Flat and volumetric geometric shapes. Geometric figures

Figure is an arbitrary set of points on the plane. A point, a straight line, a segment, a ray, a triangle, a circle, a square, and so on are all examples of geometric shapes.

Dot– the basic concept of geometry, it is an abstract object that has no measuring characteristics: no height, no length, no radius.

Line- this is a set of points sequentially located one after another. Only the length of a line is measured. It has no width or thickness.

Straight line- this is a line that does not bend, has neither beginning nor end, it can be continued endlessly in both directions.

Ray- this is part of a straight line that has a beginning but no end; it can be continued endlessly in only one direction.

Line segment is a part of a straight line bounded by two points. A line segment has a beginning and an end, so its length can be measured.

Crooked line is a smoothly curving line, which is determined by the location of its constituent points.

broken line is a figure that consists of segments connected in series at their ends.

Vertices of a broken line- This

the point from which the broken line begins,
points at which the segments that form a broken line are connected,
the point at which the broken line ends.

Links of a broken line– these are the segments that make up the broken line. The number of links of a polyline is always 1 less than the number of vertices of a polyline.

Open line is a line whose ends are not connected together.

Closed line is a line whose ends are connected together.

Polygon is a closed broken line. The vertices of the polygon are called the vertices of the polygon, and the segments are called the sides of the polygon.

Geometry is a branch of mathematics that studies shapes and their properties.

The geometry that is studied at school is called Euclidean, named after the ancient Greek scientist Euclid (3rd century BC).

The study of geometry begins with planimetry. Planimetry is a branch of geometry in which figures are studied, all parts of which are in the same plane.

Geometric figures

There are many material objects in the world around us. different forms and sizes: residential buildings, car parts, books, jewelry, toys, etc.

In geometry, instead of the word object, they say geometric figure. Geometric figure(or briefly: figure) is a mental image of a real object in which only the shape and dimensions are retained, and only they are taken into account.

Geometric figures are divided into flat And spatial. In planimetry, only plane figures are considered. A flat geometric figure is one in which all points lie on the same plane. Any drawing made on a sheet of paper gives an idea of such a figure.

Geometric shapes are very diverse, for example, triangle, square, circle, etc.:

Part of any geometric figure (except a point) is also a geometric figure. The combination of several geometric shapes will also be a geometric shape. In the figure below, the left figure consists of a square and four triangles, and the right figure consists of a circle and parts of a circle.

In today's article I would like to talk about how easy and fun it is to study geometric figures with a baby, and why bother loading a child with geometry at such an early age? What games will be interesting to a child from 1 year old, and what materials you will need for classes - read about all this in the article. In addition, here you will find several useful materials for downloading.

Why study geometric shapes with your baby?

Geometric shapes are found everywhere; they can be seen in most objects around us: a round ball, a rectangular table, etc. By analyzing the similarity of surrounding objects with geometric shapes, the child wonderfully trains associative and spatial thinking.

Studying geometric shapes is useful for general development baby, expanding his knowledge about the world around him. If you introduce your child to shapes at an early age, he will have a much easier time at school.

Many interesting educational games are based on the ability to distinguish geometric shapes. This includes construction, games with mosaics, math tablets, etc. Therefore, studying forms at such an early age will contribute to the further successful development of the child.

So, games for learning and consolidating knowledge about geometric shapes :

1. We name geometric shapes always and everywhere

If you come across any figure while playing or reading books, be sure to draw your baby’s attention to it and name it (“Look, the ball looks like a circle, and the cube looks like a square”). Even if it seems to you that the child is unlikely to remember the names of the figures, say them anyway, and they will definitely be imprinted in his head. You can do this for up to a year. At first, point out only the basic shapes (square, circle, triangle), then, when you understand that the baby has mastered them, begin to study other shapes.

2. Let's play geometric lotto

For the first lessons with your baby, it is better to use lotto, which has only 3-4 figures. When your child masters this game well, gradually complicate the task. It is also useful for the first time to make all the figures on the playing field the same color and size. In this case, the child will be guided by only one sign - shape, while other characteristics will neither distract nor prompt him.

You can place both cards with images of figures and three-dimensional figures on the playing field. Good for this purpose Dienesha blocks (Ozon, KoroBoom), figures from the sorter, frame insert.

