary to say “succession of months”, not “chain of chains of days”. It is only in this unusualness that the reason may be rooted that some of the guys will find the topic difficult at first. After all, the guys have already dealt with structures of the “double order” both in the Russian language lessons (a sentence is a chain of chains of letters) and in mathematics lessons (an arithmetic example is a structure of chains of numbers). When answering the first question, one of the guys can try to count the total number of beads included in the chains of the X chain. Of course, such a student should be advised to return to the list of definitions again. Answer: The length of the chain X is 4. The third bead of the chain X is a chain of length 3. 31 Problem 29. Note that among the presented chains there are two chains of chains of chains. These are such chains, the beads of which are chains of chains. Of course, the guys saw such a chain on the definition sheet (chain V), but seeing and understanding are not the same thing. What is, for example, chain B? This is a chain of one bead (and, therefore, of length 1), which is a chain and also consists of one bead, which is also a chain and consists of one bead. Puzzle? Recall Russian folk tales. Baba Yaga in a fairy tale tells Ivan Tsarevich: “Koshchei’s death is at the end of a needle, that needle is in an egg, that egg is in a duck, that duck is in a hare, that hare is in a wrought-iron chest, and that chest is on top of an old oak ". As you can see, here the construction is even more complicated, but the children understand it. What does the G chain look like then? Yes, the same thing, but only Ivan Tsarevich broke an egg, and it was empty there. There will probably be an additional problem with the G chain - some guys will consider it just an empty chain. This, of course, is easily verified by how they determine the truth of the fourth statement. Return with these guys again to Ivan Tsarevich. If he opened the chest and a hare ran out of it, can we assume that the chest was empty, regardless of whether Ivan eventually finds Koshchei's death in the egg or is it empty? Answer: A B C D This is a chain of chains. And And And And And The length of this chain is 1. L L L And And Each bead of this chain is a chain of chains. L I L I I There are empty chains among the beads of this chain. And L L L L Among the beads of this chain there are two identical beads. I I I L L Among the beads of this chain there are three identical beads. L L I L L Problem 30. Optional. A complete and formal solution to this problem will require quite a lot of effort: you need to sort through all the words and then mark each letter in the bag and in the word. There is, however, a way to shorten the process by first dealing with individual characteristics of words. For example, there are only 5 letters in the bag, which means that words where there are not five letters can be thrown out of consideration. There are two vowels in the bag, both O, throw out a couple more words. There is a letter P in the bag, we throw out those words where there is no P. It remains to check only two words, both of them are suitable. As always, we do not propose to explain this model of reasoning to students, but it is quite reasonable to support its elements in their reasoning, or even to push the appearance of such an element somewhere. Answer: AX and ROPOT. Problem 31. Each word of the chain J is uniquely found in the chain L by the available letters and the total number of windows. Therefore, generally speaking, the student can start solving from any word in the chain J, gradually filling in the windows (remember, we discussed a similar question in the commentary to Problem 6). An indication of the task makes the work even easier. As the found words are combined into pairs, the list of "unoccupied" words in the chain L becomes smaller and smaller, so it becomes easier to search for options for the words in the chain J. However, this task, like some others, is multilayered. It has several interesting insights into various course topics (and more). Let's try to trace possible connections. First, both L and J are chains of chains. Secondly, here we begin to gradually bring the children to the topic “Vocabulary order”. In the chain L, the words are arranged in alphabetical order, and in the chain J, they are randomly arranged. Here, of course, it is too early to start talking about the algorithm for sorting words in alphabetical order, but the guys themselves can notice that it is more convenient to work with words arranged in lexicographic order. Problem 32. Optional. The problem continues the work started in problems 18 and 24. The slight difference is that here the student will have to work with a sequence of both three and four days. That is why this task is marked as optional. Answer: Monday, Thursday, Tuesday, Friday. Problem 33. Optional. The children have already solved a similar problem (problem 4). These problems differ only in the objects that are in the bags: there were letters, and here are beads. Remind the children about the need to check - connecting the same beads in pairs. Problem 34. In solving this problem, it is convenient to use a draft. We read the first statement: "In this word, the letter E comes before O." So, we write E on the draft, and then O, but only in such a way that there is free space before E, after O and between the letters (after all, we don’t know where the rest of the letters will have to be inserted). The second statement has nothing to do with the letters already written, so let's leave it for now and deal with the third one. It turns out that Y comes later than O, so we write Y after O on the draft (again leaving space between the letters). Then we return to the second statement and get the following sequence: E-O-U-S. Now it remains to insert the letters into the boxes according to their order in the word. However, one of the guys will enter the letters right away instantly. The reason is that our chain is a meaningful word (BLOW-HAIRED), which can be simply guessed from the available letters without reading the statement at all. This is not bad either, but such guys should be asked to determine the truth of all the statements in the problem, in other words, to prove that this guessed solution suits us. Thus, our task is not to wean children from guessing (the role of intuition in solving problems can hardly be overestimated), but to teach them how to check the correctness of their guess or find an error. Problem 35. Optional. Here, the guys will need the ability to analyze not just statements, but pairs: statements and their truth values. For false statements, one will have to construct their negations – the corresponding true statements. Of course, this task will be quite difficult to solve if we analyze the statements one by one. It is easier to first read all the statements and try to somehow combine them in meaning. Indeed, we can say that some statements are “about the same thing”: the first and last are about the length of the chain E; the second and fifth are about identical beads; the third, fourth and sixth are about the length of chain beads. The easiest way is to deal with the length first. The first statement is false, so the length of the chain E is not 4. It follows from the last statement that the length of the chain is less than 5. The conclusion is that the length of the chain can be 3, 2 or 1. We analyze the second and fifth statements and see that the second the statement is semantically part of the fifth. So, in this chain there should be two identical empty chain beads. Adding this conclusion to the first one, we get that this chain consists either of two empty chains or of three chains, two of which are empty. Now let's read the remaining assertions. We see that the third statement does not add any new information to us. Since we have already found out that there are two empty chains in the chain, then it automatically becomes false. Similarly, the fourth assertion cannot be true due to the presence of empty strings. We learn something new about the chain E only from the sixth statement - among the beads of this chain there is a chain of length 3. Adding this information to the conclusion we made at the previous stage, we get that E is a chain consisting of three chains, two of which are empty, and the third is of length three. Drawing such a chain is now not at all difficult. Most likely, your guys will not be able to carry out all these arguments so smoothly and in full. Perhaps they will single out any one feature of the chain E, and then they will begin to act by the “trial and error” method, drawing different chains. This is also not bad, the main thing is that they always compare the resulting chain with the statements from the table, and if something does not converge, then draw the correct conclusions. 