Round geometric shapes. Basic Geometric Concepts

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 shapes

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.

There are an infinite number of forms. Shape is the external outline of an object.

You can start studying forms from the very beginning. early childhood, drawing your child’s attention to the world around us, which consists of shapes (the plate is round, the TV is rectangular).

From the age of two, a child should know three simple figures– circle, square, triangle. At first he should just show them when you ask. And at the age of three, you can already name them yourself and distinguish a circle from an oval, a square from a rectangle.

How more exercise to consolidate the forms will be completed by the child, the more new figures he will remember.

The future first-grader must know all the simple geometric shapes and be able to make applications from them.

What do we call a geometric figure?

A geometric figure is a standard with which you can determine the shape of an object or its parts.

Figures are divided into two groups: flat figures, three-dimensional figures.

We call plane figures those figures that are located in the same plane. These include circle, oval, triangle, quadrangle (rectangle, square, trapezoid, rhombus, parallelogram) and all kinds of polygons.

Three-dimensional figures include: sphere, cube, cylinder, cone, pyramid. These are those shapes that have height, width and depth.

Follow two simple tips when explaining geometric shapes:

Patience. What seems simple and logical to us adults will seem simply incomprehensible to a child.
Try drawing shapes with your child.
Game. Start learning shapes in a playful way. Good exercise to consolidate and study flat shapes - applications from geometric shapes. For voluminous ones, you can use ready-made store-bought games, and also choose applications where you can cut out and glue a voluminous shape.

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 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 voluntary 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 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 shapes)

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 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, 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

In this lesson you will learn what geometric shapes are. We will talk about figures depicted on a plane and their properties. You will learn about the simplest forms of geometric shapes such as dots and lines. Consider how a segment and a ray are formed. Learn the definition and different types of angles. The next shape whose definition and properties are discussed in this lesson is a circle. The following discusses the definition of triangle and polygon and their varieties.

Rice. 10. Circle and circumference

Think about which points belong to a circle and which circles (see Fig. 11).

Rice. 11. Mutual arrangement of points and circle, points and circle

Correct answer: points, belong to the circle, and only points and belong to the circle.

A point is the center of a circle or circle. Segments are the radii of a circle or circle, that is, segments that connect the center and any point lying on the circle. A segment is the diameter of a circle or circle, that is, it is a segment connecting two points lying on the circle and passing through the center. The radius is half the diameter (see Fig. 12).

Rice. 12. Radius and diameter

Let's now remember what kind of figure is called a triangle. A triangle is a geometric figure consisting of three points that do not lie on the same straight line and three segments connecting these points in pairs. A triangle has three angles.

Consider a triangle (see Fig. 13).

Rice. 13. Triangle

It has three angles - corner, corner and corner. The points , , are called the vertices of the triangle. Three segments - segment , , - are the sides of the triangle.

Let us repeat what types of triangles are distinguished (see Fig. 14).

Rice. 14. Types of triangles

Based on the types of angles, triangles can be divided into acute, rectangular and obtuse. In a triangle, all angles are acute; such a triangle is called acute. A triangle has a right angle, such a triangle is called a right triangle. A triangle has an obtuse angle, such a rectangle is called an obtuse triangle.

Triangles are distinguished based on whether the lengths of the sides are equal:

Scalene - such triangles have different lengths of all sides;

Equilateral - these triangles have equal lengths of all sides;

Isosceles - their two sides have the same lengths. Two sides of equal length are called the lateral sides of the triangle, and the third side is the base of the triangle (see Fig. 15).

Rice. 15. Types of triangles

What shapes are called polygons? If you sequentially connect several points so that their connection gives a closed broken line, then an image of a polygon, quadrangle, pentagon or hexagon, etc. is created.

Polygons are named by the number of angles. Each polygon has as many vertices and sides as there are angles (see Fig. 16).

Rice. 16. Polygons

All the figures depicted (see Fig. 17) are called quadrilaterals. Why?

Rice. 17. Quadrilaterals

You probably noticed that all the figures have four corners, but they can all be divided into two groups. How would you do it?

You probably separated quadrilaterals in which all angles are right angles into a separate group, and such quadrilaterals were called rectangular quadrilaterals. The opposite sides of the rectangles are equal (see Fig. 18).

Rice. 18. Rectangular quadrilaterals

In a rectangle and are opposite sides, and they are equal, and are also opposite sides, and they are equal (see Fig. 19).