Offer object models that help children understand the specific meaning of the concepts: line, perimeter, polyline, circle, circle, angle, rectangle. Draw a rectangle Draw a rectangle using a ruler

3. Finish the definitions: “A rectangle is called ...”, “Square ...”, “Isosceles triangle ...”, “Parallelogram ...”.

Name at least three educational games in which, as game material geometric shapes are used. State the main goal of each of these games.

5. Give specific and compelling examples different types tasks (at least 5) using geometric material, but aimed at achieving goals related to the study of arithmetic.

6. Give at least three examples of tasks related to the division of polygons into parts.

Indicate the equipment for which it is useful to provide a lesson in familiarization with the types of corners.

8. Name the types of practical work of students, during which children identify:

A) essential features the concept of "right angle";

b) property of the sides of a rectangle.

9. Connect with arrows or write using pairs of the form ( A;A), (A, b) those concepts, in the formation of which it is useful to use the method of their comparison (comparison or opposition):

Write an algorithm for constructing a rectangle with given parties using a compass, ruler, square.

Formulate (in a generalized form) construction tasks that students must confidently perform primary school.

Construct a convex and non-convex heptagon. Are there non-convex quadrilaterals? What features of polygon models should vary, and which ones should remain unchanged when forming the concept of "heptagon"?

13. Come up with at least 5 examples of recognition tasks geometric shapes.

Suggest three geometric proof problems accessible to elementary school students. When junior schoolchildren Can I suggest tasks for proof? Why?

Ticket number 24

Solving Problems with Equations

In solving problems using equations, it is necessary to observe the following: firstly, write down the condition of the problem in algebraic language, i.e. so as to get the equation; secondly, to simplify this equation to such a form in which the unknown value will stand on one side, and all known quantities on the opposite side. The ways of doing this have already been discussed previously. One of the basic principles of algebraic solutions is that magnitude must be in the equation. This will allow us to write the conditions as if the problem had already been solved. After that, only decide equation and find the total value of all known quantities. Since these values are equal unknown value on the other side of the equation, then the value of all known values will mean that the problem is solved.

Task 1. When asked how much he paid for the watch, the man answered: "If you multiply the price by 4, and add 70 to the result, and subtract 50 from this amount, then the remainder will be equal to 220 dollars." How much did he pay for the watch? To solve this problem, we must first write the condition of the problem as an algebraic expression, that is, as an equation. Let the price of the watch be xx
This price has been multiplied by 4, so we get 4x4x
70 was added to the product, that is, 4x + 704x + 70
We subtracted 50 from this, that is, 4x+70−504x+70−50Thus, we wrote the condition of the problem using numbers in algebraic form, but we still do not have equations. However, according to the last condition of the problem, all previous actions eventually led to a result that equals 220220. Therefore, this equation looks like this: 4x+70−50=2204x+70−50=220
After carrying out operations with the equation, we get that x=50x=50.

That is, the xx value is equal to $50, which is the desired price of the watch. To check that we have obtained the correct value of the desired value, we must substitute this value instead of xx in the equation that we wrote down according to the condition of the problem. If, as a result of this substitution, the values of the sides are equal, we have performed the calculation correctly.
The problem equation was 4x+70−50=2204x+70−50=220
Substituting 50 for xx, we get 4⋅50+70−50=2204⋅50+70−50=220
Hence, 220=220220=220.

2) VALUE is special property real objects or phenomena, and the peculiarity lies in the fact that this property can be measured, that is, to name the number of quantities that express the same property of objects, are called quantities of the same kind or homogeneous quantities. For example, the length of the table and the length of the rooms are homogeneous values. Quantities - length, area, mass and others have a number of properties. Methods for studying the area of \u200b\u200ba geometric figure

The method of working on the area of a figure has much in common with working on the length of a segment.

First of all, the area stands out as a property of flat objects among their other properties. Already preschoolers compare objects by area and correctly establish the relationships "more", "less", "equal", if the compared objects differ sharply from each other or are completely identical. At the same time, children use the imposition of objects or compare them by eye, comparing objects according to the space they occupy on the table, on the ground, on a sheet of paper, etc. however, comparing objects in which the shape is different, and the difference in area is not very clearly expressed, children experience difficulties. In this case, they replace the comparison by area with a comparison by length or width of objects, i.e. go over to a linear extent, especially in those cases when, in one of the dimensions, objects differ greatly from each other.

