home Epilation Print out the development of a parallelepiped for gluing. How to make a parallelepiped and a cube out of paper? Learning to make geometric shapes with children. Cubes - a game from childhood

Print out the development of a parallelepiped for gluing. How to make a parallelepiped and a cube out of paper? Learning to make geometric shapes with children. Cubes - a game from childhood

Topic: Development of a rectangular parallelepiped

Goal: to organize students’ activities to perceive, comprehend and master the concept of “development of a rectangular parallelepiped.”

Tasks

Develop an understanding of the development of a rectangular parallelepiped by performing practical tasks with parallelepiped models.

To develop the ability to apply mathematical knowledge in everyday life based on making models of parallelepipeds from developments

Develop analytical and synthetic activity when working with parallelepiped development

Develop speech through justifications and reasoning about one’s activities;

Develop independence in creative activities and self-confidence.

During the classes.

1st org moment

Hello guys! Today you will have an unusual lesson. It is unusual in that many things will be the first time for everyone in this class. We met you for the first time and will work together for the first time. What do you think is needed for us to succeed the first time? I am sure that you have these qualities, and they will help you gain new knowledge in today's mathematics lesson.

2 updating knowledge

Will you need the knowledge that you already have today? Show me your knowledge in your next job.

We are surrounded by many objects. They differ in shape, size, color, material from which they are made,... People are interested in the different qualities of these objects. And mathematicians study not the objects themselves, but their forms. Therefore, to study subjects they use geometric figures and bodies

(slide)

Name the figures and bodies depicted on the slide that you know

You have models of geometric bodies on your desks. Name them. (cube, beam, cylinder, different in color, size) Distribute them into three groups. By what criteria did you divide these bodies? Which body do you think is the odd one out in this group? (cylinder) Why? (round body) Remove the cylinder. What are the remaining bodies called? (rectangular parallelepipeds) Have you guessed which geometric body we will work with? Today we will work with a rectangular parallelepiped. More precisely, we will learn how to make a parallelepiped. For this we need a scan of a rectangular parallelepiped. What is a “sweep”, how to make it and why it is needed - you will learn during the lesson. The topic of today's lesson is called “Scanning a rectangular parallelepiped.” You have workbooks, write down the topic of the lesson in them.

3 new material

Let's start with the tasks in the notebook.

For task 1, select images of a rectangular parallelepiped. Name the number of the drawing that shows a rectangular parallelepiped.

In task 2, determine which of the objects or parts of them shown in the picture have the shape of a rectangular parallelepiped. (Check on the slide)

You have now shown very good knowledge.

- (the same slide with furniture) name in one word all the objects depicted on the slide? Are all the pieces of furniture here familiar to you? (chest of drawers) Where do people get furniture? Have you ever had to buy furniture? Will you ever buy it? For what?

Today in class we will try to arrange furniture in a new room. Do you think this knowledge will be useful to you in the future? Today we will all practice together, and in the future each of you will do it independently. What furniture will you need in your apartment?

You have now determined that some furniture has the shape (question intonation) ... of a rectangular parallelepiped. This means that in order to obtain a piece of furniture we must make a rectangular parallelepiped. Let's remember the elements of a parallelepiped.

On your desks are models of parallelepipeds made of paper. Take them in your hands. Using them and looking at the screen, do the following: highlight all the edges on your models with color, as on the screen. How many faces are there in total? (6) (at the same time, edges highlighted in different colors appear on the slide).Highlight all the edges on the models in blue (visible edges are highlighted in color on the screen) How many edges does the parallelepiped have? (12) Select all vertices on the models with black color. (similar to the vertices visible on the screen) How many vertices are there in total?(8)

Let's continue working in notebooks and complete task 3

Well done, you did a good job on this!

Can you make a rectangular parallelepiped yourself? How?

To understand how to properly make a rectangular parallelepiped, we will now unfold it and look at it in expanded form.

