To basic geometric shapes on the plane are dot and straight line.Line segment,Ray,broken line- the simplest geometric figures on the plane.
The dot is the smallest geometric figure, which is the basis of all other constructions (figures) in any image or drawing.
Any more complex geometric figure is a set points, which have a certain property that is characteristic only for this figure.
A straight line, or a straight line, can be thought of as an innumerable set points, which are located on the same line, which has neither beginning nor end. On a sheet of paper, we see only part of a straight line, since it is infinite. The straight line is shown like this:
Part straight line bounded on both sides dots, is called a line segment, or segment. The segment is shown like this:
A ray is a directed half-line that has point beginning and has no end. The beam is shown like this:
If on straight you put point, then this point divides the line into two beam, oppositely directed. Such rays are called complementary.
The broken line is a few segments connected to each other so that the end of the first segment is the beginning of the second segment, and the end of the second segment is the beginning of the third segment, etc., while adjacent (having one common point) the segments are not on the same straight line. If the end of the last segment does not coincide with the beginning of the first, then such a broken line is called open.
If the end of the last segment of the polyline coincides with the beginning of the first segment, then such a polyline is called closed. An example of a closed polygon is any polygon:
Four-link closed polyline - quadrilateral
Three-link closed polyline - triangle
Plane, like a straight line, is a primary concept that has no definition. A plane, like a straight line, has neither a beginning nor an end. We consider only the part of the plane that is bounded by a closed broken line.
There are an infinite number of forms. The shape is the outer outline of an object.
The study of forms can be started from early childhood, drawing the attention of your child to the world around us, which consists of figures (a plate is round, a TV is rectangular).
From the age of two, the baby should know three simple shapes - a circle, a square, a triangle. At first, he should just show them when you ask for it. And at the age of three, already call them independently and distinguish a circle from an oval, a square from a rectangle.
The more exercises for fixing the forms will be performed by the child, the more new figures he will remember.
The future first-grader should 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 by 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, quadrilateral (rectangle, square, trapezium, rhombus, parallelogram) and all kinds of polygons.
Volumetric figures include: sphere, cube, cylinder, cone, pyramid. These are the 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.
- A game. Start learning shapes in a playful way. Good exercises for fixing and studying flat shapes are applications from geometric shapes. For volumetric ones, you can use ready-made purchased games, as well as choose applications where you can cut and glue a three-dimensional shape.
four year old child knows and distinguishes such geometric figures as a circle, a square and a triangle. Difficulties arise in distinguishing between a circle and an oval, a square and a rectangle. When comparing objects, the child already takes into account several properties: length, width, height. The above games and tasks will help you teach your baby to distinguish between geometric shapes and compare objects according to different criteria. Older children are offered tasks with three-dimensional figures.
geometric lotto
1 . Take a sheet of paper and divide it into 6 squares or rectangles. Make as many of the same cards. Draw geometric shapes on them. If your child can read, instead of drawing a figure on paper, write the name of this figure. Let the cards be with a picture. The task of the child is to read the name of the figure and put a card with the image of this figure.
2
. Another version of the geometric lotto - you name the cell in which the child should place a specific figure.
For example: "Put a circle in the top left corner, or put a triangle in the bottom right corner." If your geometric shapes are multi-colored, then indicate the color of the shape that you want to see in the cell. This way you reinforce the concepts of right/left, top/bottom and color names. Complete your card with your child. When all the cells are filled, compare your cards.
Item Comparison
The essence of the task is that the child is invited to compare the picture with geometric shapes.
To do this, you need to find (or draw yourself) pictures of objects that will resemble a geometric figure. For example: circle - button, ball, watermelon. Oval - melon, cucumber. Rectangle - door, table, etc.
Find an item
Geometric shapes are drawn on paper. The task of the child is to draw objects similar to the figures depicted on paper or to find objects of a similar shape in the room.
"Magic Pouch"
Figures are put into the bag, and at your request, the child pulls out the object you need by touch. The baby can feel objects both through the fabric and by lowering his hands into the bag. The main condition is not to look into the bag with the figures.
Shape and size
1. Prepare paper geometric shapes of different sizes. Now ask the child to line up all the circles in ascending order (from a small circle to a large one), then all the triangles - in descending order (from a large triangle to a small one). Each row should not contain more than 5 items.
2.
Take boxes of different sizes, but the same shape. Invite the child to put toys in the boxes and close them with a suitable lid. First help the baby, show how to close the box.
When he learns to distinguish the sizes of one form, complicate the task: along with the boxes, give the child jars of different sizes with lids. Now the baby needs not only to distinguish between "big / small", but also - "round / square".
Size and color
You can work out with the child the concepts of “size”, “shape” and “color” of an object as follows: take a sheet of drawing paper and with colored tape mark (“circle”) the contours of your geometric shapes (these can be designer parts or home-made models). Now the child, taking one figure at a time, fills in all the fields on the drawing paper, taking into account the shape of the object, as well as its size and color.
To complicate the task, use one-color tape. In this case, the color will not act as a hint.