In the process of studying geometric material in grades I - II, children's ideas about area as a property of flat geometric figures are clarified. It becomes clearer the understanding that the figures can be different and the same in area. This is facilitated by exercises for cutting figures out of paper, drawing and coloring them in notebooks, etc. In the process of solving problems with geometric content, students get acquainted with some properties of the area. They make sure that the area does not change when the position of the figure on the plane changes (the figure does not become larger or smaller). Children repeatedly observe the relationship between the whole figure and its parts (a part is smaller than the whole), exercise in composing figures of different shapes from the same given parts (i.e., building equally composed figures). Students gradually accumulate ideas about the division of figures into unequal equal parts, comparing the resulting parts with an overlay, comparing the received parts with an overlay. Children acquire all this knowledge and skills in a practical way along with the study of the figures themselves.

You can familiarize yourself with the area as follows:

"Look at the pieces attached to the board and say which one takes up the most space on the board (the square AMKD takes up the most space of all the pieces). In this case, the area of the square is said to be greater than the area of each triangle and square CDMB. Compare square triangle ABC and square AMKD (the area of a triangle is less than the area of a square).

These figures are compared by superposition - the triangle occupies only part of the square, which means that its area is really less than the area of the square. Compare by eye the area of the FVS triangle and the area of the DOE triangle (they have the same areas, they occupy the same place on the board, although they are located differently). Check with an overlay.

Similarly, other figures are compared in area, as well as objects of the environment.

Ticket number 25

Lesson 1. SUBJECT "MATHEMATICS". COUNTING ITEMS

Lesson Objectives: To introduce students to subject"Mathematics"; to acquaint with the educational set "Mathematics"; reveal the ability of students to count objects.

During the classes

I. Organizational moment.

II. Acquaintance with the subject "Mathematics" and the educational set "Mathematics".

The teacher, talking with the children, tells them in an accessible form about what he is studying the subject of "Mathematics", what they will learn, what "discoveries" they will make in mathematics lessons.

Teacher. What do you guys think, what is the subject "Mathematics" for?

Further, the teacher informs the children that a textbook consisting of two books will help them in mastering mathematics, it was written for first graders M. I. Moro, S. I. Volkov and S. V. Stepanov, and they will also need two notebooks in which students will be able to draw, color, write, but only in specially designated places.

MBOU "Okskaya secondary school"

Abstract open lesson mathematics

in the 4th grade on the topic:

"Constructing a rectangle on unlined paper".

Primary school teacher: Yashina Tatyana Vasilievna

year 2013

Lesson "Constructing a rectangle on unlined paper" Grade 4

Lesson Objectives: Teach how to draw a rectangle and a square on unlined paper using a compass and ruler.

Tasks:

1. Educational:

to update the previous knowledge about the rectangle and square;

to form practical skills in constructing geometric shapes, using knowledge about them;

to consolidate the skills of solving text problems, comparing named numbers;

develop computational skills, logical thinking.

2. Developing:

develop students' spatial imagination;

to develop the communication skills of students in the course of pair work, the ability for mutual control and self-control.

3. Educators:

instill a love for mathematics;

to cultivate accuracy in the execution of constructions;

arouse in the student a sense of pride in their personal achievements and the successes of their comrades.

Lesson type:

combined

Lesson form:

practical work.

Equipment:

for students: textbook, square, sheet of unlined white paper, pencil, compass

for the teacher: textbook, laptop, TV, presentation.

During the classes .

1. Organizational moment.

2. Motivation for activity.

Oh, how many wonderful discoveries we have

Prepares enlightenment spirit.

And experience, the son of difficult mistakes,

And a genius, a friend of paradoxes.

And chance, god is the inventor.

I hope that this math lesson will be another confirmation of our motto "Mathematics is the queen of sciences", and the great people of the past and present will help us in this.

3. Oral account.

Test (Slide) Each task will be evaluated.

1. Given numbers: 713754, 713654, 713554, ... Choose the next number :

a) 713854

b) 713554

c) 713454

2. What is the minuend equal to if the subtrahend is 73 and the difference is 600?

a) 527

b) 673

c) 763

3. Find the smallest of the numbers:

a) 18215

b) 18152

c) 18125

d) 18521

4. How many tens are there in the number 387 560?

a) 6

b) 38

c) 38 756

5. How many digits will be in private 64 080: 9

a) 1

b) 2

at 3

d) 4

6. Complete the sentence “To find the unknown dividend, you need the value of the quotient…”

a) multiply by a divisor;

b) divide by a divisor;

c) divide by dividend.