Well, the easiest option is to purchase ready-made lotto with geometric shapes.

3. Playing with the sorter

At about the age of 1 year, the child begins to notice that the figurine he has chosen sorter (Ozone, Labyrinth, My-shop) cannot be pushed into every hole. Therefore, during the game it is necessary to focus on this: “So, here we have a circle - it doesn’t fit here, it doesn’t fit here, but where does it fit?” At first, turning the figure at the right angle may be a little difficult for the baby, but it’s not scary, it’s a matter of practice. The main thing is, do not forget to pronounce the names of the figures all the time during the exciting process of “pushing”, and the child will quietly remember them all.

Important! When choosing a sorter, pay attention to the fact that all the basic geometric shapes are represented there, and not just hearts and crescents.

4. Playing with the insert frame

You'll need one like this insert frame, which shows all the main figures. At its core, the game is similar to a sorter.

Here's another one interesting game for shape recognition – “” ( Labyrinth, My-shop). Despite the fact that the age indicated on it is 3-5 years, it will be of interest to a child of 2 years old and even a little earlier.

9. Learn forms using Doman cards

In fact, I believe that this method of studying forms is the most effective. If you study according to , the child will very quickly remember all the figures, and you will spend a minimum of effort on it. However, it should be noted that in order for the knowledge gained from Doman’s cards to be deposited in the baby’s head, they need to be reinforced through other games (see above). Otherwise, the child will quickly forget everything you showed him. Therefore, I recommend starting to look at Doman cards with geometric shapes at about the age of 1 year, since at this time the baby becomes interested in sorters, insert frames, drawing, appliqué, etc. And, having studied the forms from the pictures, he will be able to use the acquired knowledge in these games. By the way, you can buy "Geometric Shapes" cards HERE.

You can read about our experience of studying figures using Doman cards.

10. Watch educational cartoons

And, of course, it won’t hurt to watch cartoons on the topic “Geometric Shapes”; now you can find a lot of them on the Internet. Here are some of them:

Instead of a conclusion

Very often, the process of teaching a child geometric figures (and not only figures) is perceived by parents solely as a constant examination of the child, i.e. They show the child, for example, a square a couple of times, and later the learning comes down to the question “Tell me, what shape is this?” This approach is extremely wrong. Firstly, because, like any person, a child does not like it too much when his knowledge is tested, and this only discourages him from studying. Secondly, before asking your child anything, you need to explain and show it to him many times!

Therefore, try to keep verification questions to a minimum. Just repeat and repeat the information you are learning, be it the names of the shapes or something else. Do this while playing and talking with your baby. And you will soon see for yourself that the child has learned everything without unnecessary checks.

Lesson Objectives:

Cognitive: create conditions for familiarization with concepts flat And volumetric geometric shapes, expand your understanding of the types of volumetric figures, teach how to determine the type of figure, and compare figures.
Communicative: create conditions for developing the ability to work in pairs and groups; fostering a friendly attitude towards each other; to cultivate mutual assistance and mutual assistance among students.
Regulatory: create conditions for the formation to plan an educational task, build a sequence of necessary operations, adjust your activities.
Personal: create conditions for the development of computational skills, logical thinking, interest in mathematics, the formation of cognitive interests, intellectual abilities of students, independence in acquiring new knowledge and practical skills.

Planned results:

personal:

formation of cognitive interests and intellectual abilities of students; formation of value relations towards each other;
independence in acquiring new knowledge and practical skills;
formation of skills to perceive, process received information, and highlight the main content.

meta-subject:

mastering the skills of independent acquisition of new knowledge;
organization educational activities, planning;
development of theoretical thinking based on the formation of skills to establish facts.

subject:

master the concepts of flat and three-dimensional figures, learn to compare figures, find flat and three-dimensional figures in surrounding reality, learn to work with a sweep.

UUD general scientific:

search and selection of necessary information;
application of information retrieval methods, conscious and arbitrary construction speech utterance in oral form.

UUD personal:

evaluate your own and others’ actions;
demonstration of trust, attentiveness, goodwill;
ability to work in pairs;
express a positive attitude towards the learning process.

