Mathematical city of geometric shapes. City of geometric shapes methodical development in mathematics (middle group) on the topic. Materials for the lesson

Lesson on the development of mathematical representations

in children of the preparatory group

Subject: "Journey to the city geometric shapes»

Program content:

Clarify and consolidate the idea of ​​\u200b\u200ba geometric figure - a ball. Exercise in the ability to find in the environment objects of the shape of a circle, a ball.

Materials for the lesson:

Demonstration - flannelograph, a model of a train made of geometric shapes with separately attached square and round wheels; a set of objects of various shapes; installation for the shadow theater - a lamp, a screen; large plane figures - a circle, a square, a triangle, etc., large three-dimensional figures - a ball, a cube.

Handout - "Magic bags" with a set of figures - a circle, a ball, a square, a cube) one bag for 2-3 children; plasticine of two colors - one color per child.

Methodical methods: playful, visual, practical.

Lesson progress:

Introductory part.

Guys, today we will travel with you! And we will go with you to the city of geometric shapes. What can you travel on? We will travel by train.

Look, we will go on this train (a mock-up of a train with square wheels is displayed on the flannelograph). Do you think we can go now? Why not? (The train will not run because it has square wheels, but should be round) Why can't the train run on square wheels? (the square does not roll, but the circle rolls).

Let's check it out. (The teacher suggests that one of the children roll a square and a circle on the table).

Why doesn't the square roll? (A square has corners and sides, and they prevent it from rolling)

Why is the circle rolling? (The circle has no corners and sides) Let's put the right wheels on our train and go to the city of geometric shapes. Go!

(To the sound of a moving train, the children go to the music room decorated with geometric figures and models of houses from building material. Near each house, children are waiting for a task).

Main part.

Well, here we are in the city of geometric shapes. Look what a beautiful city! Each house is inhabited by a figure. What would you be interested in, geometric shapes have come up with different games for you. Do you want to play?

Game 1. "Magic bag"

The teacher shows the children various objects - for example, a ball, a plate, a book, a dice - and offers to name their shape. With the help of an adult, children call: a circle, a ball, a cube, a rectangle. Then the teacher divides the children into small subgroups and distributes "magic bags". Children in turn, without looking into the bag, try to determine the shape of a figure by touch, and then, to prove their innocence, they take it out, show it to everyone and put it back in the bag.

At the end of the game, the teacher offers to open the bag, puts a circle, a ball on the table and invites the children to compare them:

What do they have in common and how do they differ?

First, the children establish signs of difference: the circle is flat, and the ball is voluminous. The circle can be “flattened” and hidden between the palms, but the ball cannot be “flattened” - this is a three-dimensional (spatial) figure. The figures have in common that both figures are round, have no corners and can roll.

Game 2. "Find and tell"

Guys, geometric shapes are very fond of playing hide and seek. But the circle and the ball are so well hidden among the objects around us that other geometric shapes cannot find them in any way. Let's help them.

(Children are trying to find in the environment objects shaped like a ball, a circle. The teacher encourages the most observant ones).

Game 3. "Treat"

Guys, it turns out that soon there will be a holiday in the city of Geometric shapes and they need to cook a lot of treats. Do you want to help them? It is necessary to bake round cookies from the dough, but one cookie will look like a plate, and the other like a pea. What two molds will the cookies be made from? (Circle and ball)

(Children are divided into two subgroups - one subgroup sculpts circles from plasticine, and the other balls. During modeling, the teacher clarifies: how can you make a ball, a circle? How can you make a circle from a ball?)

Final part.

Guys, today we had a lot of fun in the city of Geometric shapes, but it's time for us to return to kindergarten. In parting, the residents of the city want to take a memorable photo. To do this, we will go with you to a photo studio and turn into photographers for a while.

Game "Photographers"

With the help of a shadow theater (a screen with a lamp), the teacher projects the shadow of the ball onto the screen - a circle.

What do you see? (Circle)

How is this figure different from a sphere? (Children make their guesses.)

Place a circle and a ball on a piece of paper. Look: did the circle fit entirely on the plane of the sheet? (Yes.) And the ball? (No.)

Why? (A circle is a flat figure, and a ball is a three-dimensional figure.)

Correct, and this is their main difference.