34 Performer Robot In third grade, we introduce the child to performer Robot. An executor is an object that can execute certain commands. Using the command language, we can control the actions of the Robot. Of course, since this is our first encounter with programming, the Robot's language (the commands it "understands") is very limited. The robot is always on the field. The shape of the field can be very diverse. It is only important that it can be divided into squares, that is, the Robot's field can be any figure cut out from a sheet of checkered paper along the borders of the cells. The shape of the field, the coloring of the cells and the position of the Robot on the field, we call the position of the Robot. In the fourth grade we will deal with various games, and there we will talk about the position of the game. We are interested in such continuity of terminology. Similarly, we will talk about the initial position of the Robot (when the program is executed) and the initial position of the game (the position from which the game starts). The robot moves through the cells of the field. It cannot go beyond the field: it will break if we give a command that the Robot must pass through the field boundary. In the further field of the Robot, it will be more complicated - walls will appear inside the field, through which it will also not be able to pass through. Also, in the future, the Robot will be able to evaluate (feel, recognize) certain parameters of the situation in which it finds itself, for example, whether there is a field boundary or a wall in front of it, etc. But so far our Robot cannot do this. Robot Program The programs we start with are simple sequences (chains) of commands. The program must be executed sequentially, command by command, starting with the first line. Do not skip lines or do them in a row. In this case, it will be a completely different program. Initially, the format of problems about the Robot is unchanged: the program and the initial position of the Robot are given in the problem. As a rule, it is necessary to finish the position after the execution of the program (execute the program). Of course, such tasks cannot be particularly difficult - only understanding of the material and attentiveness when performing is important. The only thing that can be somewhat difficult is the presence of two fields in the problem: positions before and after the execution of the program, and it is important to draw the result of the execution on the second field, although the starting point is often marked only on the first field. Give this issue a little more attention at the very beginning, so that in the future the children draw the path of the Robot and its position where it is required, and not where they want. Don't forget also: The robot always paints over the squares it passes through, and never erases the paint when it passes over a painted square. By the appearance of the cell, it is impossible to determine whether the Robot has visited it once or several times. On the insert in each part of the tutorial you will find spare fields for almost all tasks about the Robot. How you use them depends on the task and the child. This can be either a draft, from which the solution is then transferred to the textbook, or vice versa - if it is no longer possible to figure out what is crossed out and what is the final solution on the field, then you can cut out the spare field, seal the confusion with it and carefully complete the task again . Comments on Problems 36–51 of Part 1 Problems 36 and 37. These are not difficult problems for working out new definitions. Here it is very important to work out with the guys the habit of acting correctly in such tasks. It is necessary to pay attention to the following points. The work begins with the fact that the coloring of the cells in the initial position is transferred to the field of the Robot, which should become the position after the execution of the program. We do not put a bold point yet, since we are going to change the position of the Robot. In this case, only one cell is filled in the initial position, but, as follows from the definition sheet, a more complex preliminary coloring is also possible. Now let's move on to working with the program. It must be performed step by step according to the following scheme: we read the command, move one cell in the given direction, paint over the cell where the Robot has landed. In the cell where the Robot finds itself after executing the last command, put a thick dot. With this work, errors are practically eliminated. One problem remains - if the student is distracted during the execution of the program, then he will have to start work again, since he will lose the last executed command. To eliminate the possibility of such annoying interference, advise the children to mark each command in the program after it is executed. Answers: (see picture). Problem 38. Here the program is not only longer, but also more intricate. Above, we mentioned that it is possible to “slide” from the program, that is, the students lose the last command they executed, and discussed how to avoid this. However, something else is also possible - “sliding” from the current position of the Robot, that is, the loss of the cell where it is located after the execution of a particular command. In problems like 36 and 37, where the Robot does not go over the same cells twice and the program is fairly simple, 36 this usually does not happen. However, if the Robot moves with returns, as in this and in many subsequent tasks, this is quite possible. So, we need to have a recipe for this case. The idea is obvious - to mark the current position of the Robot along the way, but how to bring it to life? If we still mark the current position on the same field on which we shade the cells, then confusion and dirt may arise, because after each step the previous current position will have to be erased. It is better to do this on a different field, for example, on a spare field from a cut sheet. Then our step-by-step program execution algorithm will become somewhat more complicated and will look like this: 1) we read the next command; 2) shade the corresponding cell on the field, where the position should be after the execution of the program; 3) mark with a dot the new position of the Robot on the spare field, while erasing the previous mark; 4) mark the executed command in the program. In this task, of course, you can still do without it, but in the future the problem of losing the current position will become more acute. If you see that one of the guys is wrong, then it's worth discussing here how to avoid the problem in the future. Answer: (see picture). Problem 39. Answer: (see picture). The three colors are labeled white, gray and black. What colors they correspond to will depend on how the beads of the K bag are located on the first level. M Problem 40. In this problem, a new detail appears - a “cut