Nikitin fractions. Methods of early development of the Nikitin family How to make fractions yourself from multi-colored circles

A unique educational game guide developed by Nikitin teachers, who prioritized not the development of performing skills, but learning to think independently, invent, and create. The child completes a clearly defined task, independently choosing the path in which to solve it.
One of the best mathematical games that reinforces the child’s developing concept of fractions as parts of a whole. The game consists of three matrices, each of which contains circles of different colors: whole and divided into 2 - 6 equal parts. Playing with multi-colored circles with the help of tactile sensations lays the foundation for mastering complex mathematical material (fractional numbers, relationships and dependencies when dividing a whole object into parts), and develops the ability for synthesis and analysis, logical thinking.

By assembling circles not within frames, but on a plane, the child develops accuracy and perseverance, and improves fine motor skills.

The tasks are designed in such a way that the child himself chooses the level of difficulty he needs, gradually developing his creative abilities.

You can start the game by sorting the available parts by color: turning them over to the front, colored side, the child must figure out how to make a circle from them. In the process, one becomes familiar with the relationship between part and whole, shape, color and size.

The set includes a sample circle. First, show your child the whole circle, then take out the second one - “broken” in half. Invite your child to make it whole again, then reinforce the material by asking him to name round and semicircular objects - at home or on the street. It is worth starting the game with the first four circles, gradually adding more complex ones to them and, based on details from different circles, introducing the child to the concepts of “same” - “different”, “big” - “small”. Gradually move from these concepts to the completely mathematical “more” - “less”, “exactly”.

Children from three years old can begin to be introduced to the composition of numbers: if you turn the circles upside down with the non-colored side, he will see for himself that two is one and one, and five is three and two or four and one. Gradually introduce notation, introducing the child to the world of mathematical symbols, simple examples of addition and subtraction, and inequalities.

When this material has been mastered, you can move on to fractions: tell us what the parts of the whole are called (one third, one fifth), ask to give you this or that part of the circle. To make the explanation easier, turn the pieces over to the non-colored side: “Look, three out of five pieces are not painted. Now let’s count how many are painted and call them by the correct name.”

The game allows you to master not only fractions, but also introduce you to the concept of an angle and its varieties (straight, obtuse, acute, unfolded), learn what a degree measure is, and also, using pairs of identical parts, master symmetry and lay out multi-colored symmetrical compositions.

The Nikitin family's method is my favorite. Probably because this is the only development method that has at least somewhat suited Sanya. Once upon a time, when he was exactly one year old, I bought the first level of the game “Fold the Square”, just to add to the order, for the future. And a month later I was simply amazed that a child, who in some places didn’t even have an awl, but a whole rocket, sat in one place for 20-30 minutes, sorting through pieces of squares and folding them over and over again in different ways, like -as if trying to check all the ways in which a square can be assembled. Let me clarify - the child was 13 (!) months old at that time, and I did not at all expect such interest in such things. And he “asked” for squares 5 times a day, pointing to the shelf on which they lay, and took them away from his cousins ​​when they came to play with us. Now I understand that this was the first manifestation of his logical-mathematical mindset, but then it seemed like a miracle... and some kind of relaxation))) Because I knew for sure that if he “collects squares”, then for about 20 minutes I I can sit relatively calmly without running after him throughout the apartment)))
Needless to say, after such a resounding success of one of the Nikitins’ manuals, I bought all their games that could be bought, including Fractions.

