Paper puzzles for elementary school. Paper puzzle in the form of a kaleidoscope. Making a paper puzzle

Tetraflexagon puzzle. Master class with step-by-step photos

How to make a tetraflexagon with your own hands from paper.

1).Take a square of white paper.

2) Fold it in half. Let's expand.

To fold this tetraflexagon, we unfold the sheet in front of us with the side in which the cells with No. 1 are in the center.
Take the two free ends of cells from No. 1, holding the corner of the upper cell with the thumb and forefinger of the left hand, and the corner of the lower one with the same fingers of the right hand. Pull the corners of the squares simultaneously down and in different directions from each other, so as to turn over each cell with a one and get, if you look at the picture from above, a cell with a five. The remaining cells form, as it were, two open boxes without a lid with the number 6 at the bottom of each of them.
Now, in exactly the same way, let’s capture both inner corners of the cells with fives - i.e. corners diagonally opposite to those we just pulled down. By pulling these corners from top to bottom, we will simultaneously move them in different directions. At the same time, our boxes will be flattened, and we will get a flat tetraflexagon measuring 2 * 2 with four cells. These squares show ones on one side and four twos on the other.
Fold the tetraflexagon in half and open it along the central fold; at the same time, we get another front surface, on all the cells of which there is the same number. By bending the tetraflexagon accordingly, it is easy to obtain the front surfaces with the numbers 1,2,3,4. however, it is not so easy to unfold the surface with numbers 5 and 6.

First you need to make 13 pieces for the puzzle. The chips are made with a diameter of 5 centimeters. Thick cardboard or plywood up to 10 millimeters thick is best for making them. If you don’t have thick cardboard on hand, you can glue together several layers of plain paper and cut out chips from it, waiting for it to dry completely. If the chips are made of plywood, then it is necessary to process the edges with a thin file to avoid injury to the child.

You need to write numbers from 1 to 13. It is best to use a black permanent marker, but regular acrylic paints will also work. The outline of the chips is highlighted in a different color for better perception.

The blank itself, in which the chips will move, must be made from a sheet of whatman paper. The diameter of the chip made will dictate all other dimensions of our workpiece. According to the given figure, mark the future workpiece on whatman paper. Cut out the puzzle model along the outline. Make cuts in the workpiece where the solid lines are shown. Bend the edges of the workpiece upward to form a groove for moving the chips. The resulting puzzle model is not yet solid. To give greater stability, glue the edges that are shaded in orange together.

How to play the puzzle

The pieces are placed in random order along the length of our puzzle. The side pockets remain free. Using these side pockets, you need to move the chips so that they line up in order from 1 to 13 or vice versa. Record your time. Now shuffle the chips and ask the second player to do it faster. Whoever puts the chips in order the fastest is the winner.

You can complicate the puzzle in various ways. A sheet of paper can be placed in the gutter, in which the order of the final construction of the chips is written. Since the sheet of paper will initially be hidden by the chip, the initial number can only be found out by releasing this sheet of paper.

You can invent various ways final construction of chips. For example: odd numbers of chips are in ascending order, alternating with even numbers, which are in descending order. Such constructions will make you think a lot about this puzzle.

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Legendary stories, legendary mistakes made when choosing tattoos under duress, a storm of emotions, a broken relationship or under the influence of a substance... But in the end, you yourself are responsible for your stupid tattoos. Below is the second part of a photo gallery of prominent people who have such terrible tattoos that everyone will photograph and each for their own reasons. Well, I can think […]

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In general, if you ask other people what my hobby is, most will answer - “Ekaterina Georgievna likes to cook.”
If you ask me what my hobby is, the answer will be a little different, in fact much more interesting - I love and collect toys with a mathematical meaning.
I have already written about my toys several times. For example, But that was a long time ago. And since then something new has appeared.

In general, assembling math toys is difficult. Not every puzzle is a good math toy with deep mathematical meaning. It helps a little that you can make math toys yourself.
Here I wrote about one of my favorite mathematical toys from childhood -

Today I’ll tell you what else is in my magic box that we made ourselves.

My husband gives me a lot of math toys. (He knows the correct answer to the question about hobbies!)
The simplest thing is a non-standard dice.

A wooden cube, the corners are rounded, then painted with white paint and numbers from 0 to 5 are drawn with a marker.
And here are the cubes, winning against each other in a circle. I'll talk about them in detail. Each subsequent die wins over the previous one with a probability of 2/3, and the last one wins with a probability of 2/3. Then in my collection there were marble cubes made by my husband. And they had a slightly less equal probability of winning against each other.