Pick up the scissors. Don't forget about safety precautions when working with scissors. Repeat after me, cut your cuboid. (we cut first along the ribs of the upper base, then the side ribs) we unfolded our parallelepiped and we got a “development of a rectangular parallelepiped,” from the word “unfold.” (on slide scan for clarity: both the drawing and the word) Fold our development back. What did you get? What do you think needs to be done to make a model of a rectangular parallelepiped? Now it's time to learn how to build a sweep. Let's take a closer look at it. What figures does the development consist of? Why? How many are there? Why?

In order to obtain a development, we must first draw it. When making a drawing, we will rely on our development: where on the development are the side, top and bottom bases located? What shape do they form? What is the length of this rectangle? (in stock 4+5+4+5= 18) What is the height of this rectangle? (3) Draw this rectangle in your notebooks. Divide it into four rectangles. Where are the front and back edges located? How tall are they? (5) Draw them. Is your drawing similar to our development? Assemble your pattern again and tell me how you will fasten all the edges together? To do this, you need to make allowances for gluing. (slide with allowances) Pay attention to where they will be. Draw allowances on your drawings. (allowances are made) The drawing is ready, all that remains is to cut and glue the development. I really want to see what you can do as soon as possible.

Making a parallelepiped

4 fastening

Look at these scans. (on the slide) What can you say about them? They are all the same? How are they similar? (number of rectangles and their location) How are they different? (size of rectangles) What will the parallelepipeds made from these developments be like?

After you have made your first developments and you already have an idea of how to obtain a rectangular parallelepiped from them, it is time to put the acquired knowledge into practice. It's time for us to furnish the room! Look how beautiful the modern furniture is. (Furniture on the slide) Now you will make your own furniture. If anyone needs help, I will help.

Tasks are written on sheets marked in different colors. The tasks vary in complexity: on sheets with a red mark you need to add allowances to the pattern, cut and glue the pattern; on sheets with a yellow mark you need to cut and glue the finished pattern; on sheets with a green mark you need to glue the scan. Each of you will now choose a task according to your strengths and complete the corresponding task. Draw parallelepipeds using these developments and determine what piece of furniture or household item you will get. We will ask our guests to also work and help us make a chair.

Learn how to make a rectangular parallelepiped from paper. Scheme and detailed description will help you with this.

What materials will you need?

Thick sheets of A4 paper in white or another color;
- scissors;
- pencil;
- ruler;
- glue.

Before you start working on a figure, look or imagine what it will look like. From the school course you can remember that a parallelepiped has 6 faces and the same number of sides. Therefore, the diagram on paper will consist of six rectangles connected together in one plane.

Paper parallelepiped: step-by-step instructions

1. First, you need to decide on the size of the figure, its length, width and height. Write down these values.

2. Now it’s worth drawing a diagram on paper. Take the height and width of the future parallelepiped, add them and multiply by two. Draw a horizontal line; its length should be equal to this value.

3. From the ends of the line you need to lower two segments perpendicular to it, they should be equal to the length of the figure. Connect the segments together by drawing another line.

5. Look at the upper right corner of the resulting rectangle. From this point you need to plot two segments - height and width. After that – once again the height and width. Draw perpendicular lines from the marked points to the opposite side. You have 4 faces.

6. Pay attention to the second rectangle on the right; you need to draw two more below and above it. To do this, draw a segment as long as the height of the figure. Then swipe another one and connect them. Repeat the same steps with the second rectangle from the bottom.

7. To make it easier to glue the whole shape, you need to add a few more small parts, as shown in the picture. They should be about 1.5 cm wide and have 45 degree beveled corners.

8. The outline of the figure is ready, carefully cut it out of paper, bend all the lines. The rectangles located above and below will become the bottom and roof of the parallelepiped. In this case, all side edges must be in contact.

9. Apply glue to additional parts and connect the figure. Let the glue dry. Your parallelepiped is ready!

Now you know how to make a parallelepiped from paper, photos and videos will help you correctly draw the diagram and assemble the figure.

A parallelepiped is a three-dimensional geometric figure, the base of which is a polygon, and the faces are parallelograms. Many schoolchildren find it difficult to comprehend this concept, much less solve problems involving calculating the area and volume of a parallelepiped. In order to help your child master geometry knowledge, make a model of a figure out of paper with him.

How to make a parallelepiped from white paper

The three-dimensional model is assembled from a stencil, which is easy to make yourself. Prepare: a sheet of A4 paper, pencil, ruler, scissors, glue.