I must say that in the case of the Nikitins’ manuals, Sanya and I found it very easy to follow one of the basic tips for working with their games. The advice goes something like this: “Do not help the child complete the task, do not prompt him with a word, a movement, or a glance.” It was this rule that I tried to adhere to from the very beginning, fortunately Sanya himself did not really want help, and it is possible that this very well spurred his innate logical thinking, because he did not receive ready-made answers, and sometimes did not even receive questions))) For example, in the case of in fractions He initially worked on folding them like the same game “Fold a Square”, that is, he took the parts out of the recesses and folded them back in various ways. I don’t know what was going on in his head at that moment, he still couldn’t tell, because he was not even 1.5 years old, but clearly some concepts were forming, because he was trying to fit and identical parts, and different ones, and sometimes he had the idea to put as many parts there as possible.
In general, although in general the Montessori method is not very suitable for Sane, because he does not accept preliminary explanations, it is precisely the moment of “experiments” with the Nikitins’ manuals that, in my opinion, is very reminiscent of this method - the child does everything himself, and the adult is simply in the wings, on case of difficulty. By the way, it was from the Montessori methodology that the Nikitins drew their ideas, and their fractions-squares are nothing more than reworked and supplemented frame-inserts that Montessori used in her classes, and the approach was clearly taken from her, and the Nikitins did not hide this .
I was once amused by the story of a friend of mine who wanted to buy the Nikitins’ manuals in an offline store, and the “knowledgeable” sellers said that the Nikitins’ method was outdated, and the most modern method now is Montessori, and it is necessary to buy the manuals according to this method. It’s a pity, they apparently haven’t read either about Montessori or the Nikitins, otherwise they would have known for sure that one method follows from the other, and both of them are quite modern and in demand.
But this was a lyrical digression; I’ll return to fractions.
I must say that fractions We have a very long-lasting benefit. As I already mentioned, Sanya was introduced to them before he was 1.5 years old, and used them more as insert frames, and then they were used more for the development of fine motor skills than for the development of logic or mathematical concepts. There were periods when I put these tablets on the shelf and didn’t take them out for several months, and then Sanya grew up and we moved on to the next stage of studying the manual. For example, sometimes I could show him that if you put two red semicircles on one large yellow circle, they will coincide, and if instead of one red semicircle you put two green parts, you will again get a full circle.

I usually call the parts of the circle by their proper names - half, quarter, third, one-fifth. I can’t say that two years ago, or even a year ago, Sanya was particularly interested in such things - but after my explanations, he arranged some of his own games, drew some of his own conclusions, not always correct - but it was a process of reflection. It seems that now this process has borne fruit - against the backdrop of a passion for mathematics, and in particular, geometry, we again got fractions, and it turned out that there was no need to explain anything in particular - everything was clear and understandable to the child. Now we are learning to recognize these parts in graphical notation, as well as adding fractions and bringing them to a common denominator. Actually, all this is taught at school and not in the first grade, but when using such a manual, this is not at all a difficult task for a child, because he can clearly see why 2\4 suddenly became 1\2, or why, if you add 2 \3 and 2\6, then you get a whole one. Probably, if fractions were explained in this way at school, children’s performance in geometry would increase sharply.

It must be said that in this tutorial it is fundamentally important that all the circles are the same size - after all, this is the only way to clearly see how much 1\7 differs from 1\2, 1\4, 1\6, and that in the case of fractions, the larger the number written in the denominator, the smaller the fraction itself. This is very easy to do by simply overlaying different pieces on top of each other:

Due to the fact that all the pieces fit into the recesses, and there is no way to “spread them” wider to fit any fraction, you can again very clearly show that by adding, for example, 2\4, 2\8 and 2\11, another 1/11 will no longer fit:

Or replace one of the parts in each circle with a part of a fraction smaller by 1, and see how much smaller each of these parts is, and what can be done about it, and is it possible...

Games with fractions that Nikitins described, I think, I shouldn’t rewrite here, they are in Nikitins’ books and on their website.
I'll tell you more about the quality of the manual. They are produced in Russia, by the St. Petersburg company "Oksva". This particular set has the quality that suits me most, both in size and thickness. In this case, this is the Standard category, there is also Economy, but the planks there are much thinner and the wood is kind of brittle, I didn’t like it.
In this set, all the fractions that were assumed by the Nikitins come together - the circles are divided into parts from whole to 12.

Each “tablet” contains 4 types of fractions. Each tablet is A4 size:

The tablets are thick, 7 mm, they have recesses into which parts about 5 mm thick are inserted. The edges of the parts and the inside of the recesses are laser processed; immediately after purchase they may get dirty, but not much. On top, all the parts and the tablets themselves are covered with a colored film, it is glued very well - as you can guess, we have had this manual for about 4 years, but nothing has come off, scratched or chipped off. By the way, the game “Fold the Square”, which I mentioned above, has the same quality - nothing came off or broke either. Sanya, until about 2.5 years old, was a great rodent, he even chewed the back of the bed, but for some reason these benefits remained untouched - either they turned out to be tasteless, or they were simply very exciting, there was no time for gnawing)))

I think that these fractions will be useful to us more than once and for many years to come - after all, school is ahead, and the study of fractions there is quite serious, and having a visual embodiment of them makes learning more interesting and easier.

