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
In the world around us, there are many material objects of different shapes and sizes: residential buildings, machine 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.
Here you and your child can learn geometric shapes and their names with fun picture activities. But learning will be most effective if you also add various samples of geometric shapes to the printed assignment. Suitable items for this purpose include balls, pyramids, cubes, inflated balloons (round and oval), tea mugs (standard, cylinder-shaped), oranges, books, balls of thread, square cookies and much more - everything whatever your imagination tells you.
All of the items listed 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, after painting them in different colors.
The more different materials you prepare for the lesson, the more interesting it will be for your child to learn new concepts.
You may also like our online math simulator for grade 1 “Geometric Shapes”:
The online mathematics trainer "Geometric Shapes 1st Grade" will help first-graders practice their ability to distinguish basic geometric shapes: square, circle, oval, rectangle and triangle.
Geometric shapes and their names - We conduct a lesson with the child:
So that your 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 place it on the table along with colored pencils. Also, by this time, you should already have prepared the various items that we listed earlier.
- Stage 1. First, let the child complete the tasks on the printed sheet - say the names of the shapes out loud and color all the pictures.
- Stage 2. It is necessary to clearly show the child the differences between three-dimensional figures and flat ones. To do this, lay out all the sample objects (both three-dimensional and cut out of paper) and move away with the child from the table to 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, coming closer to the table, then further, telling you about his observations.
- Stage 3. Then the activity needs to be turned into a kind of game. Ask your child to look carefully around him and find objects that have the shape of some geometric shapes. For example, a TV is a rectangle, a clock is a circle, etc. On each piece you find, clap your hands loudly to add enthusiasm to the game.
- Stage 4. Carry out research and observational work with the sample materials that you have prepared for the lesson. For example, place a book and a flat rectangle of paper on the table. Invite your child to touch 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. Place 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. Place several different objects that are involved in the activity on the table in front of your child. Then have the child turn away for a few seconds while you hide one of the objects. Turning to the table, the child must 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
When studying geometric shapes with your child, you can use printable cards from Little Fox Bibushi during classes. 
. Download the attachments, print out a form with cards on a color printer, cut out each card along the outline - and start learning. Cards can be laminated or glued to thicker paper to preserve the appearance of the pictures, because they will be used repeatedly.
The first six cards will give you the opportunity to study the following shapes with your child: oval, circle, square, rhombus, rectangle and triangle; under each shape 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.
You can download the names of geometric shapes - Printable cards - in the attachments at the bottom of the page
With the help of the following six cards, your child will be able to become familiar with the following geometric shapes: parallelogram, trapezoid, pentagon, hexagon, star and heart. As in the previous material, under each figure you can find its name.
To diversify activities with your child, combine learning with drawing - this method will prevent the child from getting overtired, and the child will be happy to continue studying. Make sure that when tracing the figures, the child does not rush and completes the task carefully, because such exercises not only develop fine motor skills, they can also affect the child’s handwriting in the future.
You can download printable cards with images of flat geometric shapes in the attachments
In the process of how you will study three-dimensional geometric shapes and their names with your child, using the new six cards from Bibushi with images of a cube, cylinder, cone, pyramid, ball and hemisphere, purchase the figures you are studying in the store, or use objects in the house that have a similar shape.
Show your child with examples what three-dimensional figures look like in real life; the child should touch and play with them. First of all, this is necessary in order to use the child’s visual and effective thinking, with the help of which it is easier for the child to understand the world around him.
Download - Volumetric geometric shapes and their names - you can find them in the attachments at the bottom of the page
You will also find other materials on studying geometric shapes useful:
Fun and colorful tasks for children “Drawings from geometric shapes” are a very convenient educational material for preschool and primary school children to learn and memorize basic geometric shapes:
The tasks will familiarize the child with the basic shapes of geometry - circle, oval, square, rectangle and triangle. Only here there is no boring memorization of the names of figures, but a kind of coloring game.
As a rule, geometry begins to be studied by drawing flat geometric figures. The perception of the correct geometric shape is impossible without drawing it with your own hands on a sheet of paper.