These cubes are made from stearin cubes for cooling whiskey. A recess was made with a milling cutter.
You can still use them in whiskey)
One of the most magical toys with a mathematical meaning in the world, in my opinion, is Heron's chain. What is it - you can get an idea from the video:

Heron (the same Greek mathematician we remember from Heron's formula for calculating the area of ​​a triangle) according to history, made his living by performing tricks with this chain.


And you can easily make it at home from key rings. There are 50 pieces here. I highly recommend taking a large number of rings, it’s more interesting.
I made my own toys in a simpler way. For example, here is a set game. Consists of cards with pictures. There are 3 types of figures, painted in 3 colors, there are 1, 2 or 3 of them on a card, and coloring methods: just an outline, shaded, or painted over. (4 features of 3 possibilities = 81 cards in total in the set).

A “set” is a combination of 3 cards in which each feature is either the same on all three, or different on all three. In the picture Denis shows the set: the quantity is the same, the shapes are all different, the colors are different, the painting method is different. 12 cards are laid out on the table and the players find a set. Whoever finds it first takes it for himself, and more cards are laid out in the empty spaces. A very exciting and interesting game.

For training, you can remove one feature. Let's say, when the children were in kindergarten, we only took cards filled in solid.

They were made simply: printed on a printer (when we didn’t even have a color printer yet), colored with felt-tip pens.
Magnetic tangram.


One of my favorite puzzles is the tangram. You can cut a tangram out of cardboard, just like we did in childhood. And here I have it cut out from a large magnetic canvas. Nobody usually plays with a cardboard tangram. But the magnetic tangram hangs on the refrigerator all the time and everyone always plays with it. When you come, the children (or husband) have collected something new on the refrigerator.
And here is a puzzle cut out of cardboard - “Pythagorean Square”. The first task is to make a square out of 4 parts. Now add another small square to these parts and make a new square from five parts.


I recently took puzzles to university. For some reason, the students really liked this “square”.
And here are cards with words related to mathematics.


There are a lot of cards. Some are from some branch of mathematics. There is a large set for schoolchildren. There is a small set about our IMIT.
It’s clear and easy to do – print it on a printer. So as not to show through, there is a shirt with a mathematical meaning on the back.

How to play? Well, there are a lot of options here. To me Lately I like this one.
The players are divided into pairs. First round. The cards are in a stack. You take one card and in the allotted time (say, half a minute) you explain to your partner the concept on the card, without using cognate words. Explained correctly - take the next card. Etc. You can't miss it.
The second circle is the same cards, but explained without words. It helps that the cards are the same and you can remember something.
The third circle is a one-word explanation.
Well, the couple with the most total wins.

You can take any other rules of games about explaining words (such as Activity). Once I even took the test this way. And, of course, there is nothing particularly specific in mathematics here - you can make such cards for chemistry, and for the history of Russia)))
Here. And recently we got a 3D printer, and, of course, the idea arose to make toys for me using it))
For example, I got this tangram.


A tangram can also be made from cardboard, but this one is neater and more interesting. In general, I made (well, how did I do it? My husband made it for me, of course, on his 3D printer) a tangram (like this one, with the IMIT logo) as a prize in one of our competitions. And this one turned out to be a trial (and slightly unsuccessful) version of that. But the prize is magnetic (mine is not). Honestly, the magnetic tangram is a thing.
Here is such a thing: 3 identical parts from which a cube is assembled. Of course, it’s very difficult to make one like this without a 3D printer.


But the thing is very cool.)
My husband, as an engineer, and I, as a mathematician, are literally fascinated by beautiful gear mechanisms. Hence the toys.
For example, here is a cube that can be rotated. It stands on my pulpit and never stands. It is constantly in someone's hands and is being twisted.


It's almost impossible to tear yourself away.

These are such cool gears.

And here are the asymmetrical gears. These can be seen in museums like "Experimentarium" in Moscow or "Joule Park" in our Omsk. And also at my home)))

The coolest thing is that the gears rotate and don’t jam))

From about the same opera - a labyrinth box. Closing it is not so difficult - you see the lines of the labyrinth and move towards the goal. But open it! You have to go through the labyrinth without seeing it)))


Of course, it’s impossible not to combine my two hobbies: math toys and cooking. I recently talked about mathematical cookie cutters. And actually about Mesopatamian printing with Escher’s mosaics too. Wonderful, wonderful. I have several of these)


Escher mosaics? Yes, I have them not only in the form of things for cooking. And in the form of a mosaic too. It really calms the nerves to lay the lizard out flat like this.