out”, not rectangular, field. The definition sheet shows that if the Robot needs to go through the field boundary, it breaks. If the field is “shaped”, then there are more restrictions on the movement of the Robot. Subsequently, this feature will be used meaningfully: for example, when the program will need to be compiled by the children themselves. Here we simply show that this happens. Answer: (see picture). Problem 41. Optional. The task can take quite a long time for slow children, so we did not make it mandatory. The table is quite large - 4 by 5 cells, and there is a chance that someone will look at the number in the wrong cell or color the wrong fruit. To prevent this from happening, advise the children to develop a certain coloring system. For example, you can color fruits in rows (or columns) of a table. In this case, it is useful to immediately mark the cell in the table that we have already used. So, we take the first cell of the first row of the table, it contains the number 2, which means that there should be two red cherries in the bag. We color any two cherries in the bag red and put a tick in the cell, which means that we have already used this information. In this way, you can continue to work until all the cells in the table are marked (and all the fruits in the bag are colored). Problem 42. In this problem, in the initial position on the Robot's field, not one, but several cells have already been painted over. So far, this does not give a meaningful complication, the guys just need to get used to the fact that this happens, and remember that, passing through a shaded cell, the Robot does not change its color. However, here the preparatory stage is of particular relevance - the accurate transfer of the coloring of the cells of the initial position to the field where we will execute the program. Answer: (see picture). Problem 43. Optional. The third statement may cause some difficulty here: your guys, most likely, simply did not think about the fact that an empty string can also be a word - a word in which there is not a single letter. Task 44. This is the first task, where, having the position of the Robot after the execution of the program, it is required to fill in the gaps in the program itself. The main idea that "works" in solving such problems is simple - we cannot write such commands that the Robot gets into unpainted cells after the execution of the program. Answer: skipped commands are defined unambiguously: down, left, up, right. 38 Task 45. Optional. Pay attention to the letter R, which is painted over in black in the picture. On the definition sheet in the second grade, we agreed not to consider black as a separate area (for example, a border or some other lines). Using this rule, we do not consider the letter P as a separate area. Answer: There are 5 areas in this picture: the inside of the C (including the inside of the P), the inside of the T, and three background areas. Problem 46. In this problem it is very easy to stray from the current command and from the current position of the Robot, so you will have to use all the experience gained in previous similar problems. Answer: (see picture). Problem 47. Optional. It is possible that some of the children remember the Latin alphabet by heart, especially if your children study a foreign language from the second grade, however, we do not count on this. Let the children find a clue for themselves: the Latin alphabet is in the textbook in two places: on the second page of the cover and in problem 17. - children are still learning to perform within one part of the textbook. Answer: the true statements are the 3rd and 5th, the rest are false. Problem 48. This problem is, of course, more difficult than the previous problems about the Robot. The robot could start executing the program from any shaded cell of the field, including the one where it ended its journey. Therefore, if you solve the problem head-on, you will have to check each program from different starting positions. To do this, you will need to go through 45 options (9 programs for 5 possible initial positions). Let's think about how we can avoid such a cumbersome enumeration. You can simply execute all the programs on a sheet in a cell (on an "infinite" field). The main thing in this case is not to forget to mark the position of the Robot at the end of the program execution (for example, when executing the fourth program, the Robot “paints over” the same pattern, but as a result it ends up in a different cell). In this case, we will immediately understand which program suits us, because when it is executed, the Robot will “paint over” the same pattern and stop in the same place as in the position after executing program C. However, it also takes a long time to complete all 9 programs. Let's try to come up with ideas that will further reduce the search. The experience gained in all previous tasks about the Robot can tell the children that in the cell in which the Robot must be after the execution of the program, it can only get 39 from one cell by executing the command to the right. Thus, the last command of the program should be to the right: cross out all programs for which this is not true. There are three suitable programs left, which significantly reduces the enumeration. After the correct program (the second one from the left in the bottom row) is cut out and pasted, one should not forget to mark the position of the Robot in the initial position (the second cell from the left in the penultimate row of the field). Problem 49. Optional. Let's remember how often not only children, but also adults cannot clearly explain the way from one place to another. A necessary component of this skill is the indication of clear, precise and unambiguous guidelines that are understandable to everyone. Here we offer one of the ways to indicate landmarks - vocabulary from the topic “Chains”. This is quite natural when it comes to houses standing on one side of the street - they really form a chain if we indicate the direction of movement. Answer: The next house after the cinema is the supermarket. The second house after the supermarket is the bakery. The third house after the cinema is the bakery. The cinema is called "Fairy Tale". The next house after the cinema is the supermarket. The previous house in front of the supermarket is a cinema. The previous house in front of the supermarket is a cinema. Problem 50. We have already met with a similar problem in Problem 44. Let's try to use the same reasoning. Let's start by executing the first three given commands. Then the command is omitted, but we see that, remaining within the cells shaded after the execution of the program, the Robot can then execute only one command - down, and we enter it into the window. We execute the following three given commands. The situation has become a little different - from this cell, the Robot can, while remaining within the pattern, execute the command both up and down. But if the Robot now executes the command up, then it will not be able to execute the next one - to the right, which means that only the command down is suitable. We continue to execute the known commands of the program and we are left with the last empty window. We fill it in based on the position of the Robot after the execution of the program - this is the command down again. Problem 51. Optional. The task is to repeat vocabulary related to trees, as well as to work with statements that do not make sense in some situation. It should be noted that here we encounter for the first time such statements for trees. On the definition sheets on p. 4–5 this topic is discussed and statements are given that do not make sense for these trees. Remind this to those children who will take on 40
Any decoration should be perfect for a lady. To do this, you need to purchase things of the correct size. Let's analyze in detail: how to choose chains around the neck.