This activity will greatly amuse your young mathematicians. After all, now they will have to find familiar shapes of geometric figures among many pictures.
Layering shapes on top of each other is a geometry activity for preschoolers and elementary school students. The point of the exercise is to solve addition examples. These are just unusual examples. Instead of numbers, you need to add geometric shapes.
This task is designed in the form of a game in which the child will have to change the properties of geometric shapes: shape, color or size.
Here you can download tasks in pictures that show how to count geometric shapes for math classes.
In this task, the child will become familiar with the concept of drawings of geometric bodies. Essentially, this lesson is a mini-lesson on descriptive geometry.
Here we have prepared for you three-dimensional geometric paper shapes that need to be cut and glued. Cube, pyramids, rhombus, cone, cylinder, hexagon, print them on cardboard (or colored paper and then paste them on cardboard), and then give them to the child to memorize.
Here we have posted for you counting to 5 - pictures with mathematical tasks for kids, thanks to which your children will practice not only their counting skills, but also their ability to read, write, distinguish geometric shapes, draw and color.
And you can also play online math games from little fox Bibushi:
In this educational online game, the child will have to determine what is odd among 4 pictures. In this case, it is necessary to be guided by the characteristics of geometric shapes.
Lesson topic
Geometric figures
What is a geometric figure
Geometric figures are a collection of many points, lines, surfaces or bodies that are located on a surface, plane or space and form a finite number of lines.
The term “figure” is to some extent formally applied to a set of points, but as a rule, a figure is usually called a set that is located on a plane and is limited by a finite number of lines.
A point and a straight line are the basic geometric figures located on a plane.
The simplest geometric figures on a plane include a segment, a ray and a broken line.
What is geometry
Geometry is a mathematical science that deals with the study of the properties of geometric figures. If we literally translate the term “geometry” into Russian, it means “land surveying,” since in ancient times the main task of geometry as a science was the measurement of distances and areas on the surface of the earth.
The practical application of geometry is invaluable at all times and regardless of profession. Neither a worker, nor an engineer, nor an architect, nor even an artist can do without knowledge of geometry.
In geometry there is a section that deals with the study of various figures on a plane and is called planimetry.
You already know that a figure is an arbitrary set of points located on a plane.
Geometric figures include: point, straight line, segment, ray, triangle, square, circle and other figures that planimetry studies.
Dot
From the material studied above, you already know that the point refers to the main geometric figures. And although this is the smallest geometric figure, it is necessary for constructing other figures on a plane, drawing or image and is the basis for all other constructions. After all, the construction of more complex geometric figures consists of many points characteristic of a given figure.
In geometry, points are designated by capital letters of the Latin alphabet, for example, such as: A, B, C, D....
Now let's summarize, and so, from a mathematical point of view, a point is such an abstract object in space that does not have volume, area, length and other characteristics, but remains one of the fundamental concepts in mathematics. A point is a zero-dimensional object that has no definition. According to Euclid's definition, a point is something that cannot be defined.
Straight
Like a point, a straight line refers to figures on a plane, which has no definition, since it consists of an infinite number of points located on one line, which has neither beginning nor end. It can be argued that a straight line is infinite and has no limit.
If a straight line begins and ends with a point, then it is no longer a straight line and is called a segment.
But sometimes a straight line has a point on one side and not on the other. In this case, the straight line turns into a beam.
If you take a straight line and put a point in its middle, then it will split the straight line into two oppositely directed rays. These rays are additional.
If in front of you there are several segments connected to each other so that the end of the first segment becomes the beginning of the second, and the end of the second segment becomes the beginning of the third, etc., and these segments are not on the same straight line and when connected have a common point, then such the chain is a broken line.
Exercise
Which broken line is called unclosed?
How is a straight line designated?
What is the name of a broken line that has four closed links?
What is the name of a broken line with three closed links?
When the end of the last segment of a broken line coincides with the beginning of the 1st segment, then such a broken line is called closed. An example of a closed polyline is any polygon.
Plane
Like a point and a straight line, a plane is a primary concept; it has no definition and one cannot see either a beginning or an end. Therefore, when considering a plane, we consider only that part of it that is limited by a closed broken line. Thus, any smooth surface can be considered a plane. This surface can be a sheet of paper or a table.
