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 lines.

The term "figure" means several sets of points. They must be located on one or more planes and simultaneously limited to a specific number of completed lines.

The main geometric figures are the point and the line. They are flat. In addition to them, among simple figures, a ray, a broken line and a segment are distinguished.

Dot

This is one of the main figures of geometry. It is very small, but it is always used to build various forms 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 the point of view of mathematics, a point is an abstract spatial object that does not have such characteristics as area, 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. The straight line does not have a specific mathematical definition, since it consists of a huge number of points located on one infinite line, which has no limit and boundaries.

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

Also, the line can turn into a directional beam. This happens when the line starts from a point, but does not have a clear end. If you put a point in the middle of the line, then it will be divided into two rays (additional), moreover, 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 commonly called a broken line.

Corner

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

Angle is a construction consisting of a vertex and two rays that come out of it. That is, the sides of this figure are connected at one point.

Plane

Consider another primary concept. A plane is a figure that has no end or beginning, as well as a straight line and a point. During the consideration of this geometric element, only a part of it, limited by the contours of a broken closed line, is taken into account.

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

Quadrangles

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

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 faces are equal. In this case, the angles can be completely different, but in pairs. Each square is considered a rhombus. But in the opposite direction, this rule does not always work. Not every rhombus is a square.

Trapeze

Geometric shapes are 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 curvilinear.

Circle

This geometric figure implies the location on the same 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 subspecies of a polygon, located on the same plane and limited by three faces and three points of contact. These elements are connected in pairs.

Polygon

The vertices of the 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 which there are many points.

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

Curious facts

Surely you will be interested to read the information provided below.

• Geometry was formed as a science in ancient times. This phenomenon is usually associated with the development of art and various crafts. And the names of geometric shapes indicate the use of the principles of determining similarity and similarity.
• Translated from the ancient Greek, the term "trapezoid" means a table for a meal.
• If you take different figures 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 has attracted the attention of many painters since the last century. The work "Black Square" has always been mystical and mysterious. The geometric figure on a white canvas delights and amazes at the same time.

There are a large number of geometric shapes. All of them differ in parameters, and sometimes even surprise with forms.

Lesson Objectives:

• Cognitive: create conditions for familiarization with the concepts flat And voluminous geometric shapes, to expand the idea of ​​​​the types of three-dimensional figures, to teach how to determine the type of figure, to compare figures.
• Communicative: create conditions for the formation of the ability to work in pairs, groups; fostering a friendly attitude towards each other; to educate students in mutual assistance, mutual assistance.
• Regulatory: to create conditions for the formation of planning a learning task, to build a sequence of necessary operations, to adjust their 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, intellectual abilities of students; formation of valuable relations to each other;
  independence in acquiring new knowledge and practical skills;
• the formation of skills to perceive, process the information received, highlight the main content.

metasubject:

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

subject:

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

UUD general scientific:

• search and selection of the necessary information;
• application of information retrieval methods, conscious and arbitrary construction of a speech statement in oral form.

UUD personal:

• evaluate their own and others' actions;
• manifestation of trust, attentiveness, goodwill;
• ability to work in pairs;
• express a positive attitude towards the process of cognition.

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

Lesson type: learning new material.

Methods: verbal, research, visual, practical.

Forms of work: frontal, group, steam room, individual.

1. Organization of the beginning of the lesson.

In the morning the sun rose.
A new day has brought us.
Strong and kind
We meet a new day.
Here are my hands, I open
them towards the sun.
Here are my legs, they are firmly
Stand on the ground and lead
me on the right path.
Here is my soul, I reveal
her towards the people.
Come, new day!
Hello new day!

2. Actualization of knowledge.

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

To reach the goal, you must first of all go.

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

(To achieve something, you need to do something)

And indeed, guys, only one who sets himself up for composure and organization of his actions can become a target. And so I hope that we will achieve our goal in the lesson.

Let's start our journey to achieve 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 your classmates? (separate the figures into groups)

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

On what basis did you separate these figures?