Now we have photos of the inhabitants of the city of Geometric figures. Guys, the train is ready to depart. Grab your seats and go. Go!

(To the sound of a moving train, the children return to the group).

Subject: "

(project)

Objective of the project : create a layout of the city (sketch) based on the knowledge gained on the topic "Geometric bodies".Project objectives :
- to study educational and encyclopedic literature on the topic "Geometric bodies";

Use the acquired knowledge to build sweeps of geometric bodies necessary to create a layout of a fantastic city;

Develop communication skills when working in different groups;

Develop research skills and systems thinking.

Lesson plan:

1. Introductory part.

2. Implementation of the theoretical part

3. Performer of the practical part.

4.Result.

During the classes:

1. Introduction to the lesson.
Dominant activity of students: practice-oriented, creative.

Complexity of the project: monoproject (drawing)

Project duration: short-term (3 lessons)

Theoretical part

Theoretical significanceThe project lies in the fact that we have systematized encyclopedic knowledge on the following issues:

Solids of Plato, solids of Archimedes, solids of revolution

Practical part.

Practical significanceof this project is determined by the fact that we have learned how to make scans of various geometric bodies and, using models of geometric bodies, we will make a layout (sketch) of a fantastic city.

Relevance of this project, we see that any modern person in his life cannot do without knowledge of mathematics, drawing, visual arts, and in particular without the ability to see geometric shapes, bodies and objects in the world around us.

Project stages:

They develop general and individual action plans, determine the amount of material studied, questions for search activities, determine sources for finding answers to the questions posed.

1.4

Determination of forms of expression of the results of project activities

Takes part in the discussion, offers his options.

In groups, and then in the class, they discuss the forms of presenting the result of research activities.

2

Project development

Advising and coordinating student work

Carry out search activities.

2.1

Together with groups of students, it selects the necessary theoretical material on the issue under study

They search for answers to the questions posed using literary sources, the Internet. Perform the selection of the necessary material.

2.2

Implementation of the practical part of the project

Helps students in building sweeps of various geometric bodies, determining the required dimensions.

Build scans of various geometric bodies, glue models. Determine the number, shape and size of geometric bodies required to complete the layout of the tutorial. Produce selected models.

3

Registration of results

Advises, coordinates the work of students, helps in drawing up the layout of the textbook.

First, by groups, and then in cooperation with other groups, they draw up the results in accordance with the accepted rules.

5

Reflection

Evaluates own performance and student performance

They express wishes, collectively discuss the difficulties that have arisen and offer ways to solve them in future work.

Implementation of the theoretical part of the project

Exercise 1 . (1 group)

To study the theoretical material on the topic "Plato's Solids".

Plato's solids are regular polyhedra. A polyhedron is called regular if: it is convex, all its faces are equal , in each the same number of edges converge.
Regular polyhedra have been known since ancient times. Their ornamental models can be found on created during the late , V , at least 1000 years before Plato. In the dice with which people played at the dawn of civilization, the shapes of regular polyhedra are already guessed. To a large extent, regular polyhedra have been studied . Some sources (such as ) are credited with the honor of their discovery . Others argue that only the tetrahedron, cube and dodecahedron were familiar to him, and the honor of discovering the octahedron and icosahedron belongs to a contemporary of Plato. In any case, Theaetetus gave a mathematical description of all five regular polyhedra and the first known proof that there are exactly five. Regular polyhedra are characteristic of philosophy , in honor of which they received the name "Platonic solids". Plato wrote about them in his treatise (360 BC), where he compared each of the four elements (earth, air, water and fire) to a certain regular polyhedron. Earth was compared to a cube, air to an octahedron, water to an icosahedron, and fire to a tetrahedron. There were the following reasons for the emergence of these associations: the heat of the fire is felt clearly and sharply (like small tetrahedrons); air is made up of octahedrons: its smallest components are so smooth that they can hardly be felt; water pours out when taken in the hand, as if it were made of many small balls (which are closest to icosahedrons); in contrast to water, cubes that are completely unlike a ball make up earth, which causes the earth to crumble in the hands, in contrast to the smooth flow of water. With regard to the fifth element, the dodecahedron, Plato made a vague remark: "... God defined it for the Universe and resorted to it as a model." added a fifth element, ether, and postulated that the heavens were made of this element, but he did not juxtapose it with the Platonic fifth element. gave a complete mathematical description of regular polyhedra in the last, XIII book . Propositions 13-17 of this book describe the structure of the tetrahedron, octahedron, cube, icosahedron and dodecahedron in this order. For each polyhedron, Euclid found the ratio of the diameter of the circumscribed sphere to the length of the edge. Proposition 18 states that there are no other regular polyhedra. Andreas Speiser defended the point of view that the construction of five regular polyhedra is the main goal of the deductive system of geometry, as it was created by the Greeks and canonized in Euclid's Elements . A large number of information of the XIII book of the "Beginnings" is possibly taken from the writings of Theaetetus.
In the 16th century, a German astronomer tried to find a connection between the five planets known at that time (excluding the Earth) and regular polyhedra. In The Secret of the World, published in 1596, Kepler outlined his model solar system. In it, five regular polyhedra were placed one inside the other and separated by a series of inscribed and circumscribed spheres. Each of the six spheres corresponded to one of the planets ( , , , , And ). The polyhedra were arranged in the following order (from inner to outer): octahedron, followed by icosahedron, dodecahedron, tetrahedron, and finally the cube. Thus, the structure of the solar system and the relationship of distances between the planets were determined by regular polyhedra. Later from original idea Kepler had to be abandoned, but the result of his search was the discovery of two laws of orbital dynamics - , - which changed the course of physics and astronomy, as well as regular stellated polyhedra (Kepler-Poinsot bodies).