4. Actualization of basic knowledge.

1. Guess the riddle:

This important science

Exploring everything around

Dots, lines, squares,

Triangles and circle...

For her, a ruler, compasses

These are best friends.

But this science to you

You can't forget!

That's right, this science is called GEOMETRY.

What does this word mean?

Translated from Greek, this word means "surveying" ("geo" - earth, "metrio" - to measure). This name is explained by the fact that the origin of geometry was associated with various measuring work, which had to be performed when marking land, laying roads, constructing buildings and other structures. As a result of this activity, various rules related to geometric measurements appeared and gradually accumulated. Thus, geometry arose on the basis of the practical activity of people and at the beginning of its development served mainly practical purposes.

In the future, geometry was formed as an independent science, in which geometric figures and their properties are studied.

The world around us is the world of geometry. HELL. Alexandrov(Slide)

2. Guys, look carefully at the drawing.

Name how many triangles? (9)

How many quadrilaterals are in the drawing? (2).

How do they differ from each other?

(One is a rectangle and the other is not).

- What do you know about the rectangle?

In a rectangle, all angles are right.

Opposite sides of a rectangle are equal.

The diagonals at the point of intersection are bisected

The diagonal of a rectangle divides it into two equal triangles.

3. Well done! You have said a lot about the rectangle.

Now solve the problem:(Slide)

A diagonal is drawn in a rectangle. The area of one of the resulting triangles is 25 cm 2 . What is the area of the rectangle?

Solve the problem.

How did you find the area of the rectangle?

(We know that the diagonal of a rectangle divides it into two identical triangles. The area of one triangle is 25 sq. cm, so the area of \u200b\u200bthe entire rectangle will be 25 * 2 \u003d 50 cm 2 ).

That's right, well done! Ahow to draw rectangle if we only know its area?

What do you need to know for this? (Its length and width).

How to find out the dimensions of a rectangle?

(Selection method. Knowing that the area is found by multiplying the length by the width, 50 sq. cm can be obtained by multiplying 5 cm by 10 cm or 25 cm by 2 cm.).

Right. Choose which rectangle is more convenient to draw in a notebook. (It is more convenient to draw a rectangle with sides of 5 cm and 10 cm.).

Right. Draw such a rectangle.

5. Goal setting.

–Guys, tell me, was it easy for you to draw a rectangle in a notebook? (Yes Easy).

Why? (there are cells)

In the last lesson, we learned how to draw a rectangle on unlined paper using a square, and I asked you to draw at homepattern . Let's check what you got, and one person at the board will draw a rectangle using a square.

(Exhibition of works, checking the student at the blackboard - construction algorithm)

What do you think, is it easy to draw a rectangle on unlined paper, for example, on a landscape sheet, if you do not have a square? (difficult)

So there is a way to build with other tools. Today in the lesson we need a compass and a ruler.

What do you think, whatlesson topic ? ( Constructing a rectangle on unlined paper using a compass and ruler) (Slide)

Whichthe purpose of the lesson can be put in connection with the topic? (Learn how to draw a rectangle on unlined paper using a compass and ruler) (Slide)

– Where in our life can the ability to construct a rectangle or square be useful on unlined paper?

Tasks:

1) To form practical skills in constructing geometric shapes, using knowledge about them.

2) Develop spatial imagination.

3) To cultivate accuracy when performing constructions.

The topic is defined, the goals are set - on the way for new knowledge!

6. Discovery of new knowledge

For work, we need a compass and a ruler.

To use these tools safely, you need to remember

safety regulations:

You can not bring the compass to your face, there is a needle at the end, you can prick yourself.

You can not pass the compass with the needle forward, you can prick your friend.

There must be order on the desktop.

Can anyone figure out what to do?

If not, look at the board.

BWITH

Rice. 1 Fig. 2

What do we do first? (It is necessary to draw a circle).

What is "diameter"? (This is a segment that connects two points on a circle and passes through its center).

Let's make an algorithm for constructing a rectangle. (Slide)

Draw a circle.

Draw two diameters in it.

Connect the ends of the diameters with segments. The result is a rectangle.