• Flat and three-dimensional figures
• Based on three-dimensional figures

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

What is the topic of our lesson? (The teacher adds the words on the board: voluminous, the topic of the lesson 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 they are one and the same?

What is the difference between a cube and a square?

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

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

! What is the name of a figure that can be placed entirely on one flat surface? (Flat figure.)

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

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

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

CONCLUSIONS: What is the difference between flat and volumetric figures? (The teacher writes the conclusions on the blackboard.)

• Can be placed entirely on one flat surface.

VOLUMETRIC

• occupy a certain space
• rise above a flat surface.

Volume figures: pyramid, cube, cylinder, cone, sphere, parallelepiped.

4. Discovery of new knowledge.

1. Name the figures shown in the figure.

What shape are the bases of these figures?

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

2. Figures and lines on the surface of three-dimensional figures have their own names.

Suggest your names.

The sides that form a flat figure are called faces. And the side lines are ribs. The corners of polygons are vertices. These are elements of three-dimensional figures.

Guys, what do you think, what are the names of such voluminous figures that have many faces? Polyhedra.

Working with notebooks: reading new material

Correlation of real objects and three-dimensional bodies.

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

The box is a parallelepiped.

• An apple is a ball.
• A pyramid is a pyramid.
• Bank - cylinder.
• The flower pot is a cone.
• The cap is a cone.
• Vase - cylinder.
• The ball is a ball.

5. Physical minutes.

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

(Pupils wrap their hands around and stroke an imaginary ball.)

Now imagine a cone, touch its top. The cone grows upward, now it is already above you. Jump to its top.

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

The cylinder became a small gift box. Imagine that you are the 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, write down the conclusions in a card prepared by the teacher.)
Group 1.(To study the parallelepiped)

Group 2(To study the pyramid)

Group 3.(To study the cube)

7. Crossword solution

8. The result of the lesson. Reflection of activity.

Solving a crossword in a presentation

What new did you discover today?

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

And I learned the names of three-dimensional figures

Little kids are ready to learn anywhere and anytime. Their young brain is able to capture, analyze and remember as much information as it is difficult even for an adult. What parents should teach their kids has generally accepted age limits.

Children should learn the basic geometric shapes and their names at the age of 3 to 5 years.

Since all children are multi-educational, these boundaries are only conditionally accepted in our country.

Geometry is the science of shapes, sizes and arrangement of figures in space. It may seem that this is difficult for babies. However, the subjects of this science are all around us. That is why having basic knowledge in this area is important for both children and adults.

To captivate children in the study of geometry, you can resort to funny pictures. In addition, it would be nice to have aids that the child can touch, feel, circle, color, recognize with his eyes closed. The main principle of any activity with children is to keep their attention and develop a craving for the subject using game techniques and a relaxed, fun environment.

The combination of several means of perception will do the job very quickly. Use our mini-manual to teach your child to distinguish geometric shapes, to know their names.

The circle is the very first of all figures. In nature around us, much is round: our planet, the sun, the moon, the core of a flower, many fruits and vegetables, the pupils of the eyes. A volumetric circle is a ball (ball, ball)

It is better to start studying the shape of a circle with a child by looking at drawings, and then reinforce the theory with practice by letting the child hold something round in his hands.

A square is a figure in which all sides have the same height and width. Square objects - cubes, boxes, house, window, pillow, stool, etc.

It is very simple to build all sorts of houses from square cubes. Drawing a square is easier to do on a piece of paper in a cage.

A rectangle is a relative of a square, which differs in that it has the same opposite sides. Just like a square, a rectangle is all equal to 90 degrees.

You can find many items that have the shape of a rectangle: cabinets, appliances, doors, furniture.

In nature, mountains and some trees have the shape of a triangle. From the immediate environment of the kids, one can cite as an example the triangular roof of the house, various road signs.

Some ancient structures, such as temples and pyramids, were built in the shape of a triangle.

An oval is a circle that is elongated on both sides. For example, an oval shape is possessed by: an egg, nuts, many vegetables and fruits, a human face, galaxies, etc.

An oval in volume is called an ellipse. Even the Earth is flattened from the poles - ellipsoidal.