Equipment: textbook, interactive whiteboard, emoticons, models of figures, development of figures, individual traffic lights, rectangles - means of feedback, Explanatory dictionary.

Lesson type: learning new material.

Methods: verbal, research, visual, practical.

Forms of work: frontal, group, pair, individual.

1. Organization of the beginning of the lesson.

In the morning the sun rose.
A new day has been brought to us.
Strong and kind
We are celebrating a new day.
Here are my hands, I open them
Them towards the sun.
Here are my legs, they are firm
They stand on the ground and lead
Me on the right path.
Here is my soul, I reveal
Her towards people.
Come, new day!
Hello new day!

2. Updating knowledge.

Let's create a good mood. Smile at me and at each other, sit down!

To reach your goal, you must first go.

There is a statement in front of you, read it. What does this statement mean?

(To achieve something, you need to do something)

And indeed, guys, only those who prepare themselves to be collected and organized in their actions can hit the target. And so I hope that you and I will achieve our goal in this lesson.

Let's begin our journey to achieving the goal of today's lesson.

3. Preparatory work.

Look at the screen. What do you see? (Geometric figures)

Name these figures.

What task can you offer to your classmates? (divide the shapes into groups)

You have cards with these figures on your desks. Complete this task in pairs.

On what basis did you divide these figures?

Flat and volumetric figures
Based on volumetric figures

What figures have we already worked with? What did you learn to find from them? What figures do we encounter for the first time in geometry?

What is the topic of our lesson? (The teacher adds words on the board: volumetric, the lesson topic appears on the board: Volumetric geometric shapes.)

What should we learn in class?

4. “Discovery” of new knowledge in practical research work.

(The teacher shows a cube and a square.)

How are they similar?

Can we say that these are the same thing?

What is the difference between a cube and a square?

Let's do an experiment. (Students receive individual figures - cube and square.)

Let's try to attach the square to the flat surface of the port. What do we see? Did he lay down (entirely) on the surface of the desk? Close?

! What do we call a figure that can be placed entirely on one flat surface? (Flat figure.)

Is it possible to press the cube completely (entirely) to the desk? Let's check.

Can a cube be called a flat figure? Why? Is there space between your hand and the desk?

! So what can we say about the cube? (Occupies a certain space, is a three-dimensional figure.)

CONCLUSIONS: What is the difference between flat and three-dimensional figures? (The teacher posts conclusions on the board.)

Can be placed entirely on one flat surface.

VOLUMETRIC

occupy a certain space,
rise above a flat surface.

Volumetric figures: pyramid, cube, cylinder, cone, ball, parallelepiped.

4. Discovery of new knowledge.

1. Name the figures shown in the picture.

What shape do the bases of these figures have?

What other shapes can be seen on the surface of a cube and a prism?

2. Figures and lines on the surface of volumetric figures have their own names.

Suggest your names.

The sides that form a flat figure are called faces. And the lateral lines are the ribs. The corners of polygons are vertices. These are elements of volumetric figures.

Guys, what do you think, what are the names of such three-dimensional figures that have many sides? Polyhedra.

Working with notebooks: reading new material

Correlation between real objects and volumetric bodies.

Now select for each object the three-dimensional figure that it resembles.

The box is a parallelepiped.

An apple is a ball.
Pyramid - pyramid.
The jar is a cylinder.
Flower pot - cone.
The cap is a cone.
The vase is a cylinder.
The ball is a ball.

5. Physical exercise.

1. Imagine a big ball, stroke it from all sides. It's big and smooth.

(Students “wrap” their hands around and stroke an imaginary ball.)

Now imagine a cone, touch its top. The cone grows upward, now it is already taller than you. Jump to the top of it.

Imagine that you are inside a cylinder, pat its upper base, stomp on the lower one, and now with your hands along the side surface.

The cylinder became a small gift box. Imagine that you are a surprise that is in this box. I press the button and... a surprise pops out of the box!

6. Group work:

(Each group receives one of the figures: a cube, a pyramid, a parallelepiped. The children study the resulting figure, and write down the conclusions on a card prepared by the teacher.)
Group 1.(To study the parallelepiped)

Group 2.(For studying the pyramid)

Group 3.(For studying the cube)

7. Crossword solution

8. Lesson summary. Reflection of activity.

Crossword solution in presentation

What new things have you discovered for yourself today?