Exercise machine
Before you start playing, review the table with your child. Please note that the table has rows and columns (columns). List shapes and colors. Make sure your child recognizes shapes by size. Now start exercising:
1. Count!
- How many small circles are shown in the table?
- How many small red circles?
How many big green squares?
How many blue pieces are there? etc.
2. Who lives where?
The child needs to name the location of the indicated figure. For example, you are pointing to a large oval. The child should answer that the large oval is in the first column, in the second row.
You can play vice versa: you name the "address" of the figure (for example, the fifth row, fifth column), and the child finds the figure you have guessed and names it (large blue square).
3. Right/left, top/bottom
On this simulator you can learn (repeat) the directions of the sides. For example, what shape is to the left of the big red rectangle? (big blue circle) What's on top of the big blue circle? (large blue square), etc.
Fold the figure
Invite the child to fold a circle (square, etc.) from pre-prepared parts. First, offer to fold the figure from two parts (two identical semicircles for a circle), then from 3, etc. At first, keep the details for each figure in separate envelopes. Later, details from different geometric shapes can be mixed. To facilitate the task, paint each shape in a separate color (circle - red, square - blue, etc.).
Classification of objects by shape
The child needs to arrange the pictures in envelopes or piles in accordance with the shape of the image, thus creating several groups. First, offer to sort the pictures into two groups: round objects in one envelope, square ones in another. At this stage, it is important that the child distinguishes round objects from objects with corners - quadrangular, so the second group will include both square objects (for example, a wall clock) and rectangular objects (for example, a book). Then add a group with triangular items.
Later, you can complicate the task by adding images that are similar in shape, for example, round and oval, square and rectangular, triangular and trapezoidal. The most difficult type of task is to sort all the pictures at once.
figurine house
Show the child images of dwellings (hut, igloo, multi-storey building). Ask what geometric shapes they remind the baby. Now he needs to find a suitable house for geometric shapes (triangle, circle, square). 
Draw and Guess
An adult and a child take turns drawing in the air and guessing various geometric shapes. You can draw figures with your finger on the back.
Count geometric shapes
Ask the child to look at the picture. Name the geometric shapes yourself. Then ask him to count, name and indicate with the help of numbers the number of squares, rectangles, triangles, rhombuses, trapeziums, circles and ovals depicted.
figure outline
Cut out geometric shapes from thick cardboard (circle, square, rectangle, triangle, rhombus, trapezoid, oval). Ask your child to trace the outline of the shape. Let the child, circling the figure, consider its sides.
Basic elements in a figure
Offer your child:
- show the sides of a square (rectangle, triangle, trapezoid, circle, oval). Show how to move your finger along the side of the figure;
- count the vertices of a square (rectangle, triangle, trapezoid) or mark the vertices with dots on the image with a colored pencil;
- show the corners of a square (rectangle, triangle, trapezoid). Teach your child to show the angle with two fingers: thumb and forefinger;
- circle the border of the depicted figure with a colored pencil;
- shade the inner area of the depicted figure with a colored pencil;
- find the similarities of geometric shapes (for example, a rectangle, a square and a trapezoid have 4 sides, 4 vertices and 4 corners);
- name similar geometric shapes in one word (square, rectangle, trapezium, rhombus - quadrangles; triangle, quadrilateral, five-hexagon - polygons).
Volumetric figures
1. Talking about volumetric figures, try to get the child to understand the difference between flat and three-dimensional geometric shapes (square - cube, circle - sphere (ball), etc.). Compare them, try to make them out of cardboard or plasticine.
2. Consider sides voluminous figures. Please note that they can be different even for one figure. For example, a cone has 2 sides: one is a circle at the base, and the other is the entire side surface of the cone.
3. Ask your child to compare cone and pyramid.
Explain that the base of a pyramid can be a triangle, a quadrilateral, or a polygon. And the side faces of the pyramid will be triangles converging at one vertex. If there is a circle at the base, then a cone will be obtained.
4. Ask your child name or draw objects resembling three-dimensional geometric shapes.
Geometry is a branch of mathematics that studies shapes and their properties.
The geometry that is studied at school is called Euclidean, after the ancient Greek scientist Euclid (3rd century BC).
The study of geometry begins with planimetry. Planimetry- This 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 various shapes and sizes: residential buildings, machine parts, books, jewelry, toys, etc.
In geometry, instead of the word object, they say a geometric figure. Geometric figure(or short: figure) is a mental image of a real object, in which only the shape and dimensions are stored, and only they are taken into account.
Geometric shapes are divided into flat and spatial. In planimetry, only plane figures are considered. A flat geometric figure is one whose all points lie on the same plane. An idea of such a figure is given by any drawing made on a sheet of paper.
Geometric shapes are very diverse, for example, a triangle, a square, a circle, etc.:
A part of any geometric figure (except for a point) is also a geometric figure. The union of several geometric shapes will also be a geometric figure. In the figure below, the left figure is made up of a square and four triangles, while the right figure is made up of a circle and parts of a circle.
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