How to determine the length?
Finding out the length of the chain you like is not so easy. But this is necessary in order to choose the right outfit and pendant.
Each young lady should rely only on her own taste preferences. Someone likes products that are in close contact with the neck, while someone prefers longer specimens. It all depends on the wishes of the lady.
Most modern manufacturers manufacture chains in accordance with a single standard. It is completely independent of the material.
According to the standard, the length should be a multiple of five.
Varieties
There are several varieties of accessory lengths. Let's consider them in more detail.
- 40 cm - a short chain. It is better to wear it to young fashionistas, teenage girls or fashionable boys.
- 45 cm - slightly longer products. They are also suitable for young girls and fit perfectly into romantic bows, especially when complemented with a charming heart pendant.
- 50 cm is a classic size that advises the standard. Such options go to almost all the ladies. Such copies will be a great solution for a gift.
- 55 cm or more - chains with such a length are better to buy for tall people with a dense physique. They are able to visually stretch the figure and make it more elegant.
- 60-70 cm - things of this length are rare. But if you still decide to decorate the image with such an accessory, then it is recommended to purchase models made according to your own order.
Of course, you can choose the perfect decoration yourself. It won't take too much of your time.
Before you go to the store, just wrap the thread around your neck. It must be fixed exactly at the length at which you would like to pick up the chain. Now the thread can be removed and measured.
Do not forget that the length of the accessory must be a multiple of five, so the resulting number must be rounded up to five, up.
Take the ruler with you. This way you can measure the selected circuit if in doubt.
The chain is a great gift option. It is very easy and simple to pick up:
- If you are choosing a present for a young fashionista, then you should turn to charming specimens of small length. Short accessories will look incomparably on the neck of a fashionable girl.
- Older ladies are recommended to present medium and large length options as a gift.
When choosing the perfect jewelry, rely on your wardrobe. The chain should be in harmony with the clothes. For example, a shorter model will look spectacular with a sexy neckline. But if this detail in clothes is more modest and is located higher, then you should turn to long copies.
Thickness
When choosing a suitable jewelry, not only its length, but also its thickness plays an important role. It is measured in millimeters. Let's take a closer look at the table of these parameters.
- The thinnest and neatest models do not exceed 2-3 mm in width. They very successfully emphasize the graceful female neck.
- The thickness standard does not exceed 4-5 mm. Such chains are designed for charming pendants and other stylish additions.
- The thickest options are chains whose width exceeds 7 mm. As a rule, they are not complemented by decorative elements.
It is very easy to choose a product of the ideal thickness. The younger the young lady, the better a thin chain will look on her. Older ladies are better off wearing thicker accessories.
The chain should fit not only the age of the lady, but also her figure.
For example, short and thin models visually make the neck shorter and fuller, so it is recommended that only thin young ladies turn to such options.
Long jewelry has the opposite effect. They make their owner more slender, stretching the silhouette. Such specimens should be addressed to people who are overweight.
How to care?
Each lady decides for herself: how and when to wear a chain. Some take it off when they come home, others do not want to part with the jewelry even at night. But the chain still needs to be removed, because without proper care it will lose its attractiveness.
A well-maintained product will serve its owner for a very long time. It is necessary to protect the chain from exposure to any chemicals. If your jewelry is made of gold or platinum, this does not mean that it can be exposed to the negative effects of chemicals.
These metals do not oxidize and do not enter into chemical reactions, but aggressive products will definitely not benefit your favorite jewelry.
Try to protect the chain from sudden temperature changes. This can lead to the formation of cracks in the metal and the loss of its original luster.
The accessory must be cleaned periodically. It is carried out using an ordinary soapy solution, to which you can add a few drops of ammonia. Just dip the chain into this solution and then gently wipe it with a dry cloth or small towel.
With what and how to wear?
The selection of a stylish ensemble depends on your tastes and the characteristics of the chain (length, thickness). On most models, a variety of pendants harmoniously look. But do not forget that on too thin women's chains, such additions will look ridiculous.
The size of the pendant plays an important role in a stylish look. If it has a length and an elongated shape, it will visually make the ladies' silhouette more slender.
The color of this part should match the chain. For example, if it is made of red or yellow gold, then it will be more difficult to find a suitable pendant for it. A more versatile metal is white gold. To him, as well as to silver, a lot of different jewelry is suitable.
Women who prefer timeless classics are advised to turn to sets that have one color palette. You should not adhere to this rule for creative young ladies who love bright and rich combinations.
Not the last role is played by how exactly you wear accessories complete with clothes. For example, short chains are versatile, so they can be combined with almost any thing. The only exceptions are dresses with a high neck.
The trend of recent seasons are thick and long models. They will look harmonious with both office and evening ensembles. In a stylish decoration, you may well go to a noisy party, where you are sure to attract attention.