And this is an irregular mosaic known as Penrose's Hens (oops, the word hens is no longer underlined). So, Penrose chickens, on the contrary, are annoying)))


Here's my latest addition to the collection. This can easily be made from cardboard.
In the English version it is called "T-puzzle", in Russian "Collect the letter T".


There are parts (such as shown in the picture). From them you need to assemble the letter T.

Why are there 2 sets in the top picture? Because there are two of these most famous puzzles. One is attributed to Martin Gardner (the one that is paler in the picture) and the other is attributed to the Japanese puzzle inventor Nobu (the one that is darker). They differ in the proportions of the letter T.
They say that if you give the details and tell them to form the letter T, 80% of people give up without solving the problem. Well, besides the tangram-type letter T, you can collect a bunch of other interesting things.
I'm a little sorry that the letter T cannot be made magnetic - then most of the interesting pictures will not be collected from it. But it's a very cool thing.
A! Conclusion. A good post should always have a conclusion. To my husband bukov_ka respect and respect! And behind the scenes there is immense love and kisses.

Well, the second conclusion is that in general, of course, it’s cool when there are good stores that sell not “puzzles made of nails,” but proper mathematical toys. And, of course, it’s very cool when there is a 3D printer on which you can make something. But in general, a lot of mathematical entertainment can be made from simple paper using improvised means.

You can come up with an incredible amount of interesting fun and educational games for your children. Plain stationery paper is an excellent material for crafts. All it takes is a little time.

How to make a puzzle out of paper? Is it difficult for children of primary school age? Here are some examples of solving puzzles for children.

Paper puzzles

It is important to get a child interested in crafts from an early age. World virtual games not very useful for development. But working with paper and scissors will develop both imagination and finger motor skills, and the desire to do something with your hands, and not just watch cartoons. Also, by engaging in such creativity, children develop memory and neural connections that will help them learn further.

Many interesting things are made from paper. Various kusudama, toys and puzzles. But, of course, before you teach a child, you will have to learn how to make crafts yourself.

Types of puzzles for primary school children

Let's move on to practice. How to make a puzzle out of paper? We always start by choosing the scheme we like.

Serious origami kusudama for younger children is difficult, but children can do puzzles such as tangrams, flexagons, and various folding paper transformers. We will describe several simple paper puzzles, diagrams and methods for constructing them.

Miracle Triangle

So, how to make a paper puzzle? Will 4th grade cope with the problem or not? For a child, it is not so important how much a puzzle costs. He will be interested in thinking with you about the task you give him. Cut out a regular triangle from hard cardboard and ask your child to divide it into 4 sectors so that these parts make a square.

The puzzle has a name - “haberdasher's puzzle”, since the author of the puzzle was the first to cut out such a triangle from a piece of fabric, and then he himself did not know whether the square would form or not. But still, folding a quadrilateral is quite possible.

How to make a haberdasher's puzzle out of paper? It's pretty easy. Using a stencil, draw a triangle on the cardboard and outline it as shown in the picture. This is the solution to the problem.

An adult needs to cut the parts and decorate them with any colored paper to make the parts look more interesting to the child. And then ask your child to assemble first a triangle and then a square from these parts.

Puzzle toy

How to make a puzzle out of paper that can be assembled, glued and turned into a toy? Try with your child to collect 12 elements of different colors or 4 elements of 3 color shades. And leave it to the little know-it-all to make a circle out of them himself.

If you can’t fold the parts so that they hold tightly, you can glue the corners. However, it will be unsightly if glue stains are visible. All parts must have strictly the same dimensions - millimeter to millimeter, otherwise the elements will turn out crooked and it will be difficult to fold them.

And now the craft turns into a wonderful colored puzzle toy called fireworks origamy. The scheme is very simple.

The child, perhaps, after you fold the first craft with him, will already fold the rest on his own. All you need to do is interest the baby.

DIY paper puzzle?

A puzzle such as a hexaflexagon is made from cut regular strips of paper. This is also very interesting for schoolchildren of 3 or 4 years of study. How to make a paper puzzle with your own hands? To work, you need to print a sheet with a graphical calculation blank or make the same one using the example.

How to make this type of puzzle out of paper? The selected workpiece is folded into a polyhedron. The sectors, united together, form a certain pattern when the toy is turned inside out.

Each puzzle surface consists of 6 triangular sectors. There are schemes according to which they perform a puzzle with 9 and even 12 drawings. But more often they make the simplest one - 3 or 6 planes with drawings.

A hexaflexagon is a polyhedron with 6 patterns. Since paper wears out quickly, it is better to use hard cardboard.

The drawing should be interesting for your child. Think about what characters he likes and draw them. Then you need to cut each one into 6 triangles and stick them on those planes that will make up a separate picture.