Types of Platonic Solids

Tetrahedron

3

3

4

6

4

Task 2. (Group 2)

To study the theoretical material on the topic "The bodies of Archimedes".

The bodies of Archimedes are called semi-regular homogeneous convex polyhedra, that is, convex polyhedra, all polyhedral angles of which are equal, and the faces are regular polygons of several types (this is how they differ from the Platonic solids, whose faces are regular polygons of the same type)

Some types of bodies of Archimedes

Task 3. (group 3)To study the theoretical material on the topic "Body of revolution".

Solids of revolution - three-dimensional bodies that arise when a flat figure, bounded by a curve, rotates around an axis lying in the same plane.

Examples of bodies of revolution:

2. Implementation of the practical part of the project. Exercise 1. (individual)Learn how to build sweeps of geometric bodies: a cube, a rectangular parallelepiped, a pyramid, a cylinder. Make a model of each geometric body from paper. Task 2. (group)Draw a sketch of a part of a fantasy city. Calculate how many and what geometric bodies are needed to complete the layout of a part of a fantastic city.Run models of the necessary geometric bodies. Run a mock-up of a part of a fantastic city, prepare to defend the project.

The first group made a layout of the central part of the city. This layout consists of 4 cubes, 8 parallelepipeds, 3 pyramids. With the help of the listed geometric bodies, the buildings of the bank, museum, shop were made. In the center of the layout is a fountain in the form of a hexagonal pyramid.

The second group made a layout of the residential quarter of the city. This layout consists of 13 cubes, 4 parallelepipeds, 14 pyramids, 2 cylinders. With the help of the listed geometric bodies, residential buildings and a water tower were made.

The third group made a model of the school of the fantastic city. This layout consists of 4 cubes, 6 boxes. With the help of the listed geometric bodies, the school building, the children's zoo, the stage, and the sports ground were made.

Outcome.
During the implementation of this project, we have learned to recognize the geometric bodies in the buildings and structures around us, and we will be able to describe the geometric composition of any building. All students in the class are able to make scans and models of geometric bodies: a cube, a rectangular parallelepiped, various regular pyramids. During the project, we learned to evaluate the work of each participant, and were able to express our opinion. This project is the first experience of the whole class on the project technology of studying educational material mathematics.

The results can be used in the lessons of mathematics and geometry, drawing, art.

State budgetary educational institution of the Samara region

secondary school "Educational Center" p.g.t. Roshinsky

municipal district Volzhsky, Samara region

Subject:

« Construction of a fantastic city from geometric shapes.

(Lesson extracurricular activities)

5th grade

Teacher of fine arts, MHC, drawing

Tatarinova A.N.