Rhombus

A rhombus is the same square, only elongated, that is, it has two obtuse angles and a pair of sharp ones.

You can study a rhombus with the help of visual aids - a drawn picture or a three-dimensional object.

Memorization techniques

Geometric shapes are easy to remember by name. Learning them for children can be turned into a game by applying the following ideas:

• Buy a children's picture book that contains fun and colorful drawings of figures and their analogies from the outside world.

• Cut out more different figures from multi-colored cardboard, laminate them with adhesive tape and use them as a constructor - you can lay out a lot of interesting combinations by combining different figures.

• Buy a ruler with holes in the shape of a circle, square, triangle and others - for children who are already friends with pencils, drawing with such a ruler is an interesting activity.

You can come up with many opportunities to teach kids to know the names of geometric shapes. All methods are good: drawings, toys, observation of surrounding objects. Start small, gradually complicating the information and tasks. You will not feel how time flies, and the baby will surely please you with success in the near future.

The sphere of study of the science of geometry includes flat (two-dimensional) figures and three-dimensional figures (three-dimensional).

From flat:

They are studying planimetry. A point is also a flat figure.

Of the bulk known:

They are studying stereometry.

Two-dimensional figures - triangle, square, rectangle, rhombus, trapezoid, parallelogram, circle, oval, ellipse, polygons (pentagon, hexagon, heptagon, octagon and others).

The dot also applies to figures.

Three-dimensional figures - a cube, a sphere, a hemisphere, a cone, a cylinder, a pyramid, a parallelepiped, a prism, an ellipsoid, a dome, tetrahedra and many others coming from the above. Then there are very complex geometric shapes - various polyhedra, which in fact can contain an infinite number of faces. For example, a large wedge crown - consists of 2 squares and 16 regular triangles or a wedge crown made up of 14 faces: 2 squares and 12 regular triangles.

Speaking of geometric shapes, we can distinguish two regular groups such as:

1) Two-dimensional figures;

2) And three-dimensional figures.

So, in more detail about two-dimensional, they include such figures as:

But as for three-dimensional figures, here's what they can be:



The outlines of figures and all possible actions with them are studied by the mathematical sciences of geometry (studies flat figures) and stereometry (the subject of study is three-dimensional figures). At school, I loved both science and science.

This is how flat (2D) shapes are classified:



With three sides, it's a triangle. With four sides - a square, rhombus, rectangle, trapezoid. And there can also be a parallelogram and a circle (oval, circle, semicircle, ellipse).

Volumetric figures (3D) are classified as follows:



This is a cube, parallelepiped, tetrahedron, cylinder, pyramid, icosahedron, ball, dodecahedron, cone, octahedron, prism, sphere. In addition, there are truncated figures (pyramid, cone). Depending on the base, the pyramid, prism are divided into triangular, tetrahedral and so on.

Children's toys (pyramids, mosaics and others) make it possible to introduce children to geometric three-dimensional figures from early childhood. And flat figures can be drawn and cut out of paper.

Of the two-dimensional, we can name the following:

• circle;
• oval;
• square;
• rectangle;
• parallelogram;
• trapezoid;
• pentagon (hexagon, etc.);
• rhombus;
• triangle.

With three-dimensional a little more difficult:

• cylinder;
• cone;
• prism;
• sphere or ball;
• parallelepiped;
• pyramid;
• tetrahedron;
• icosahedron;
• octahedron;
• dodecahedron.

I think many, after reading the last names, asked themselves: What-what?. For clarity - illustration:



In fact, there are enough figures in mathematics. Plane figures are rectangles, squares, triangles, pentagons, hexagons, and circles. Volumetric figures or 3D figures are like a pyramid, a cube and a dodecahedron, and so on.

• Personally, I know:

  1 From 2D shapes:

  circle, triangle, square, rhombus, rectangle, trapezoid, parallelogram, oval and polygon. Another star (pentagram), if you can call it a figure.