Educational games Nikitin

Boris Nikitin came up with many educational games for his children. These games and exercises are truly unique, and so far nothing has been created either in our country or abroad that could surpass Nikitin’s cubes in their didactic capabilities: “Fold the pattern,” “Fold the square,” “Unicube.”

Educational games Nikitin combine one of the basic principles of learning - from simple to complex - with a very important condition for creative activity - doing everything yourself. This union allowed the game to solve several problems related to the development of creative abilities:

1. Educational games can provide food for the development of creative abilities from a very early age.

2. Their stepping stone tasks always create conditions that are ahead of the development of abilities.

3. Rising each time independently to his “ceiling”, the child develops most successfully.

4. Educational games can be very diverse in their content, and besides, like any games, they do not tolerate coercion and create an atmosphere of free and joyful creativity;

5. By playing these games with their children, parents quietly acquire a very important skill - to control themselves, not to interfere with the child’s thinking and making decisions, not to do for him what he can and should do himself.

Game Features

The main difference between Nikitin’s games is that when playing them, the child acts as an active party and he is not taught the ability to perform work according to the proposed template, but develops logical and imaginative thinking, creativity, the ability to recognize and construct an image, and the ability to be independent.

Most games are presented in the form of multifunctional puzzles that provide scope for creativity. You can customize them to suit yourself, your level, your interests. Each game has a set of problems that the child solves with the help of cubes, bricks, squares made of cardboard or plastic, parts of a mechanical designer, etc.

Nikitin's games can be expanded, improved, and new tasks can be invented.

Rules of the game

At first, no one explains to the child the rules of the game, no one shows him how to do it. The kid solves the problem himself from start to finish.

This technique allows the child to independently search for solutions to problems unknown to him and create new ones, which precisely leads to the development of his creative abilities. The adult makes sure that the level of the task is not too easy and not too difficult, and “corrects” and “directs” the child’s actions. And rejoicing will be the reward for a successfully found solution, and an incentive for future victories.

Using Nikitin’s educational games in classes with a child, certain principles must be adhered to (based on the book by B. Nikitin “Steps of creativity or educational games”):

1. The game should bring joy to both the child and the adult. Every baby’s success is a mutual achievement: both yours and his. Rejoice at it - it inspires the baby, it is the key to his future success. Observe how happy children are if they manage to make us laugh or make us happy.

2. Get your child interested in playing, but don’t force him to play, don’t let him play games to the point of satiety. And one more thing... refrain from making offensive comments like: “Oh, you’re a fool!”, “How stupid you are!” etc. Do not offend the child in the game.

3. Educational games - creative games. Children must do all tasks independently. Be patient and do not suggest with a word, a sigh, a gesture, or a look. Give the opportunity to think and do everything yourself and find mistakes too. By rising gradually and coping with more and more difficult tasks, the child develops his creative abilities.

4. To get a feel for the relative difficulty of tasks, be sure to try them yourself before assigning tasks to children. Write down the time it took you to complete a particular task. Learn to do it faster.

5. Be sure to start with feasible tasks or with simpler parts of them. Success at the very beginning is a prerequisite.

6. If a child fails to complete a task, it means you are overestimating his level of development. Take a break, and after a few days, start with easier tasks. It’s even better if the child himself begins to choose tasks based on his capabilities. Don't rush him.

7. If there is more than one child in a family, then everyone needs a set of games; it is best if there are boxes for all those playing.

8. In what order should the games be given? The author would start with the game “Fold the Pattern” or “Montessori Frames and Inserts”. Here the child needs to distinguish colors and shapes. And the general rule is to observe the child’s development, record his progress in a diary and determine when and which of the games to “turn on.” This is a creative task for dad and mom.

9. Children’s hobbies come in “waves”, so when a child’s interest in the game cools down, “forget” about the game for a month or two or even more, and then “accidentally” (show it, for example, to guests or a friend and teach him to play) let the baby remember her. Returning to the game can often feel like catching up with an old friend you haven't seen for a long time. Try to record the successes, shifts, achievements of each of the “waves” of passion for the game.

10. Take care of games, do not put them on par with other toys in terms of accessibility. After all, the forbidden fruit is sweet, and it is better if the child asks for them or offers to play. Let them stand in a visible, but not very accessible place.

11. For the little ones (1.5-3 years old) enliven the game with a fairy tale or story, give “names” (together with the baby, of course) to patterns, models, drawings, figures, invent, fantasize until the child begins to be captivated by the process of overcoming difficulties in solving problems, achieving the desired goal.