Maria Malakhova
Summary of the lesson "Journey to the city of geometric shapes" in the middle group

Integration of educational regions: "Cognitive Development", « Speech development» , , "Physical development".

Target: develop ideas about geometric shapes.

Tasks:

2. To form the ability to respond to questions: "How many?", "Which one?", "Which place?" ("Cognitive Development").

3. Strengthen the ability to distinguish and name colors ( "Cognitive Development").

4. Exercise in the ability to distinguish and name geometric figures: circle, square, triangle, rectangle ( "Cognitive Development").

5. To form the ability to conduct a dialogue with teacher: listen and understand the question asked, answer clearly, speak slowly, without interrupting ( "Speech development").

6. Develop attention, thinking, ability to guess riddles ( "Cognitive Development").

7. Cultivate interest in mathematics ( "Social and communicative development").

Methods and techniques:

- practical: posting pictures

- visual: viewing, showing geometric shapes

- verbal: riddles, situational storytelling

Materials and equipment:

Demo Material: layout cities« geometric shapes» ; geometric figures: circle, triangle, square, rectangle.

Handout: boards (15x25cm) for each child, a set of colored geometric shapes for each child.

Forms and methods of joint activities

Children's activities Forms and methods of organizing joint activities

Cognitive and research tour of "Magic, geometric city» , problem solving

Game Game situations

Communicative Guessing riddles, situational conversations, questions

Motor Fizkultminutka

construction game

Logic of educational activity

1 The teacher offers to join hands and stand in a circle to give each other their warmth so that everyone has good mood. Children fulfill the request of the teacher An interest in the upcoming activity has been formed

2 The teacher talks about what is unusual in the world city« geometric shapes» and yesterday this city bewitched by an evil wizard, and no one can disenchant. The teacher suggests going to journey, V city« geometric shapes» and try to disenchant him Children accept the teacher's offer

3 The teacher makes riddles in order to open the gate cities:

“Since childhood, I have been your friend, every corner here is straight

All four sides are the same length.

I am glad to introduce myself to you, but my name is ... "

I have no corners and I look like a saucer,

On a plate and on a lid, on a porch, on a wheel"

"My riddle is short : 3 sides and 3 corners. Who am I?" Children guess puzzles:

(square (circle (triangle) Success situation organized

4 The teacher thanks the children, opens the gate and draws attention to an interesting path from geometric shapes different colors Children answer from which geometric shapes what color is the path (from circles) Improved ability to recognize and name geometric figure(circle, distinguish color (red, yellow, blue, green)

7 The teacher offers a game "What changed?" To do this, you need to look carefully at the circles, remember in what order they lie. Offers to close their eyes and swaps two circles Children remember where the circles are, close their eyes.

Children open their eyes and tell what has changed, what circles have changed The ability to remember the location of objects and determine the new location of objects is fixed

8 The teacher praises the children for the completed task and offers to go further along the path that leads to the houses with geometric shapes. The teacher reports that the evil wizard has bewitched geometric figures, and now they don't know what they're called. Children go to the houses with geometric shapes Created interest in upcoming activities

9 The teacher offers to help name and disenchant shapes Children name geometric shapes, defining and naming the form by the window of the house The ability to compare, analyze, draw conclusions is fixed

10 The teacher draws attention to the circle and the triangle, which quarreled and cannot reconcile, as they are also bewitched. The teacher offers to dance "We quarreled and reconciled" Children dance to music "We quarreled and reconciled" Success situation organized

11 The teacher reports that journey to the city of geometric shapes has come to an end and proposes that the inhabitants of this cities no longer quarreled and they always had a good mood, lay out from friends figures funny pictures. Children put pictures on boards geometric shapes The idea of geometric shapes

Final event: looking at funny pictures.

Related publications:

Summary of the lesson "Journey to the country of geometric shapes" Circle of joy: Hello golden sun, hello blue sky. Hello free breeze, Hello little oak. Hello morning.

Synopsis of the GCD in the middle group "Journey to the forest of geometric shapes" Software content. 1. Consolidate children's knowledge of geometric shapes (circle, square, triangle, rectangle); name the form.