  2 From 3D shapes:

  Prism, pyramid, parallelepiped, prism, ball (sphere), cylinder, hemisphere (half of a sphere, that is, a ball cut in half) and a cone. Pyramids are divided into triangular, quadrangular and so on (almost to infinity). The more corners a pyramid has at its base, the more it resembles a cone.

2D shapes (2D): angle; polygon (varieties of polygons: triangle, quadrilateral varieties of a quadrilateral: parallelogram, rectangle, rhombus, square, trapezoid, deltoid, pentagon, hexagon, etc. to infinity); circle, circle, circular segment, circular sector, ellipse, oval…

Three-dimensional figures (3D): dihedral angle, polyhedral angle; polyhedron (varieties of polyhedra: prism, prism varieties: parallelepiped, cube, antiprism, pyramid, tetrahedron, truncated pyramid, bipyramid, octahedron, dodecahedron, icosahedron, wedge, obelisk); cylinder, truncated cylinder, segment of a cylinder (aka a cylindrical horseshoe or hoof), cone, truncated cone, sphere, ball, spherical segment, spherical layer, spherical sector, ellipsoid, geoid ...

From the very beginning, in geometry lessons, we study simple figures that are flat, that is, they are located on the same plane.

So, a list of the main figures can be studied below.





Recently, I just had to tell my granddaughters and grandson what geometric shapes can be.

Starting with flat figures cut out of cardboard or made of plastic, children learned to distinguish between a triangle and a square, an oval and a circle, a rectangle, a rhombus and a polygon.

They helped in memorizing the names of the figures and these are special toys with holes of a certain shape.



Later they switched to volumetric figures, cubes and cones, parallelepipeds, balls and rings, pyramids and cylinders.



They have not grown up to school yet, and when they go, they will be taught to distinguish between isosceles and equilateral triangles, they will learn about a ray and a point, about a circle and everything else.

Here you and your child can learn geometric shapes and their names with the help of fun picture tasks. But training will be most effective if you add various samples of geometric shapes to the printed task. For this purpose, objects such as balls, pyramids, cubes, inflated balloons (round and oval), tea mugs (standard, in the form of a cylinder), oranges, books, balls of thread, square cookies and much more - everything what your fantasy tells you.

All of these items will help the child understand what a three-dimensional geometric figure means. Flat figures can be prepared by cutting out the desired geometric shapes from paper, pre-painting them in different colors.

The more different materials you prepare for the lesson, the more interesting it will be for the child to learn new concepts for him.

You may also like our online math simulator for grade 1 "Geometric shapes":

The online math simulator "Geometric Shapes Grade 1" will help first graders practice their ability to distinguish between basic geometric shapes: a square, a circle, an oval, a rectangle and a triangle.

Geometric shapes and their names - We conduct a lesson with a child:

So that the child can easily and naturally remember geometric shapes and their names, first download the picture with the task in the attachments at the bottom of the page, print it on a color printer and put it on the table along with colored pencils. Also, by this time, you should already have prepared various items that we listed earlier.

• Stage 1. First, let the child complete the tasks on the printed sheet - say the names of the figures aloud and color in all the pictures.
• Stage 2. It is necessary to clearly show the child the differences between volumetric figures and flat ones. To do this, lay out all sample objects (both three-dimensional and cut out of paper) and move away from the table with the child at such a distance from which all three-dimensional figures are clearly visible, but all flat samples are lost from sight. Draw your child's attention to this fact. Let him experiment by moving closer and further away from the table, telling you about his observations.
• Stage 3. Further, the lesson needs to be turned into a kind of game. Ask the child to carefully look around him and find objects that have the shape of any geometric shapes. For example, a TV is a rectangle, a clock is a circle, etc. On each found figure - loudly clap your hands to add enthusiasm to the game.
• Stage 4. Conduct research and observational work with those sample materials that you have prepared for the lesson. For example, put a book and a flat rectangle of paper on the table. Invite the child to feel them, look at them from different angles and tell you their observations. In the same way, you can explore an orange and a paper circle, a children's pyramid and a paper triangle, a cube and a paper square, an oval-shaped balloon and an oval cut out of paper. You can add to the list of items yourself.
• Stage 5 Put various three-dimensional samples in an opaque bag and ask the child to touch a square object, then a round one, then a rectangular one, and so on.
• Stage 6 Lay out in front of the child on the table several different items from those that are involved in the lesson. Then have the child turn away for a few seconds while you hide one of the objects. Turning to the table, the child should name the hidden object and its geometric shape.