12. The more developed a certain quality is in a child, the more eager it is to be manifested. The strong want to fight, the fast want to run and play outdoor games, but the weak don’t like this. A child may “not be interested in playing” for two main reasons: he has poorly developed the qualities needed in the game, or... adults have discouraged him by forcing him to play or causing trouble at the very beginning. Therefore, praise more for successes and in case of failure, encourage the baby.

13. Create a relaxed atmosphere in the game. Don’t restrain your child’s physical activity so that you can jump with delight, do somersaults on the rug, and fly to the ceiling in daddy’s arms.

14. When folding patterns or models using ready-made tasks has already been mastered, move on to inventing new ones. Get a notebook and sketch there (or better yet, if the child does it himself) new tasks, patterns, figures.

15. It’s better to use a stopwatch, but you can also organize competitions on the speed of solving problems by the clock. Rapidly developing children can already defeat adults from the age of 6-7. In this case, you must muster courage and honestly admit your defeat in a knightly manner. It's hard to think of a great reward for a child. Don't think that your credibility will suffer.

16. etc. - these are the rules that you... find yourself to make the game even more exciting.

Briefly about the most popular games of B. Nikitin

Montessori frames and inserts . This game is accessible to the little ones. It consists of 16 frames with inserts in the form of geometric shapes: circle, square, triangle, ellipse (oval), rectangle and so on. The main task is to choose your own insert for this frame. In addition, frames and inserts can be outlined and then shaded.

Fold the pattern. This game consists of 16 wooden cubes, where each side has a certain color. The cubes must be placed in a wooden or cardboard box (its presence is required). Nikitin advises starting to play with them at the age of one and a half years. With such small children, you can lay out paths from cubes: blue, red, yellow. Then the child learns to place the blocks in a box with a certain color facing up. And only after this the baby begins to make simple patterns.

With this set you can study using the books “Miracle - Cubes. Album with tasks for the game “Fold the Pattern” for children 2-5 years old and “Miracle - Cubes - 2.” Album with tasks “Fold the Pattern” for children 4-8 years old.

Fold it into a square. This puzzle game is for children aged two years and older. The game includes 12 multi-colored squares, cut into pieces: two rectangles, two triangles, etc. The child needs to reassemble the squares from the cut pieces.

Unicube. These are universal cubes that introduce the baby to the world of three-dimensional space. "Unicube" consists of 27 small wooden cubes with colored edges. The child needs to put them together into various three-dimensional shapes and compositions according to the proposed patterns. The game is intended for children from 1.5 years old.

Dots. Dots from zero to ten are marked on square multi-colored cards. In addition, there are cards with numbers. First, the child needs to arrange the squares by color, then in order: from 0 to a card with ten dots (or numbers), etc.

Cubes for everyone. The game consists of small cubes, glued together in different ways in the form of 7 figures, different in shape and painted in certain colors. From such figures it is necessary to construct various models, resembling a cube or parallelepiped, houses, cars, animal figures, etc., according to the proposed drawings-tasks. Toddlers can build their models using only 2-3 shapes.

Fractions. The game is intended for children from 3 years old. It is a set of three plywood. On each there are 4 equally sized circles of different colors. The first circle is whole, the second is cut into two equal parts, the third into three, and so on, up to 12 “slices”. With their help, you can repeat the colors, count the inserted pieces, and you can make a multi-colored circle and compare them with each other.

B. Nikitin's educational games are described in more detail in his book, which is called “Intellectual Games”. It also provides tips on how to play with your child.

You can refer to Lena Danilova’s book “A New Look at Nikitin’s Games”, in which she complements and enriches the tasks for Nikitin’s games and helps parents look at his games a little differently. In her book she writes: “The Nikitins’ games can be compared to musical instruments, unique, multi-voiced universal instruments.”

Material for the lesson.

Game - Fractions

A child constantly encounters the concept of whole - part in everyday life from birth. We cut pies, divide pizza and oranges, look at the clock, pour a certain amount of liquid into a measuring cup. Why not tell your child what fractions are? You can also introduce your child to fractions using special aids. To warm up, you should take an ordinary orange and divide it, accompanying the division with the famous rhyme:

We shared an orange
There are many of us - but he is one!
This slice is for the hedgehog!
This slice is for the siskin!
This slice is for ducklings!
This slice is for kittens!
This slice is for the beaver!
And for the wolf - peel!
She is angry with us - trouble!
Run away in all directions!