Abstract of an open lesson in mathematics in the senior group "Journey to the city of geometric shapes" Purpose: systematization of knowledge about geometric shapes and their properties. Program tasks: - to consolidate knowledge about geometric shapes;

Abstract of the lesson in the middle group on cognitive development "Journey to the country of games and geometric shapes" Synopsis of GCD on cognitive development (mathematical representations) in the middle group. Prepared by the teacher Dubrovina E.V. Topic: Journey.

Picture 121 from the presentation "Area and Volume" to geometry lessons on the topic "Volume"

Dimensions: 960 x 720 pixels, format: jpg. To download a picture for a geometry lesson for free, right-click on the image and click "Save Image As...". To show pictures in the lesson, you can also download the full presentation "Area and Volume.ppt" with all the pictures in a zip archive for free. Archive size - 1687 KB.

Download presentation

Volume

"Polygons" - Soloninkina T.V. Material for self-study on the topic "Polygons" Tasks for the game. Content. Name the links and vertices of the polyline. Polygons. Are there simple broken lines in the figure? Quadrangular-nick (square). What is the smallest number of links that a simple broken line has that is closed? Compiler.

"The concept of the area" - Development, Theme: "Circumference" No. 4. (1 hour). Students are preliminarily informed of an approximate list of tasks to be taken out for credit. Upbringing. Learning, To realize the triune didactic tasks: through the use of different levels of learning. Formation and education of a versatile personality. Topic: "Vector" No. 5 (1 hour).

"Parallelogram" - The diagonals of a parallelogram are bisected by the point of intersection. If a quadrilateral has opposite sides equal in pairs, then the quadrilateral is a parallelogram. In a parallelogram, opposite sides and opposite angles are equal. If two sides of a quadrilateral are equal and parallel. What is a parallelogram?

“Lesson 2 class Rectangle area” - We are great students! Mathematics Grade 2 Lesson-opening The area of ​​a rectangle. Formulas. ?. We are friendly! We are careful! Expressions with a variable. R - ? L. Triangle segment polygon rectangle quadrilateral square. b. 8: a P \u003d (a + b) 2 4 - x c: 3 P \u003d a + b + a + b P \u003d a 2 + b 2 14 + y.

"Honeycomb bees" - Found information. A honeycomb is a rectangle covered with regular hexagons. We have: Author: Andrey Shedikov, Grade 9, Solerudnikovskaya Gymnasium. Made a report. Stages of work: Euclid himself could learn from the geometry of my honeycombs. Made a conclusion. Why did the bees choose the hexagon?

"Polygon area" - You have been given the task of painting the house! 5. 4. Trouble! ? 8. A. Paint consumption per unit area? 2.1.3.7.

There are 35 presentations in total in the topic

After the completion of the project Journey to Tsifrograd» We received many letters asking us to continue our mathematical journeys. And we, on reflection, decided to give the project a second life, continuing the adventures of the boy Dima and the girl Dasha in the country of Mathematics.

In the new project Journey to Geometrograd» waiting for your kids 4 big trips into the fascinating world of geometry, where they can get acquainted with the whole "families" of geometric figures, shapes, as well as with geometric tools!

"Geometrograd" is an unusual city, it is inhabited by geometric "inhabitants" - figures, shapes, geometric tools and a funny, cheerful friend of all kids - Pencil! We again set off on a journey together with inquisitive heroes who love mathematics - Dima and Dasha.

IN first trip, your kids will get acquainted with the city of Geometrograd, its founders - dot And line, With compass and whole the Krug family: circle, semicircle, oval, sphere, cylinder and ellipsoid. To get to the city, get to know its inhabitants and meet the Krug family, Dima and Dasha will have to solve a lot of geometric riddles and hear many interesting geometric stories. The heroes of the geometric journey are waiting for interesting adventures, acquaintance with new geometric concepts: dot, one, many, near, vertical row of dots, horizontal row of dots; straight line, horizontal, vertical, oblique, "along", "between", "above", "under", "on"; around, closed curve, circle, circle, border, oval; shape, body, volume, ball, ellipsoid, thickness; compass.

The project is age-appropriate 3 to 7 years old.

Objective of the project- to give the child the initial geometric concepts, to form the child's skills of orientation in space, the basics of the worldview, to develop logical thinking and memory, fine motor skills of the hand.

Within the framework of the project, there is an acquaintance with the families of geometric shapes and forms, as well as geometric tools.