You can download geometric shapes and their names - Task Form - in the attachments at the bottom of the page.

Names of geometric shapes - Printable cards

Studying geometric shapes with your baby, you can use printable cards from Bibushi the Fox during classes . Download the attachments, print the form with cards on a color printer, cut out each card along the contour - and start learning. Cards can be laminated or stuck on thicker paper to keep the look of the pictures, because they will be used repeatedly.

The first six cards will give you the opportunity to study with your child such shapes: oval, circle, square, rhombus, rectangle and triangle, under each figure in the cards you can read its name.

After the child has memorized the name of a certain figure, ask him to do the following: circle all the samples of the figure being studied on the card, and then color them in the color of the main figure located in the upper left corner.

Download the names of geometric shapes - Printable cards - you can in the attachments at the bottom of the page

With the help of the following six cards, the child will be able to get acquainted with such geometric shapes: a parallelogram, a trapezoid, a pentagon, a hexagon, a star and a heart. As in the previous material, under each figure you can find its name.

To diversify activities with the baby, combine learning with drawing - this method will not allow the child to overwork, and the baby will continue to study with pleasure. Make sure that when tracing the figures along the lines, the child is not in a hurry and performs the task carefully, because such exercises not only develop fine motor skills, they can further affect the baby's handwriting.

You can download printable cards depicting flat geometric shapes in attachments

In the process, how you will study volumetric geometric shapes and their names with your child, using the new six cards from Bibushi with images of a cube, a cylinder, a cone, a pyramid, a ball and a hemisphere, purchase the studied figures in the store, or use objects in the house that have a similar shape.

Show the baby with examples how three-dimensional figures look in life, the child should touch and play with them. First of all, this is necessary in order to use the visually - effective thinking of the baby, with the help of which it is easier for the child to learn about the world around him.

Download - Volumetric geometric shapes and their names - you can in the attachments at the bottom of the page

Other materials on the study of geometric shapes will also be useful to you:

Fun and colorful tasks for children "Drawings from geometric shapes" are a very convenient educational material for children of preschool and primary school age to study and memorize basic geometric shapes:

The tasks will introduce the child to the basic shapes of geometry - a circle, an oval, a square, a rectangle and a triangle. Only here is not a boring memorization of the names of the figures, but a kind of coloring game.

As a rule, they begin to study geometry by drawing flat geometric figures. The perception of the correct geometric shape is impossible without drawing it out with your own hands on a piece of paper.

This lesson will greatly amuse your young mathematicians. After all, now they will have to find familiar shapes of geometric shapes among many pictures.

Stacking shapes on top of each other is a geometry activity for preschoolers and younger students. The meaning of the exercise is to solve addition examples. These are just unusual examples. Instead of numbers, here you need to add geometric shapes.

This task is designed as a game in which the child has to change the properties of geometric shapes: shape, color or size.

Here you can download tasks in pictures, which present the calculation of geometric shapes for math classes.

In this task, the child will get acquainted with such a concept as drawings of geometric bodies. In fact, this lesson is a mini-lesson on descriptive geometry.

Here we have prepared for you volumetric geometric shapes made of paper that need to be cut and glued. Cube, pyramids, rhombus, cone, cylinder, hexagon, print them on cardboard (or colored paper, and then stick on cardboard), and then give the child to remember.

Here we have posted counting up to 5 for you - pictures with math tasks for kids, thanks to which your children will train not only their counting skills, but also the ability to read, write, distinguish geometric shapes, draw and color.

And you can also play math games online from Bibushi the fox:

In this educational online game, the child will have to determine what is superfluous among 4 pictures. In this case, it is necessary to be guided by the signs of geometric shapes.