The 3rd grade course starts with a new but very simple topic. By now, the children are familiar with the concept chain and other concepts related to the order of beads in a chain. On the “Chain length” definition sheet, only the name of the concept is new for children: chain length. The children had already worked with him meaningfully, but they described the situation in other words, for example: “the chain consists of 5 beads”. Using the concept chain length, children can say the same thing in a shorter and simpler way, this will allow them to formulate the conditions of the tasks in a shorter way.
Answer: WAKE UP, JUMPER, TALKER, BRAWNER.
Answer:
Task 3. The task of repeating concepts next/previous and concepts related to the general order of beads in a chain. In this problem, a new concept is also used - chain length. There are many suitable solutions in the problem, in particular, because the second and third beads of the chain are not mentioned at all in the condition. But the fourth bead refers to two statements at once - the first and third.
Task 4. When solving, children can use different strategies. Someone will immediately mark all pairs of identical letters in the bags. Someone will mark and add letters at the same time. Some may not want to use notes at all. In the process of work, “extra” letters may appear in the bags, for example, the student will add the letter Sh to one of the bags. Ask the children to check their solution on their own - pair the same letters and check if there are any “unpaired” letters left.
Task 5. Optional. We repeat the theme “Table for the bag”, while using traffic signs. The task is not difficult, but quite voluminous. This task can become a flip bridge to the class hour according to the rules of the road. You can discuss the signs used in this problem, you can play with the guys in the game "Who knows what this sign means?". Mark all the signs that the guys remember directly in the table. The rest of the signs can be distributed in rows and ask the children to find out their purpose from their parents or look in the "Rules of the Road". Below are the names and purpose of the signs found in the problem, and the completed table.
At the end of the solution, you can organize a mutual check: ask the students who solved the problem to compare the tables and, if they are not the same, find out who made the mistake. After filling in the table, the guys will easily find four identical signs - "Lane for route vehicles."
Answer:
Task 6. Optional. This task is not easy, because there are quite a lot of statements in the condition. All these statements must be analyzed separately, and then compared with each other. At the same time, the new concept (the length of the chain) is used more meaningfully than in the similar Problem 3. After such work with statements, it turns out that it is required to construct two chains, each of which consists of five identical digits, with the lower chain consisting of five fives, and the upper - out of five "not fives".
Computer lesson "Chain length", tasks 1 - 8
Task 1. In this problem, children choose from the totality all chains of length 4. In such problems, a complete enumeration of objects is required. In this case, you can use marks: if the chain fits, mark it immediately with an orange checkmark, if it doesn’t fit, you can mark it with a checkmark of a different color.
Task 2. Here the children need to find the length of each chain. The string F is empty, so its length is zero. When finding the chain length R, computational errors are possible. In this case, advise the student to combine the letters in fives and then in tens, using marks as they do so.
Task 3. Here you need to select the chains according to the description, including the concept of "the length of the word (chain)". The solution strategies here may be different. For example, you can check all statements for each word, or you can use statements in turn. When choosing the second strategy, you must first check the first statement for all words and discard unsuitable words. Then for all the remaining words, you need to check the second statement, and so on. As a result, exactly 2 words correspond to the description: LILAC and WORLD.
Task 4. This task is somewhat more difficult than all the previous ones - here the guys need to build a chain according to the description containing the concept of “chain length”. First you need to figure out what figures the chain consists of. It is clear that there is an apple, a pear, a watermelon and a lemon in the chain. What other figurine will be in the chain, given that the length of the chain is 5? It turns out that it can be either a pear or a lemon (if it's an apple or a watermelon, then the second or third statement is meaningless). Now it remains only to line up the selected figures in the desired order.
Task 5. In this task, the guys repeat the concept of “identical bags”. It is clear that all the beads that are in at least one of the bags must be in each bag. Therefore, in the first bag you need to put orange triangular, blue square and red round beads, in the second bag - yellow square and red round, and so on. After that, we have 4 identical bags, but in each of them there are not 8, but only 5 beads. So, now in each of the bags you need to put the same (any!) triple of beads.
Task 6. To begin with, we will collect any bag of 18 rubles. Let's say we have a bag of coins: 10-ruble, 5-ruble, 2-ruble and ruble. But there are only 4 coins in this bag. This means that in order for the bag to match the description, it is enough to exchange one of the coins for two. You can exchange a coin for 10 rubles or 2 rubles. So we get the two required bags. In general, the exchange can almost always be used to improve your decision. Therefore, if the student does not know where to start, advise him to build any bag of 18 rubles, and then, depending on what he did, ask him to make the necessary exchange.
Task 7. The task is to repeat the topic "A bag of chain beads." From the courses of grades 1 and 2, children should remember that different chains can correspond to one bag of beads. In the case of chains of letters (words), it is sometimes possible to build several words of the Russian language for one bag of letters. That is exactly what happens in this issue. Pairs of words with the same bags of letters: CASTOR AND BEAUTY, FRAMES and HOLE, ELSE and DONkey.
Task 8. Optional. Here, children will have to match several conditions with each other, which is why we marked this task as optional. Note that there are 5 roosters in the library, the largest feather in the tail of which is yellow, we use three of them for our chain. Further, we understand that the first rooster is also the third from the end. Therefore, the first rooster has a blue head and a purple body. Among the remaining four roosters, two have a yellow head and one has a blue head, and there are no roosters with a yellow or blue body in the library at all. Therefore, only a rooster with a green head is suitable for us as the latter, and there is only one solution to this problem.