All geometric shapes can be divided into three-dimensional and flat.

And I learned the names of three-dimensional figures

Geometric figures are a complex of points, lines, solids or surfaces. These elements can be located both on the plane and in space, forming a finite number of straight lines.

The term “figure” implies several sets of points. They must be located on one or more planes and at the same time limited to a specific number of completed lines.

The main geometric figures are the point and the straight line. They are located on a plane. In addition to them, among simple figures there is a ray, a broken line and a segment.

Dot

This is one of the main figures of geometry. It is very small, but it is always used to build various shapes on a plane. The point is the main figure for absolutely all constructions, even the highest complexity. In geometry, it is usually denoted by a letter of the Latin alphabet, for example, A, B, K, L.

From a mathematical point of view, a point is an abstract spatial object that does not have such characteristics as area or volume, but at the same time remains a fundamental concept in geometry. This zero-dimensional object simply has no definition.

Straight

This figure is completely placed in one plane. A straight line does not have a specific mathematical definition, since it consists of a huge number of points located on one endless line, which has no limit or boundaries.

There is also a segment. This is also a straight line, but it starts and ends from a point, which means it has geometric restrictions.

The line can also turn into a directional beam. This happens when a straight line starts from a point, but does not have a clear ending. If you put a point in the middle of the line, then it will split into two rays (additional), and oppositely directed to each other.

Several segments that are sequentially connected to each other by ends at a common point and are not located on the same straight line are usually called a broken line.

Corner

Geometric figures, the names of which we discussed above, are considered key elements used in the construction of more complex models.

An angle is a structure consisting of a vertex and two rays that extend from it. That is, the sides of this figure connect at one point.

Plane

Let's consider another primary concept. A plane is a figure that has neither end nor beginning, as well as a straight line and a point. When considering this geometric element, only its part, limited by the contours of a broken closed line, is taken into account.

Any smooth bounded surface can be considered a plane. This could be an ironing board, a piece of paper, or even a door.

Quadrilaterals

A parallelogram is a geometric figure whose opposite sides are parallel to each other in pairs. Among the particular types of this design are diamond, rectangle and square.

A rectangle is a parallelogram in which all sides touch at right angles.

A square is a quadrilateral with equal sides and angles.

A rhombus is a figure in which all sides are equal. In this case, the angles can be completely different, but in pairs. Each square is considered a diamond. But in opposite direction this rule does not always apply. Not every rhombus is a square.

Trapezoid

Geometric shapes can be completely different and bizarre. Each of them has a unique shape and properties.

A trapezoid is a figure that is somewhat similar to a quadrilateral. It has two parallel opposite sides and is considered curved.

Circle

This geometric figure implies the location on one plane of points equidistant from its center. In this case, a given non-zero segment is usually called a radius.

Triangle

This is a simple geometric figure that is very often encountered and studied.

A triangle is considered a subtype of a polygon, located on one plane and limited by three edges and three points of contact. These elements are connected in pairs.

Polygon

The vertices of polygons are the points connecting the segments. And the latter, in turn, are considered to be parties.

Volumetric geometric shapes

prism;
sphere;
cone;
cylinder;
pyramid;

These bodies have something in common. All of them are limited to a closed surface, inside of which there are many points.

Volumetric bodies are studied not only in geometry, but also in crystallography.

Curious facts

Surely you will be interested in reading the information provided below.

Geometry was formed as a science back in ancient times. This phenomenon is usually associated with the development of art and various crafts. And the names of geometric figures indicate the use of the principles of determining similarity and similarity.
Translated from ancient Greek, the term “trapezoid” means a table for a meal.
If you take different shapes whose perimeter is the same, then the circle is guaranteed to have the largest area.
Translated from Greek, the term “cone” means a pine cone.
There is a famous painting by Kazemir Malevich, which, since the last century, has attracted the views of many painters. The work “Black Square” has always been mystical and mysterious. The geometric figure on the white canvas delights and amazes at the same time.

Exists a large number of geometric shapes. They all differ in parameters, and sometimes even surprise in shape.