Main directions of development, according to which the child is taught in the process of working with a thematic play set to get acquainted with geometric shapes and forms:

1. intellectual development (memory, attention, imagination, thinking)
2. Logico-mathematical development (analysis, synthesis, comparison, generalization, classification, analogy, seriation, orientation)
3. sensory development and fine motor skills (lacing, didactic games, work with scissors, strokes, puzzles, work with various objects)
4. Speech development (finger games, reading author's fairy tales, task poems)
5. Creative development, imaginative thinking, fantasy (application, modeling, drawing)

The authors and organizers of the project have built a system for presenting the material in such a way that the kid gets basic geometric knowledge in a practical, interesting and accessible way. To study a group (family) of geometric shapes and forms prepared a separate thematic game set.

Today we are pleased to present you the first (out of four) part of the project

"Journey to Geometrograd" - Circle family.

Kids get acquainted not only with geometric concepts,

but also with the environment!

In the kit you will receive the following materials:

• Author's fairy tale – "Journey to Geometrograd" part 1, which consists of 4 mini-tales and introduces your kid to the main characters of the tale - the boy Dima, the girl Dasha, the inhabitants of the city of Geometrograd: Pencil, geometric shapes, forms and geometric tools. In this fairy tale, kids get to Geometrograd and get acquainted with the founders of geometry - Point and Line, as well as with the tool - Compasses. For the first time, in Geometrograd, children get acquainted with the family of the Circle: the Circle, the Semicircle, the Oval, the Sphere, the Cylinder and the Ellipsoid.

• Folder lapbook "Circle Family" with original author's tasks, with the help of which the child will get acquainted with the basic geometric shapes - a point and a line, with 6 geometric shapes and forms of the "Circle Family", and also learn to distinguish flat figures and volumetric forms. It will consolidate the concepts of "long - short", "wide - narrow", "thin - thick". The child will be able to learn to draw each geometric figure and shape, write their names. Learn to visually compare real objects with their geometric counterparts and much more.

This is what the finished folder looks like after it is made:

• Detailed instructions for manufacturing lapbook-folder "Krug Family" and work with her.

• With the kit you get lacing, puzzles "Shapes and forms - the family of the circle", applications and creative tasks with author's poems and original recommendations for children to create their own masterpieces.

• Cards in the palm of your hand "Geometrograd" part 1 containing 9 cards of a convenient format, for getting acquainted with geometric shapes and forms: a point, a straight line, a curved line, a circle, a semicircle, an oval, a ball, an ellipse, a cylinder. The cards contain descriptions, author's poems, interesting and informative information, practical tasks for getting to know shapes and forms.

• Guidelines for parents and teachers with detailed recommendations for the entire complex of games and activities. IN guidelines described best practices and methods for introducing a child to geometric shapes and forms, the concept of a flat and three-dimensional figure, illustrations of techniques are given, and you will also receive a set of exercises with real objects and geometric tools to better consolidate the concepts being studied. Also along with the recommendations you will receive class calendar, which will help you record and mark the progress of your baby, his possible difficulties in mastering the material.

Together with a themed play set ( additionally!) You are getting – Poster “Geometric shapes and forms” which you can print, hang on the wall and play with the child, repeating all the geometric shapes and forms . In part 1 of the project, you get the basis of the poster and the geometric shapes and forms of the “Circle family”.

Open the mysterious world of geometry to your kids!

Buy the first part of "Journey to Geometrograd»

in PDF format

Price 1100 rubles

But this is not all the materials that we have prepared for you!

We have prepared for the set 30 page workbook, which you can use for individual lessons , and for group lessons .

The advantage of an electronic notebook is that you can print as many notebook sets as you need. This is especially important when you are working with a large number of children. You can’t do this with ready-made notebooks on a printed basis. After all, for each child you need to purchase these notebooks. Benefits of the electronic version of the notebook High Quality– is obvious!

Buy workbook "Family of the Circle»

in PDF format

Price 300 rubles

At the time of buying set plus notebook

price 1300 rubles

PS. The authors of the kit warn! With the participation of the kit in clubbing, repurchases and any distributions, the kit will immediately be removed from sale and no one else will be able to get it. Let's treat each other with respect!

IN present time purchase project materials at a Happy Day discount IT IS FORBIDDEN!