The game "Nikitin's Fractions" consists of twelve multi-colored circles. One circle is whole, the rest are divided into parts: two, three, four, five, six, and so on until twelve. “By using the whole circle and its parts in the game,” Nikitin believed, “kids acquire many ideas about fractions and their relationships, although for some reason the school postpones their mastery by 5-6 years - to the 3rd-4th grade.” In the game "Nikitin's Fractions" there is no clear sequence of tasks, as in other games. Each time, all 78 parts must be poured onto the table or floor, and then again put in circles in a box, if, of course, you use the wooden "Oksva" manual. In this case, Nikitin defines the first problem:

a) pour fractions onto the table or floor
b) turn them over with the colored side up
c) arrange the fractions in groups so as to bring together equally colored ones
d) make a circle of the same color from each pile
e) put the mugs in frames.

What are the parts of the circles called? For little ones, this task can last for days, weeks and even months, Nikitin believes. There is no need to force things, just be happy if the child immediately names some: “green quarter”, “yellow half”, etc. For those who can count to 100, this task can be solved in one sitting. The names of the parts should be given not only everyday, but also mathematical: one second, one third, one fourth, one fifth.

Put it in a row put one part of all colors in a row: a) in order: put the largest part first, then smaller and smaller, and so on until the smallest, so that each next one is smaller than the previous ones. b) place the same parts next to each other, but in a stack. Place the largest one at the bottom and the smallest one at the top.

Which part is bigger One fifth or one fourth? How can I check this? Yes, just superimpose a smaller one on a larger one, and everything will be OBVIOUS, as N. Zaitsev likes to say. Problems of this kind can be given until it becomes clear to you that the child has grasped the principle of definition: “the more parts a circle is divided into, the smaller the parts.” By the way, how do you write down that 1/4 is greater than 1/5 mathematically? This is where the “more than” sign and the “less than” sign will appear.

How many pieces fit? How many quarters fit on one half? How many sixths, eighths, tenths, twelfths? How many times is one second greater than one fourth? One sixth? What parts and how many will fit exactly on one third, but on half? How many times is one sixth less than one third? Is it possible to make a whole circle out of pieces of different colors? What parts do you need to take for this? How many multi-colored circles can you add from the game "Nikitin's Fractions"? What is the largest number?

With your own hands Nikitin's book gives detailed instructions on how to make a manual yourself, so if for some reason the finished game is ready, it can be easily cut out of polystyrene foam. The sheets must be marked using a compass, divided into parts and cut with scissors or a sharp paper knife. And then move on to the actual games. Overall they are similar to the classic games with a plywood purchase manual. But there are also differences due to the lack of wooden frames.

First, let's take out a whole circle and show that it is a whole. Let's ask, what does it look like? To an apple, to the moon, to a wheel? Then let's take the second circle and show that it breaks into two halves. Let's ask for half of the second circle, apply it to the whole circle, etc. You can outline the circles with a felt-tip pen, then add colored faces. From half, if you circle it, you can make an umbrella or a mushroom. Using parts of a circle, you can talk about concepts such as “same”, “different”, “same”, “not the same”. Ask questions to fill in: “what is more: one second or one third.” And then show it, give the children the opportunity to select the parts themselves. Line up the pieces from smallest to largest. Go through each circle, naming the parts. If there are two parts, then one will be called one second or half. If there are three parts, then one third, and if there are twelve, then one twelfth. Let the child have the entire set of the game "Nikitin's Fractions", that is, all 78 parts. Now ask for one sixth, two sixths, six sixths? What different parts can be used to make a whole? Is it possible to divide a circle into two parts? How about three? How to make a circle using only red and yellow parts? Is this possible in principle? Let your classes have as much kinesthetics as possible, let the kids let everything pass through their hands. Fractions are a complex topic; it is better to approach it from different angles, inventing new tasks. Lay out four slices of the eight-piece green circle. Ask how much is missing. Go through all the circles with this question. When playing, focus on the following expressions: “divide into equal parts”, “whole”, “half”, “in half”, “one of two”, “one second”, “one twelfth”, “part”.

Game description

The idea of ​​a fraction as a part of a whole can form early in a child. After all, in life he sees half an apple or even a quarter, gives it a bite or breaks off half of a candy, cookie, or cracker. You can cut a pie or a round cake into equal parts.