7.Practical work

Take a landscape sheet.

Draw a circle with a radius of 5 cm.

We carry out two diameters.

We connect the ends of the diameters.

Denote the vertices of the rectangle

How to check that the result is a rectangle? (You can measure the sides of the figure, opposite sides must be the same, you can measure the angles using a right angle, the corners must be right).

Check if you have a rectangle.

Interested in building?

“Inspiration is needed in geometry no less than in poetry” A.S. Pushkin

(Slide)

Rememberproperties of the diagonals of a square

The diagonals of a square are equal,

form right angles when they intersect

the intersection point of the diagonals divides them into equal segments.

How do we start building? (Let's draw a circle).

We found only two vertices of the square, how to find two more? (Let's spendperpendicular to the straight line to the diameter, we get another diameter . These lines intersect at right angles like a square. Thus, we found two more vertices of the square).

Let's make an algorithm for constructing a square. (Slide)

Draw a circle.

Draw one diameter.

Draw a perpendicular line to this diameter.

Connect the points of intersection with the circle with segments. Got a square.

8. Practical work on the algorithm.

9. Physical education minute.

10.Inclusion in the knowledge system .

Choose your level. (Slide)

1.Find the area and perimeter of the rectangle and square.

R etc. = (6+8)*2=24(cm)

S etc =6*8=48(cm 2 )

R sq. =7*4=28(cm)

S sq. =7*7=49(cm 2 )

2. The Ivanov family has a summer cottage measuring 20 meters by 40 meters, and the Sidorov family has 30 meters by 30 meters. Whose fence is longer?

P \u003d (20 + 40) * 2 \u003d 120 (m.)

R=30*4=120(m)

Answer: their fences have the same length, which means they are equal.

3. Consider the plan of the school garden, on which 1 cm represents 10 m. Find the area of \u200b\u200bthis garden in ara (p. 7)(Choose the best option).

triangle movement;

measuring the sides of the resulting rectangle;

finding the area in m 2 ;

express in ars.

S=60*30=1800(m 2 .)=18 a.

Did all constructions and calculations come easily to you?

- "There is no royal way in geometry" Euclid.(Slide)

Well done! You have done well in this task. You have proved that you have the right to call yourself friends of GEOMETRY.

11. Consolidation of the material covered.

1) Geometry seemed to me very interesting and some kind of magical science. I.K. Andronov(Slide)

A) Find equal values.

b) What is the excess?

V) Continue the pattern:

Well done, now you can easily cope with No. 33 p.7

Let's check the solution.(Slide)

(6 km 5 m = 6 km 50 dm

2 days 20 h = 68 h

3 t 1 q > 3 t 10 kg

90 cm2< 9 дм 2 )

2) Solution of the problem.

Solving a difficult mathematical problem can be compared with the capture of a fortress. N.Ya.Vilenkin(Slide)

Read problem number 31. Write a short note

How many boys were in the club?

How many girls?

What is the height of all boys?

What is the height of all girls?

What is asked in the problem? (The table is filled in during work).

Make a plan for solving the problem:

express your height in centimeters

find the average height of the boys;

find the average height of girls;

compare.

Solve the problem yourself.

11m04cm=1104cm

12m60cm=1260cm

1) 1104: 8 = 138 (cm) - the average height of boys

2) 1260: 9 = 140 (cm) - the average height of girls

3)140-138=2(cm)-more

Answer: on average, the growth of boys is 2 cm more than the height of girls.

Let's check the solution. Well done, we have taken another mathematical fortress!Rate your work.

3) Work on computing skills.

Solve 1 example #34 on page 7.

Let's remember the procedure. What action do we do first?

After completion - verification.

(100 000 - 62 600) : 4 + 3 * 108 = 9 674

- Rate the work.

12) Summing up the lesson and reflection.

1) What was the topic of our lesson?

What goals and objectives did you set for yourself?

Have we reached them?

– What tools can be used to draw a rectangle on unlined paper? (Using a compass and ruler, using a square)

- Let's repeat the algorithm for constructing a rectangle and a square.

-What remains unclear?

2 ) Let's go back to the rectangle that was built at the beginning of the lesson. Color in on it that part of the tasks that you coped with and evaluate your work in the lesson.

GOOD FELLOWS!!!

13) Homework.

Optional: (Slide)

Literature.