Corner
A figure that has two rays and a vertex is called an angle. The junction of the rays is the vertex of this angle, and its sides are the rays that form this angle.
Exercise:
1. How is an angle indicated in the text?
2. What units can you use to measure an angle?
3. What are the angles?
Parallelogram
A parallelogram is a quadrilateral whose opposite sides are parallel in pairs.
Rectangle, square and rhombus are special cases of parallelogram.
A parallelogram with right angles equal to 90 degrees is a rectangle.
A square is the same parallelogram; its angles and sides are equal.
As for the definition of a rhombus, it is a geometric figure whose all sides are equal.
In addition, you should know that every square is a rhombus, but not every rhombus can be a square.
Trapezoid
When considering a geometric figure such as a trapezoid, we can say that, in particular, like a quadrilateral, it has one pair of parallel opposite sides and is curvilinear.
Circle and Circle
A circle is the geometric locus of points on a plane equidistant from a given point, called the center, at a given non-zero distance, called its radius.
Triangle
The triangle you have already studied also belongs to simple geometric figures. This is one of the types of polygons in which part of the plane is limited by three points and three segments that connect these points in pairs. Any triangle has three vertices and three sides.
Exercise: Which triangle is called degenerate?
Polygon
Polygons include geometric figures of different shapes that have a closed broken line.
In a polygon, all points that connect the segments are its vertices. And the segments that make up a polygon are its sides.
Did you know that the emergence of geometry goes back centuries and is associated with the development of various crafts, culture, art and observation of the surrounding world. And the name of geometric figures is confirmation of this, since their terms did not arise just like that, but due to their similarity and similarity.
After all, the term “trapezoid” translated from the ancient Greek language from the word “trapezion” means table, meal and other derivative words.
“Cone” comes from the Greek word “konos,” which means pine cone.
“Line” has Latin roots and comes from the word “linum”, translated it sounds like linen thread.
Did you know that if you take geometric figures with the same perimeter, then among them the circle turns out to have the largest area.
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 computing 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 of 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 the surrounding reality, learn to work with development.
UUD general scientific:
- search and selection of necessary information;
- application of information retrieval methods, conscious and arbitrary construction of speech utterances orally.
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 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 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 solid figures are solid bodies that occupy a non-zero volume in Euclidean (three-dimensional) space. These figures are studied by a branch of mathematics called “spatial geometry”. Knowledge about the properties of three-dimensional figures is used in engineering and the natural sciences. In the article we will consider the question of geometric three-dimensional figures and their names.
Geometric solids
Since these bodies have a finite dimension in three spatial directions, a system of three coordinate axes is used to describe them in geometry. These axes have the following properties:
- They are orthogonal to each other, that is, perpendicular.
- These axes are normalized, meaning the basis vectors of each axis are the same length.
- Any of the coordinate axes is the result of the vector product of the other two.
Speaking about geometric volumetric figures and their names, it should be noted that they all belong to one of 2 large classes:
- Class of polyhedra. These figures, based on the name of the class, have straight edges and flat faces. A face is a plane that limits a shape. The point where two faces join is called an edge, and the point where three faces join is called a vertex. Polyhedra include the geometric figure of a cube, tetrahedrons, prisms, and pyramids. For these figures, Euler's theorem is valid, which establishes a connection between the number of sides (C), edges (P) and vertices (B) for each polyhedron. Mathematically, this theorem is written as follows: C + B = P + 2.
- Class of round bodies or bodies of revolution. These figures have at least one surface forming them that is curved. For example, a ball, a cone, a cylinder, a torus.
As for the properties of volumetric figures, the two most important of them should be highlighted:
- The presence of a certain volume that a figure occupies in space.
- The presence of a surface area for each volumetric figure.
Both properties for each figure are described by specific mathematical formulas.
Let us consider below the simplest geometric volumetric figures and their names: cube, pyramid, prism, tetrahedron and ball.