Place the sheet in front of you with the wide side (lengthwise). Divide its side part, equal to 21 cm, in half on both sides and draw a line.
Let's assume that the height of the edge of the parallelepiped is 10 cm. Measure from the middle from the two edges up and down 5 cm and connect the marks with segments.
To form the sides of the figure, put aside on the first and last lines alternately - 8, 5, 8, 5 cm. Connect the lines at the points to each other - you get the edges of a parallelepiped.
On the second and third vertical lines, mark 5 cm from their beginning and end (up and down), since our width of one side is 5 cm, and connect the ends of the segments to form a quadrangle.
Step back from the outline of the figure 1.5 cm on each side and draw a mark that will indicate places for fastening.

Important: do not go beyond the protruding side rectangles, so as not to accidentally cut them later.

Cut out the resulting shape, cut off the corners of the ends of the strips for gluing.
Bend the workpiece along the edges, kneading them with your hands. Transfer the base to the other side so that the pencil grid remains inside, and push the basting along the entire surface.
Apply glue to the seam allowance on one side. Roll up the shape and, starting from the outermost strip, glue the opposite edge to it, then the top base. Repeat the procedure on the other side and the parallelepiped is ready.

How to make a rectangular parallelepiped from paper - a cube

A cube is also a parallelepiped, only rectangular, the sides of which are squares. It is drawn according to the same scheme as in the first version.

Build successively four squares in the horizontal direction and two on the sides of the second along the vertical axis. Draw the valves onto the glue.

Cut out the development, crease the edges, apply glue to the allowances and glue the cube.

How to make a parallelepiped from paper using the origami technique

This method is good because to make a figure you only need square sheet paper.

Bend the sheet in half on both sides, divide the resulting corners in half so that a blank of folded triangles comes out.

Flip the shape 90º. Bend the left and right corners until they touch, pressing the folds with your fingers. Put down the sheet reverse side, repeat the steps.

Turn away the folded corners and fold the others, formed from the free ends of the sheet and pointing their apexes towards the folds.

Insert the corners into the resulting pockets.

Insert a pencil or blow into the hole formed at the bottom of the model, and the figure will gain volume.

A paper parallelepiped can be used not only as a visual aid in geometry. If the figures are made from colored cardboard, they will be useful in children's games, and those made from decorative paper– will help you wrap a gift or souvenir beautifully.

By playing with various geometric figures with your child, you help him develop spatial thinking and imagination. He begins to understand what square, round, cubic, spherical, rectangular means and can easily imagine it in his head. Even at school, during geometry lessons, teachers always show models of various figures to students, which contributes to a better understanding of geometric theorems and axioms. And, perhaps, the most difficult and difficult word for a child to pronounce is “parallelepiped”. In order to master this figure and understand its patterns, we suggest you and your child make a parallelepiped out of paper with your own hands.

To do this you will need:

thick paper (but not cardboard, otherwise such a craft will cause a lot of difficulties for the child), you can use a sheet from an album;
pencil;
ruler;
scissors;
PVA glue.

To understand how to make a parallelepiped from paper, you need to remember what it looks like and what it is. This figure has 6 faces, each of which is a rectangle. Consequently, the scan will consist of 6 interconnected rectangles located in the same plane.

1. Like any volumetric figure, a parallelepiped has length, width and height. The size of the resulting fake will depend on their value. Let's determine the desired values and write them down.

2. Let's start drawing a diagram of a rectangular parallelepiped on paper. Remember that the paper should not be too thin, it will easily get wet from the glue and warp, then the figure will not turn out smooth, and excessively thick cardboard will bend poorly and crack at the bends.

3. Draw a horizontal line, the length of which will be equal to the sum of the width and height multiplied by two. Then from each end of the line we lower a perpendicular equal to the length of the intended parallelogram. Between them we will draw a line parallel to the first.

4. Now from the upper right corner we will set aside the height of the parallelogram, then the width. Then again the height, and again the width. From the obtained points we draw perpendicular lines to the opposite side, which will be equal to the length of the parallelogram. Thus, we got 4 sides of the figure. There are still 2 left.