Solving problems 1-6 from the textbook
Task 1. As usual, the first task of the topic is not difficult - it checks the understanding of the definition sheet material (and at the same time makes the children remember the material from the mathematics course about the difference between strict and non-strict inequalities).
Answer: WAKE UP, JUMPER, TALKER, BRAWNER.
Task 2. Here, as in the previous problem, it is enough to understand what the length of the chain is to solve.
The solution of the problem:
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Chain |
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chain length |
Task 3. The task is to repeat the concepts of "next", "previous" and concepts related to the general order of beads in a chain. In this problem, a new concept is also used - “chain length”. There are many suitable solutions in the problem, in particular, because the second and third beads of the chain are not mentioned at all in the condition. But two statements belong to the fourth bead at once - the first and the third.
Task 4. When solving a problem, children can use different strategies. Someone will immediately mark all pairs of identical letters in the bags. Someone will mark and add letters at the same time. Some may not want to use notes at all. In the process of work, “extra” letters may appear in the bags, for example, the student will add the letter Sh to one of the bags. Ask the children to check their solution on their own - connect the same letters in pairs and check if there are any unpaired letters left.
Task 5 (optional). We repeat the theme “Table for the bag”, while using traffic signs. The task is not difficult, but quite voluminous. This task can become a flip bridge to the class hour according to the rules of the road. You can discuss the signs used in this problem, you can play with the guys in the game "Who knows what this sign means?". Mark all the signs that the guys remember directly in the table. The rest of the signs can be divided into rows and asked to find out their purpose from their parents or look at the rules of the road. Below are the names and purpose of the signs found in the problem, and the completed table.
At the end of the solution, you can organize a mutual check: ask the students who solved the problem to compare the tables and, if they are not the same, find out who made the mistake. After filling out the table, the guys will easily find four identical signs - "Lane for route vehicles."
Task 6 (optional). This task is not easy, because there are quite a lot of statements in the condition. All these statements must be analyzed separately, and then compared with each other. At the same time, the new concept (“length of the chain”) is used more meaningfully than in the similar problem 3. After such work with statements, it turns out that it is required to build two chains, each of which consists of five identical digits, and the lower chain consists of five fives, and the top - of the five "not fives".
Lesson "Chain of chains"
By now, children are already accustomed to chains and easily distinguish them in objects and phenomena of the world around them. Chains of chains, however, may seem exotic to them. At the same time, many examples of chains of chains can be found around us. For example, when talking about what a child usually does in the morning, he says: “I got up in the morning, did my exercises, washed, dressed, had breakfast, went to school.” At the same time, in each event of this chain, it is not difficult to single out the internal structure: divide the exercises into separate exercises; clarify in what order the child puts on the items of clothing; divide the route to school into separate straight sections and turns. Spoken language is perceived as a sequence of words (and in some scripts almost every word is represented by its own hieroglyph), but in many languages words are written as chains of letters. In arithmetic expressions, individual numbers can either be treated as string beads or represented as sequences of digits. The use of parentheses and the substitution of an expression for a variable are examples of phenomena of the same kind.
Lists and programming languages
The very first computers were used only for numerical calculations. At a certain point, however, most of the tasks solved by computers began to relate to texts, images, sounds. Today, word and image processing is the main occupation of computers.
To explain to the computer what to do with the text, it was necessary to create special programming languages (a language in which a person gives instructions to a computer). The most famous language for processing texts and writing programs that simulate human intellectual activity has become the LISP language. In developing it, mathematicians and computer scientists used a language invented by mathematicians back in the 1930s. 20th century (In general, a lot of what was used in computer technology was discovered in mathematics even before the advent of computers.) Chains of chains were the main information object of this language. In LISP they are called lists(in English lists). English word list entered the name of the famous language: LISt Processing (translated into Russian - list processing). The LISP language has served as the basis for many systems of so-called artificial intelligence, in which people have tried to assign tasks to a machine, such as image recognition (how a robot moves around in space, takes a part and processes it) and human speech (how a computer understands verbal commands from a person).
Today, personal computers recognize printed text, understand spoken language, and play chess at a very high level. Today, in many factories, the number of workers and technicians is only in the tens, and the number of robots is in the thousands; The simplest robots, for example, image recognition robots, are assembled by schoolchildren from LEGO DACTA parts. And it all starts with chains of chains. (By the way, bags also appeared in scientific papers on artificial intelligence in the 60s of the last century.)
Solving problems 7-13 from the textbook
Task 7. Children should learn that X is a chain, which, as they are used to, has a beginning, an end, and beads that go in a strict order. There is only one difference from those chains with which we worked before: each bead of the X chain is itself a chain of beads. That is why we call the new object chain of chains. As much as this name is natural for the language of formal logic, it is unusual for colloquial and literary language. In Russian, it is customary to avoid repeating words with the same root in one sentence. Therefore, structures that look like a chain of chains are trying to be called a phrase from two different words. For example, it is customary to say "sequence of months" rather than "chain of chains of days." It is only in this unusualness that the reason that the topic may seem difficult at first may be rooted. After all, the guys have already dealt with double-order structures both in the Russian language lessons (a sentence is a chain of chains of letters) and in mathematics lessons (an arithmetic example is a structure of chains of numbers).
In answering the first question, someone may try to count the total number of colored beads that make up the strings of the X chain. Such a student should be advised to return to the definition sheet again.
Answer: the length of the chain X is 4, the third bead of the chain X is a chain of length 3, the second bead is a chain of length 0.