M.I.Moro and other textbook "Mathematics, Grade 4", M. "Enlightenment" 2011

L.I. Semakina "To help the teacher", M., "Vako", 2011

The concepts of "perpendicular lines", "perpendicular". Construction of a right angle on unlined paper (using a compass).

Construction of symmetrical figures using a square, ruler and compass.

Construction of symmetrical segments, figures using drawing tools on checkered and unlined paper.

Parallelism of lines.

Construction of parallel lines using a square and a ruler.

Construction of rectangles.

Repetition of basic properties opposite sides rectangle and square. Construction of drawings with a ruler and a square on unlined paper.

Time measurement.

Time units. Relationship between units of time. Instruments for measuring time.

Project "How Time Was Measured in Antiquity"

Examples of sub-topics: ancient calendar, sundial, water clock, flower clock, measuring instruments in antiquity.

Solving logical problems. Text encryption.

Logical tasks associated with measures of length, area, time. Graphic models, diagrams, maps. Modeling from paper based on a graphic card with instructions.

Project "Encryption of location" (or "Transmission of secret messages")

Examples of subtopics: ways of encrypting texts, devices for encryption, encryption of location, signs in encryption, game "Treasure Hunt", competition of decoders, creation of a device for encryption.

Class (34 h)

Decimal number system.

The value of a digit depending on the place in the number entry. Decimal number system: why is it called that? (study)

Project "Number systems"

Examples of subtopics: decimal number system, binary number system, computers and number system, number systems in various professions.

coordinate angle.

Acquaintance with the coordinate angle, the ordinate axis and the abscissa axis. Introduce the concept of image transmission, the ability to navigate by the coordinates of points on a plane. Construction of the coordinate angle. Reading, writing named coordinate points, designating points of a coordinate beam using a pair of numbers.

Graphs. Diagrams. Tables. Construction of diagrams, graphs, tables using MS Office.

Use in reference literature and media of graphs, tables, charts. Collection of information on tables, graphs, diagrams. Types of charts (bar, pie). Construction of diagrams, graphs, tables using MS Office.

Project "Strategy".

Examples of subtopics: games with winning strategies, strategies in games, strategies in sports, strategies in computer games, strategies in life (behavioral strategies), combat strategies, strategies in antiquity, strategy in advertising, strategy computer game championship, a collection of games with winning strategies, an album of battle patterns won with the right strategies, sports team games, commercials and posters.

Polyhedron.

The concept of "polyhedron" as a figure, the surface of which consists of polygons. Faces, edges, vertices of a polyhedron.

Rectangular parallelepiped.

Determining the number of vertices, corners, faces of a polyhedron. Introduction to the rectangular parallelepiped. Surface area cuboid.

cube. Cube unwrapping.

A cube is a rectangular parallelepiped, all of whose faces are squares. We build a development of a geometric body (a parallelepiped and a cube) from paper. Surface area of a cuboid and a cube.

Wireframe model of a parallelepiped.

Making a wireframe model of a rectangular parallelepiped and a cube. Solution of practical problems (material calculation).

Dice. Cube games.

Making a dice for board games. Collection of dice games.

The volume of a rectangular parallelepiped.

The concept of "volume of a geometric body". Cubic centimeter. Making a cubic centimeter model. cubic decimeter. Cubic meter. Two ways to find the area of a rectangular parallelepiped.

Grids. The game "Sea battle", "Tic-tac-toe" (including on the endless board)

The new kind visual relationship between quantities. Construction of a coordinate on a ray, on a plane. Organization of games "Sea battle", "Tic-tac-toe" on an endless board.

13. Dividing a segment into 2, 4, 8, ... equal parts using a compass and ruler.

Practical task: how to divide a segment into 2 (4, 8, ...) equal parts, using only a compass and a ruler (without a scale)?

Angle and its magnitude. Protractor. Angle comparison.

Repetition and generalization of knowledge about the angle as a geometric figure. Angle value (degree measure). Measure an angle in degrees using a protractor. Different ways to compare angles. Construction of angles of a given value.

Types of corners.

Classification of angles depending on the magnitude of the angle. Acute, straight, obtuse, developed angle. Construction and measurement.

Classification of triangles.

Classification of triangles depending on the size of the angles and the length of the sides. Acute-angled, right-angled, obtuse-angled triangle. Scalene, isosceles, equilateral triangle.

Constructing a rectangle using a ruler and a protractor.