5. Above the second rectangle on the right, draw two more below and above. In this case, from the second mark on the right, which we made in step 4, we will draw a perpendicular upward equal to the height of the figure. Let's repeat the same thing from the second mark. Let's connect the perpendiculars with a segment equal to the width of the parallelogram. Using a similar method, we will construct the lower rectangle on the opposite side.

6. To make it easier to glue the parallelepiped from paper, we will add additional “wings” to the drawing, as indicated in the figure. Their width should be about 1.5 cm. It is also necessary to make them beveled corners (45 degrees) so that when gluing they do not look out.

So, the development of a parallelepiped made of paper is ready. It is important that all the details of the drawing are even and strictly measured, otherwise the figure will not stick together smoothly and will be crooked.

7. Cut out the blank and bend it along all the lines so that our side edges touch, and the upper and lower rectangles become the “bottom” and “lid” of the figure.

8. Lubricate the additional “wings” with glue and assemble the parallelepiped, tucking them inside. Let's wait until the glue dries.

If you have mastered making this figurine, you can begin assembling an inclined parallelepiped from paper, the edges of which are acute rhombuses.

There may be many reasons when you need to make a parallelepiped yourself: school homework to make a model of the simplest geometric body, a desire to make something, or even a unique home interior design.

What does a three-dimensional polygon have to do with it?

Frankly speaking, all this is possible in such a simple form as a parallelepiped. It is easiest and fastest to make from paper. Let's consider the most interesting options: gluing a figure from a pattern according to a given drawing, origami and modular assembly.

Lesson #1: 3D model

In order to make a rectangular parallelepiped from paper, you will need cardboard, a ruler, a pencil and scissors.

First of all, you must know exactly what size model you want to get. On a separate piece of paper, write down the main dimensions of the parallelepiped: the height of the side surfaces, length and width.

It is important not just to redraw the sample, but according to the necessary parameters. Then the result will not be disappointment and the need to do double work.

When your diagram is ready, trace the resulting drawing under the ruler with the tip of a pair of scissors. This must be done so that the cardboard folds neatly at the folds and does not “dictate” its lines.

In front of you is an unfolded parallelepiped. Cut out a blank from paper with your own hands. Fold it with reverse side along the marked lines.

All that remains is to glue the side allowances from the inside to the adjacent sides of the model and your parallelepiped is ready.

Lesson #2: Origami

As a child, you probably played with cubes. Of course, at that time you had no idea that you were dealing with parallelepipeds. During the game, parallelism of all sides does not matter, but functionality is important. And you can’t reprimand the child. The main thing is that the delight of childhood can be repeated, but at a new level. How? Make a parallelepiped out of paper using the origami technique. Yes, not just one model, but as many as the number of light bulbs on your halogen garland. See what you end up with.

Step 1

Take a square piece of paper. Bend it in half. Unfold and fold again on the other side.

Step 2

Repeat the same steps, only in the direction away from the corners.

Step 3

Keep two opposite sides of the sheet centered with your fingers. Also point the other two opposite surfaces towards each other and smooth the resulting triangle, thereby fixing the new fold lines.

Step 4

First, on one side, and then on the other, lift the corners of the triangle to the top.

Step 5

The result is a so-called rhombus. Bring its right and left corners together in the center. Smooth out the future paper parallelepiped again.

Don't forget to turn it over and fold the corners on the other side.

Step 6

Do the opposite. Open the corners you just folded and fold the others. They are formed from the free ends of a paper sheet and are directed with their vertices towards the fold lines in directions opposite to each other.

All this is difficult to understand only until you see what it is actually about.

Step 7

Insert the newly obtained corners into the formed pockets, as shown in the example.

Step 8

So, the paper parallelepiped is ready! It's just still folded. You can add volume to it in two ways. First: inflate. Second: take a long rod from an ordinary ballpoint pen and use it. Both methods are carried out through a single hole that you will find at the bottom of the model (the one closest to you). When you do these manipulations, you will get this wonderful shape:

In the same hole through which the cube was inflated, the

Lesson #3: Modular Assembly

Another interesting way to make a very nice parallelepiped from paper.