Task 8. Children have worked with chains of words before, but now they will be able to form a complete picture of objects such as chains of chains of letters. In addition to the topic of the current list of definitions, this problem also repeats previous topics, in particular, the concept of “chain length” actively works in the problem. At the same time, the statements deal with both the length of the chain of words itself and the length of the chains included in it. This can cause difficulties. The easiest way to start is to choose from all the names of the months those whose length is more than 6, there are only four of them: February, September, October, December. Since there should not be identical words in the chain and the length of the chain must be greater than 3, it is these bead words that the desired chain will consist of. Thus, children's answers will differ only in the order of months (this order can be any).
Task 9. Answer:
Task 10 (optional). Here is an example of a chain of chains of chains of beads. This is a chain whose beads are chains of chains. The students saw such a chain on the definition sheet (this is chain W), but seeing and understanding are not the same thing. In order for strong children to understand this, they are asked to answer a few questions about chain E. Chain E consists of two chains of chains (hence, it is of length 2). The first bead of the chain E is a chain consisting of two chains (which means that it is also of length 2). The second bead of the chain E is a chain consisting of three chains (which means it is 3 long).
Task 11. To complete the task, you need to go through all the words and mark each letter in the bag and in the word. There is a way to shorten the process by paying attention to individual characteristics of words. For example, there are only 5 letters in a bag, which means that words with more than five letters can be ignored. There are two vowels in the bag, both O: throw out a couple more inappropriate words. There is a letter R in the bag: we throw out those words where the letter R is not. Now it remains to check only two words. We do not propose to explain this model of reasoning to students, but it is quite reasonable to support elements of such a model in their reasoning.
Answer: AX and ROPOT.
Task 12. The task reminds the children of a method of counting the elements of the bag, in which the working table is first filled in and only then the final summary table is filled in. This method justifies itself only when working with a large number of objects, so we offer a bag with a large number of Georgian letters in this problem. We hope that the solution of this problem will not take the children too much time.
Georgian letters, unlike familiar letters or figures, are just squiggles for children, which are very easy to confuse with each other. Remind the children of the principle of work: we mark the letter from the bag and put a cross in the worksheet in the column corresponding to this letter, etc. The table for the bag given in the task is filled out only after the worksheet is filled out.
Task 13 (optional). The idea of order already familiar to children works here: the concepts of “yesterday” and “today” for the days of the week are similar to the concepts of “previous” and “next” for beads in a chain.
Answer: Friday, Sunday, Thursday.
Lesson "Table for the bag (on two grounds)"
Bags Vectors
The guys are already familiar with bags and one-dimensional tables for bags. We hope that working with these mathematical objects will not cause them any special difficulties. However, for mathematics, the introduction of these objects turned out to be quite an important step. The fact is that numbers, primarily natural ones, are very convenient for measuring, for example, time (in seconds), or weight (in grams), or the distance traveled (in meters). But if we want to indicate not how far we have gone, but where we have come, then the situation becomes more complicated. We have to specify two dimensions - two numbers or two characters. This is similar to how we indicate the position in the city (for example, we say: “the corner of Lenin and Rosa Luxembourg”) or the field on the chessboard (for example, e2). The most common method in mathematics is that a grid is applied to the surface, as on paper in a cage. If you take a sheet of checkered paper, then with each cell on it you can match two natural numbers. One of these numbers means how many steps you need to take from our cell to get to the left edge of the sheet, and the other - how many steps you need to take to get to the bottom edge. Two such numbers are called coordinates square, they cannot be interchanged - this is not just a bag in which two numbers lie, but ordered pair(chain!), which we agreed that the first number is always the distance to the left edge of the sheet, and the second is the distance to the bottom edge.
However, the coordinates can be put into a bag. To do this, you need two types of beads: a bead of one type will indicate one step to the left, and a bead of the other - one step down. What kind of beads will be - a matter of agreement. For example, square and round or blue and green. And there may be cards that say “Left” and “Down”. Thus, each cell on the sheet can be associated with a bag, which will contain a certain number of "Left" beads and a certain number of "Down" beads.
Having built a one-dimensional table for such a bag, we get a pair of numbers similar to coordinates: after all, in the table for each number it is clear which number of cards it indicates. Get the so-called vector. Of course, a vector can have not only two, but also more parameters (the corresponding chain of numbers can be longer). And in our bag there can also be beads of many types. Unlike a set, a bag (multiset) can contain several objects of the same type. This means that in the table for the bag there will be not only ones and zeros.
With the concept of "vector" begins the study of science, which is called analytical geometry. This concept lies at the foundation of physics and many branches of mathematics.
The topic of the new lesson is two-dimensional tables for bags. From a scientific point of view, two-dimensional tables are the next most complex structure, vector set. Of course, there is no need to burden children with this complex terminology now. It is enough that they learn to sort and classify the elements of the bag according to two features and accurately fill in the table.
Solving problems 14-18 from the textbook
Task 14. There are quite a lot of fruits in bag G. If one of the children gets confused, advise him to somehow mark the counted figures. That is why we have placed a copy of the bag in the workbook. So, let's choose a cell in the table and look for all the fruits of the corresponding type and color in the bag. At the same time, we will mark the counted fruits in the bag - circle, cross out, etc. If, after filling out the table, not all figures are marked, it will be easy to find which cell in the table is filled incorrectly and correct the error. It is possible that children will use other strategies during the solution. For example, they will first count all yellow fruits - apples, and then - pears.
Task 15. First, you need to fill in four (one-dimensional) tables, i.e., classify faces in turn according to four different features - the type of nose, the type of mouth, the type of eyes and the type of eyebrows. A strong child can be asked how to check the correctness of filling in all four tables: the sum of the numbers in each table must be the same. Ask the student to explain why this is so. Indeed, no matter what (one) feature we classify faces, in total we should get the number of figures that are in the bag.