Cube figure: description
The geometric figure cube is a three-dimensional body formed by 6 square planes or surfaces. This figure is also called a regular hexahedron, since it has 6 sides, or a rectangular parallelepiped, since it consists of 3 pairs of parallel sides that are mutually perpendicular to each other. It is called a cube whose base is a square and whose height is equal to the side of the base.
Since a cube is a polyhedron or polyhedron, Euler's theorem can be applied to it to determine the number of its edges. Knowing that the number of sides is 6, and the cube has 8 vertices, the number of edges is: P = C + B - 2 = 6 + 8 - 2 = 12.
If we denote the length of the side of a cube by the letter “a”, then the formulas for its volume and surface area will look like: V = a 3 and S = 6*a 2, respectively.
Pyramid figure
A pyramid is a polyhedron that consists of a simple polyhedron (the base of the pyramid) and triangles that connect to the base and have one common vertex (the top of the pyramid). The triangles are called the lateral faces of the pyramid.
The geometric characteristics of a pyramid depend on which polygon lies at its base, as well as on whether the pyramid is straight or oblique. A straight pyramid is understood to be a pyramid for which a straight line perpendicular to the base, drawn through the top of the pyramid, intersects the base at its geometric center.
One of the simple pyramids is a quadrangular straight pyramid, at the base of which lies a square with side “a”, the height of this pyramid is “h”. For this pyramid figure, the volume and surface area will be equal: V = a 2 *h/3 and S = 2*a*√(h 2 +a 2 /4) + a 2, respectively. Applying Euler's theorem for it, taking into account that the number of faces is 5 and the number of vertices is 5, we obtain the number of edges: P = 5 + 5 - 2 = 8.
Tetrahedron figure: description
The geometric figure tetrahedron is understood as a three-dimensional body formed by 4 faces. Based on the properties of space, such faces can only represent triangles. Thus, a tetrahedron is a special case of a pyramid, which has a triangle at its base.
If all 4 triangles forming the faces of a tetrahedron are equilateral and equal to each other, then such a tetrahedron is called regular. This tetrahedron has 4 faces and 4 vertices, the number of edges is 4 + 4 - 2 = 6. Applying standard formulas from plane geometry for the figure in question, we obtain: V = a 3 * √2/12 and S = √3*a 2, where a is the length of the side of an equilateral triangle.
It is interesting to note that in nature some molecules have the shape of a regular tetrahedron. For example, a methane molecule CH 4, in which the hydrogen atoms are located at the vertices of the tetrahedron and are connected to the carbon atom by covalent chemical bonds. The carbon atom is located at the geometric center of the tetrahedron.
The tetrahedron shape, which is easy to manufacture, is also used in engineering. For example, the tetrahedral shape is used in the manufacture of anchors for ships. Note that NASA's Mars Pathfinder space probe, which landed on the surface of Mars on July 4, 1997, also had the shape of a tetrahedron.
Prism figure
This geometric figure can be obtained by taking two polyhedra, placing them parallel to each other in different planes of space, and connecting their vertices accordingly. The result will be a prism, two polyhedra are called its bases, and the surfaces connecting these polyhedra will have the shape of parallelograms. A prism is called straight if its sides (parallelograms) are rectangles.
A prism is a polyhedron, therefore it is true for it. For example, if the base of the prism is a hexagon, then the number of sides of the prism is 8, and the number of vertices is 12. The number of edges will be equal to: P = 8 + 12 - 2 = 18. For a straight line a prism of height h, at the base of which lies a regular hexagon with side a, the volume is equal to: V = a 2 *h*√3/4, the surface area is equal to: S = 3*a*(a*√3 + 2*h).
Speaking about simple geometric volumetric figures and their names, we should mention the ball. A volumetric body called a ball is understood as a body that is limited to a sphere. In turn, a sphere is a collection of points in space equidistant from one point, which is called the center of the sphere.
Since the ball belongs to the class of round bodies, there is no concept of sides, edges and vertices for it. the sphere bounding the ball is found by the formula: S = 4*pi*r 2, and the volume of the ball can be calculated by the formula: V = 4*pi*r 3 /3, where pi is the number pi (3.14), r - radius of the sphere (ball).