Dividing or crushing an entire circle turned out to be convenient for the game. And by using the whole circle and its parts in the game, children acquire many ideas about fractions and their relationships, although for some reason the school postpones their mastery by 5-6 years - to the 3rd-4th grade.

How to make a game

To play the game you need to find or cut out of cardboard, plastic, plywood or similar materials 12 identical circles with a diameter of approximately

200 mm, thickness 1–2 mm. Paint the mugs on one side in 12 different colors so that they can be easily distinguished. Take technical paints - nitro paints or oil paints. You can, of course, limit yourself to gluing the circles with colored paper, but then they will quickly wear out.

Accurately mark each circle and divide it into equal parts:

The 1st circle remains intact;

The 2nd circle is divided into 2 parts by diameter;

3rd – into 3 parts along the radii;

4th - into 4 parts, etc. up to 12 parts, as shown in fig. 55.

On the back of the whole circle, write large number 1, and on the parts, respectively, 1/2, 1/3, 1/4, etc. up to 1/12.

To store fractions, you need a strong square box with a lid to hold all the fractions, placed in whole circles, like the one shown in Fig. 54. Such a box is not difficult for a skilled dad to bend from thin tin. Just make sure that the child can open the lid himself.

Rice. 54

Rice. 55

How to play

As in other games, this depends on the age and level of development of the child, i.e. his strength, ability to count, intelligence. If your child hasn’t seen how you made the game, then show him the closed box and, of course, intrigue him with questions: “What’s hidden in the box?” and “Can you open it?” You can even shake it and listen to what is making noise inside it.

It’s good if the child was able to discover on his own that the lid here does not open like on cardboard boxes, but moves to the side, like in a school pencil case. If you had to help and show how to open the lid, it means that the child did not acquire something important, you did not allow him to make one micro-opening.

This game does not have such a clear sequence of tasks as in other games; and each time all 78 pieces must be poured out of the box onto the table or floor, and then, at the end, they must be placed again in circles in the box. That's why task No. 1 for the baby will consist of several parts:

a) open the lid of the box;

b) pour all the fractions onto the table or floor;

c) turn them over with the painted side up, since when pouring them out of the box, many may fall with the back side up; d) arrange the fractions in groups so as to put together equally colored ones (similar to the problem in “Fold a square”);

e) make a circle of the same color from each pile;

f) after playing, put the fractions in the box and close the lid.

In the first task, the circles can be folded in any order, it is important that a circle comes out and the parts fit snugly together.

If the elders feel that 78 pieces at once is too much and the baby cannot cope with packing them all, then only the first few should be placed in the box, for example the 1st–5th, where there are only 15 pieces, and in the following days gradually increase their number.

Task No. 2. What is the name of parts of circles?

For little ones, this task can take days, weeks and even months. And there’s no need to force it, just be happy if he names some right away: “pink half” or “orange quarter.”

Give the parts names not only your own, family, household, but also mathematically correct: “one second”, “one third”, “one quarter”, “one fifth”, etc.

Task No. 3. Place in a row one part of all colors: a) in order: put the largest part first, then smaller and smaller, and so on until the smallest, so that each next one is smaller than the previous ones; b) place the same parts next to each other, but in a stack.

Place the largest one at the bottom and the smallest one at the top. Fold so that the stack is beautiful (for example, a “ladder” or “steps” on one side, on both sides, etc.).

Task No. 4. Which part is bigger: one fifth or one fourth? how to check this? (Put the smaller one on top of the larger one.)

Problems regarding which part is larger or smaller can be given in a variety of ways until it becomes clear to you that the child has grasped the principle of determination: “the more parts a circle is divided into, the smaller the parts.”

How to write that 1/4 more 1/5 mathematically? (1/4 > 1/5). How to write that 1/5 less 1/4 mathematically? (1/5< 1/4).

Task No. 5. How many quarters fit on one half? How many sixths, eighths, tenths, twelfths?

At what timeone and two times more fourth, sixth, eighth, tenth, twelfth?

Task No. 6. Which parts and How many Will they fit exactly on one third (sixths, ninths, twelfths)?

How many timessixth (ninth, twelfth) less one third?

Task No. 7.Is it possible from parts different color fold whole circle(two-color, three-color, four-color)?

What parts do you need to take for this?

Task No. 8.How many whole multi-colored circles can be added from the game “Fractions”? (What is the largest number?)

Task No. 9.Is it possible to make 12 different colored circles from all 78 parts?

Come up with new problems from the game “Fractions”.