Practical task: how to construct a rectangle with given sides using a protractor and a ruler. Repetition of methods for finding the area and perimeter of a rectangle.

Plan and scale.

Plan. The concept of "scale". Reading the scale, determining the ratio of length on the plan and terrain. Recording the scale of the plan. A plan drawing of a classroom, one of the rooms in your apartment (optional). Maintaining scale.

First, let's remember what shape is called a rectangle (Fig. 1).

Rice. 1. Definition of a rectangle

Look at the figures shown (Fig. 2).

Rice. 2. Shapes

We need to determine if there is a rectangle among them.

For this we need a square. Let's find a right angle at the square and apply it to each of the corners of our figures. Applying a square to all corners of the first figure, we see that it coincided with all corners. This means that figure number 1 is a rectangle.

We apply the right angle of the square to figure No. 2 and see that the angle does not coincide with the right angle. This means that figure #2 is not a rectangle.

We apply the right angle of the square to figure No. 3. The first angle is straight. The second corner of the figure is straight. The third corner of the figure is also right. And the fourth corner is also right. The third figure is a rectangle.

Figure number 4. We apply the right angle of the square, and it coincides with the corner of the figure. We apply it to the second corner of the figure, and it also matches. We apply the right angle of the square to the third corner. The third corner is also the same. The fourth corner is also the same. This means that figure #4 is a rectangle.

Figure number 5. We apply the right angle of the square to the first corner. This angle does not coincide with the right angle of the square. This means that figure #5 is not a rectangle.

It turns out that the rectangles are figures numbered 1, 3, 4 (Fig. 4).

Rice. 3. Rectangles

We have established that figures 1, 3 and 4 have right angles.

A square is a drawing tool for drawing corners. Squares are made of metal, plastic or wood (Fig. 3).

Rice. 4. Square

Figures 1 and 3 have equal sides that lie opposite each other. Figure 4 has all sides equal. Such figures have a special name.

A quadrilateral whose sides are equal in pairs is called a rectangle.

A rectangle with all sides equal is called a square.

Let's build a rectangle using a square and a ruler.

To do this, first put a point on the plane. Then we find the corner on the square and apply it so that the point is the vertex of the corner (Fig. 5).

Rice. 5. Point - the top of the corner

Now we outline the sides of the corner (Fig. 6).

Rice. 6. Side angle

We do the same with the second corner of the rectangle (Fig. 7).

Rice. 7. Sides of two corners

Now we take a ruler and use it to measure segments of a given length. Using the same ruler, we will draw the fourth side (Fig. 8).

Rice. 8. Drawing the sides of the figure

We have a geometric figure. Let's name her. Let's name each vertex of our rectangle (Fig. 9).

Rice. 9. Notation of the vertices of the rectangle

We built a rectangle ABCD using a ruler and a square.

In the lesson, we learned how to distinguish a rectangle from other quadrilaterals. We also learned how to draw a rectangle on a sheet of paper using a square and a ruler.

Bibliography

Alexandrova E.I. Mathematics. Grade 2 - M.: Bustard - 2004.
Bashmakov M.I., Nefyodova M.G. Mathematics. Grade 2 - M.: Astrel - 2006.
Dorofeev G.V., Mirakova T.I. Mathematics. Grade 2 - M.: Enlightenment - 2012.

Proshkolu.ru ().
Social network education workers Nsportal.ru ().
Illagodigardarivista.com ().

Homework

Select rectangles from the proposed shapes (Fig. 10):

Rice. 10. Drawing for the task

Prove that the figure shown in Figure 11 is a rectangle.

Rice. 11. Drawing for the task

Build a rectangle yourself with sides of 5 cm and 8 cm using a square and a ruler.

Class: 4

Presentation for the lesson

Back forward

Attention! The slide preview is for informational purposes only and may not represent the full extent of the presentation. If you are interested this work please download the full version.

The purpose of the lesson: To teach how to build a rectangle on unlined paper using a square.

1. Educational:

to update the previous knowledge about the rectangle and square;
to form practical skills in constructing geometric shapes, using knowledge about them;
to consolidate the skills of solving text problems for proportional division, comparing named numbers.

2. Developing:

develop students' spatial imagination;
to develop the communication skills of students in the course of pair work, the ability for mutual control and self-control.

3. Educators:

to cultivate accuracy in the execution of constructions;
arouse in the student a sense of pride in their personal achievements and the successes of their comrades.