Problem solution (one-dimensional tables):
The second part of the task - filling in two-dimensional tables - is technically more difficult. The difficulty, firstly, is that children must remember two signs at the same time and completely disconnect from the rest. Secondly, although the signs are meaningful, they are of the same type (sticks and squiggles), therefore they are easily confused, and the objects in the bag do not differ in shape, size, or color. Thirdly, simultaneously with the search for faces, the student must also count them. The task is specially designed in such a way that each child feels the need to develop their own system of work. If someone starts to get confused, you can help him and discuss what system he uses for work, or develop such a system in the course of a joint discussion. Depending on what the student will tend to, we offer you one of three possible approaches.
First approach consists in filling in the cells of the table one by one, i.e. each time looking for all those persons in which there are two signs corresponding to this cell. The main problems with this work:
1. Slipping from the standard - when transferring attention from the table to the objects of the bag, the child may forget which signs he is looking for at the moment and switch to others.
2. Difficulty at the same time looking for faces and counting them, even using different marks.
To eliminate the first problem, you can use a template: draw on the draft the eyes and nose that he is looking for, and periodically glance at this sample. To eliminate the second problem, you can use marks: first find and mark all faces, and then count them. It is only necessary to remember: the marks should be such that the children do not confuse the faces marked at the current and previous stages. To do this, you can use different colors of marks, or, conversely, work with a simple pencil and erase the marks after each stage of work.
Second approach is to alternately take faces from the bag and correlate them with a certain cell in the table. For example, the face in the lower left corner has a straight line mouth and furrowed eyebrows, which means it should be in the top cell of the leftmost column of the second table. We put a stick in this cell with a pencil and mark the corresponding face in the bag with a pencil (for example, circle it). When all the faces in the bag are marked, we count the sticks in each cell of the table and replace them with the resulting numbers.
Third Approach- copy a page of the textbook, cut out all the figures from the bag and sort them on the table according to the necessary features. After counting how many figures were in each pile, fill in the table. This method is the easiest. You should not offer it to children who somehow manage without it. But if you see that the child cannot concentrate in any way (attention is scattered), offer him this method and give him a copy of the page.
Having developed a system of work with the child, approach him from time to time and discuss again what he is doing. After all the children have decided on a strategy and started working, they may begin to get ideas about the relationship between one-dimensional and two-dimensional tables and how this can be used in solving and checking. For example, many will notice that there are no faces with one type of eye in the bag. Someone will make a completely fair conclusion that combinations of this type of eye with all forms of the nose are all the more absent, therefore, in all lines of the last column of the left two-dimensional table, you can immediately write zeros. We can continue to discuss the relationship between one-dimensional and two-dimensional tables in the course of the test. For example, ask the guys: “Where are all the faces with a rounded nose in the left two-dimensional table?” (Clearly, in the top line.) “And how many round-nosed faces do we have in total?” This information can be found in the first one-dimensional table - there are only 15 such persons. Conclusion: the sum of all numbers in the top line should be equal to 15. If the student fulfills this condition, he can go to the second line, if not, let him look for an error in the cells of the top lines. After checking by rows, you can check by columns based on the information of the third one-dimensional table. If everything converges, this guarantees the correct filling of the two-dimensional table (of course, provided that the one-dimensional tables were previously filled correctly). Thus, there is no need for a frontal check. We remind you that the most useful test is a test in which the child independently found his mistakes.
Solution of the problem (two-dimensional tables):
Task 16. For sure, the largest number of errors in solving this problem will be associated with filling the background, which in the picture consists of three areas, two of which are relatively small, and the third occupies the entire remaining background.
Discuss with the children where they might have seen this sign. You can give the task to look for packages with such an ecological sign at home and bring them to the next lesson. You can also ask the children to think at home why such a sign is drawn on the goods, is it good or bad that the product is marked with this sign, etc.
Answer: There are nine areas in this picture (each of the three arrows contains two areas and three more background areas).
Task 17 (optional). Structures similar to chains and bags can be found anywhere, including, of course, in fairy tales. Even everyday knowledge of the guys will be enough to complete this task. Nevertheless, before solving the problem, each of the children must understand for himself that a row of household members pulling a turnip is a chain, the first bead of which is a grandfather, and the last bead is a mouse. In this task, children repeat all the concepts related to the order of the beads in the chain, including concepts related to partial order (for example, "second before the bug"). Please note that in those statements where the concepts "earlier", "later" are used, there may be several correct solutions.
Grandfather pulls a turnip from the ground.
The next after the grandmother is the granddaughter.
The previous one in front of the mouse is a cat.
The mouse is the last one to pull.
The second before the Bug is the grandmother.
The third after the granddaughter is a mouse.
The bug pulls the turnip before the cat (mouse).
The mouse pulls the turnip later than the cat (Bugs, granddaughters, grandmothers, grandfathers).
Task 18 (optional). The different pairs of words in the bags are unrelated, so starting with any pair of words will lead the student to the correct solution. Any partial solution can be extended to a complete solution, any pair of matched words is part of the final solution. With such an arbitrary construction, there are no deadlocks. Not all course tasks have this property of autonomy of each part of the solution. Tasks are also more complicated, when comparing words, we could identify two words by filling in the gaps, and then it would turn out that this identification could not be continued until the solution of the entire problem, because another word with gaps remained unclaimed. Problems with similar deadlocks will appear in the course later.
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