Type of lesson: learning new material.

Lesson form: practical work.

Equipment:

for students: textbook, square, sheet of unlined white paper, simple pencil;

for the teacher: textbook, computer, multimedia projector, screen.

During the classes

1. Organizational moment.

2. Oral account.

– Find the mistakes in the calculations on the board.

Correct answers: 100,024; 12,548; 6504.

3. Checking homework.

Checking squares on unlined paper. (Show on the board how to construct a square using a compass and straightedge.)

- What knowledge about the square helped to cope with the construction? (The diagonals of a square are equal, intersect, forming four right angles.)

4. Actualization of students' knowledge about the rectangle.

- In the last lesson, we learned how to build a rectangle using a compass and a ruler. Remember, please, what kind of geometric figure is a rectangle. (A rectangle is a quadrilateral with all right angles.)

What else do you know about the rectangle? (Opposite sides are equal. Diagonals are equal.)

This knowledge will be useful to us today.

5. Demonstration of the presentation. Explanation of new material.

SLIDE 1. Announcement of the topic of the lesson: “Constructing a rectangle on unlined paper.”

- What tools will be needed for practical work? (Square, pencil)

SLIDE 2. Purpose: To learn how to build a rectangle on unlined paper using a square.

SLIDE 3. Tasks: 1. To form practical skills in constructing geometric shapes using knowledge about them.

2. Develop spatial imagination.

3. Cultivate accuracy when performing constructions.

SLIDE 4. Algorithm for constructing a rectangle using a square.

SLIDE 5. Draw an arbitrary ray HELL. One of the sides of the square was applied to the beam so that the vertex of the right angle coincided with the beginning of the beam at point A. Draw a beam AB along the second side of the square with a pencil. We got one right angle VAD.

SLIDE 6. One of the sides of the square was applied to beam AB so that the vertex of the right angle coincided with point B. Draw a beam BC with a pencil along the second side of the square. We got the second right angle ABC.

SLIDE 7. One of the sides of the square was applied to the AD beam so that the vertex of the right angle coincided with point D. Draw a DS beam with a pencil along the second side of the square. We got the third right angle ADS.

SLIDE 8. Students are asked a problematic question - did the rectangle turn out.

Students express their assumptions and suggest ways to solve this problem.

SLIDE 9. Checking students' assumptions.

It is necessary to find out whether the angle of the VSD will be right. If yes, then the rectangle turned out (since, by definition, a rectangle is a quadrilateral in which all corners are right). If not, then ABCD is not a rectangle.

The check is carried out using a square. One of its sides must be attached to the beam BC so that the vertex of the right angle coincides with point C. Next, we look to see if the beam SD coincides with the second side of the square. In our case, this happened, that is, we can conclude that the angle VSD is a right angle and the quadrilateral ABSD is a rectangle.

Further independent work students to build a rectangle on unlined paper using a square on the material of the presentation algorithm involves returning to slides 4-9 (using a hyperlink).

The teacher at this time controls the construction process and provides individual assistance to students.

6. Physical education for the eyes(using SLIDES 10-12 of the presentation)
7. Work with the textbook.

– Open the textbook on page 7. Task number 33. (Work on options. There are 2 students at the blackboard.)

- What quantities will we need to remember? (Mass and time.)

Compare named numbers.

(6 km 5 m = 6 km 50 dm	2 days 20 h = 68 h
3 t 1 q > 3 t 10 kg	90 cm2< 9 дм 2)

Checking 2 students. Behind the desks - mutual verification.

– Task 34. Calculate the value of the first expression. At the blackboard 1 student.

(100 000 – 62 600) : 4 + 3 108 = 9 674

Checked by 1 student.

- Task 30. A table has been prepared on the board for a short note. We fill everything together. What are the names of the table columns? (Per 1 page/Number of pages/Total)

One student solves the problem on the board.

1) 90: 6 = 15 (p.) - on one page

2) 75: 15 = 5 (page)

Answer: 5 pages are required.

Checked by 1 student.

*Additional task - No. 31.

8. The result of the lesson.

– What did you learn new?

– What have you learned?

What tools can be used to draw a rectangle on unlined paper? (Using a compass and ruler, using a square)

- Where in our life can the ability to construct a rectangle or square be useful precisely on unlined paper?

What remains unclear?