Perpendicularity of lines. Offer subject models that help children understand the specific meaning of concepts: straight line, perimeter, broken line, circle, circle, angle, rectangle Algorithm for constructing a rectangle using a square

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10.07.2020

MBOU "Okskaya Secondary School"

Summary of an open lesson in mathematics

in 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” 4th grade

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

Tasks:

1. Educational:

    update previous knowledge about rectangles and squares;

    develop practical skills in constructing geometric figures using knowledge about them;

    consolidate skills in solving word problems, comparing named numbers;

    develop computational skills and logical thinking.

2. Developmental:

    develop students’ spatial imagination;

    develop students’ communication skills during pair work, the ability for mutual control and self-control.

3. Educators:

    instill a love of mathematics;

    cultivate accuracy when performing formations;

    awaken in the student a sense of pride in his personal achievements and the successes of his comrades.

Lesson type:

combined

Lesson format:

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

The spirit prepares for enlightenment.

And experience, the son of difficult mistakes,

And genius, friend of paradoxes.

And chance, God the inventor.

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

3. Oral counting.

Test (Slide) We will evaluate each task.

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 there be in the quotient 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 the divisor;

b) divide by the divisor;

c) divide by the dividend.

4. Updating of basic knowledge.

1. Guess the riddle:

This important science

Explores everything around:

Dots, lines, squares,

Triangles and circle...

For her, a ruler, a compass

These are best friends.

But this science is also for you

There is no way to forget!

That's right, this science is called GEOMETRY.

What does this word mean?

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

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

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

2. Guys, look carefully at the drawing.

Name how many triangles? (9)

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

How are they different from each other?

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

- What do you know about a rectangle?

    In a rectangle, all angles are right.

    The opposite sides of the rectangle are equal.

    The diagonals at the intersection point are divided in half

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

3.Well done! You talked 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, which means the area of ​​the entire rectangle will be equal to 25 * 2 = 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?

(By 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 multiplied by 2 cm.).

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

Right. Draw a rectangle like this.

5. Goal setting.

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

Why? (there are cells)

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

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

Do you think it’s easy to draw a rectangle on unlined paper, such as a landscape sheet, if you don’t have a square? (difficult)

This means there is a way to build using other tools. Today in the lesson we will need a compass and a ruler.

What do you think?lesson 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 to build a rectangle on unlined paper using a compass and ruler) (Slide)

– Where in our lives can the ability to construct a rectangle or square on unlined paper come in handy?

Tasks:

1) To develop practical skills in constructing geometric figures using knowledge about them.

2) Develop spatial imagination.

3) Cultivate accuracy when performing constructions.

The topic has been determined, the goals have been set – let’s go for new knowledge!

6.Discovery of new knowledge

To work we will need a compass and a ruler.

To use these tools safely, you need to remember

safety regulations:

    You cannot put the compass close to your face; there is a needle at the end, you can prick yourself.

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

    There should be order on the desktop.

Maybe someone has guessed what needs to be done?

If not, look at the board.

BWITH

KM

AD

Rice. 1 Fig. 2

What do we do first? (You need to draw a circle).

What is "diameter"? (This is a segment connecting two points on a circle and passing through its center).

Let's create 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 whose radius is 5 cm.

We carry out two diameters.

We connect the ends of the diameters.

Let's denote the vertices of the rectangle

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

Check if you have a rectangle.

Were you interested in building?

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

(Slide)

Rememberproperties of square diagonals

    The diagonals of a square are equal,

    when intersecting they form right angles,

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

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

We found only two vertices of the square, how to find two more? (Let's carry outperpendicular 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 create an algorithm for constructing a square. (Slide)

    Draw a circle.

    Draw one diameter.

    Draw a line perpendicular to this diameter.

    Connect the points of intersection with the circle with segments. The result is 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 kv =7*4=28(cm)

S kv =7*7=49(cm 2 )

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

Р= (20+40)*2=120(m.)

Р=30*4=120(m)

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

3. Consider the plan of the school garden, in which 1 cm represents 10 m. Find the area of ​​this garden in ares (p. 7)(Selecting the best option).

    moving the triangle;

    measuring the sides of the resulting rectangle;

    finding the area in m 2 ;

    express in ar.

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

Was all the constructions and calculations easy for you?

- “There is no royal path in geometry” Euclid.(Slide)

Well done! You did a good job on this task. You have proven 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 quantities.

b) Which quantity is extra?

V) Continue the pattern:

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

Let's check the solution.(Slide)

(6 km 5 m = 6 km 50 dm

2 days.20 hours = 68 hours

3 t 1 c > 3 t 10 kg

90 cm 2< 9 дм 2 )

2) Solving the problem.

Solving a difficult mathematical problem can be compared to taking a fortress. N.Ya.Vilenkin(Slide)

Read task No. 31. Let's make a short note

How many boys were in the club?

How many girls?

How tall are all the boys?

How tall are all the girls?

What does the problem ask? (The table is filled in during the work process).

Make a plan to solve the problem:

    express height in centimeters

    find the average height of boys;

    find the average height of girls;

    compare.

Solve the problem yourself.

11m04cm=1104cm

12m60cm=1260cm

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

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

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

Answer: on average, boys' height is 2 cm greater than girls' height.

Let's check the solution. Well done, we've conquered another math fortress!Evaluate your work.

3)Work on computing skills.

Solve 1 example No. 34 on page 7.

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

After completion - mutual verification.

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

    1. 37 400

      9 350

      324

      9674

- Evaluate 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 achieved them?

– What tools can you use to construct 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 return to the rectangle that we built at the beginning of the lesson. Color on it the part of the tasks that you completed and evaluate your work in class.

Well done!!!

13) Homework.

Optional: (Slide)

    1. Construct a rectangle and a square on unlined paper, find and compare their areas.

      Make a geometric pattern using your new knowledge.

Literature.

    M.I.Moro and other textbook “Mathematics, 4th grade”, M. “Enlightenment” 2011.

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

Class: 4

Presentation for the lesson












Back forward

Attention! Slide previews are for informational purposes only and may not represent all the features of the presentation. If you are interested in this work, please download the full version.

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

1. Educational:

  • update previous knowledge about rectangles and squares;
  • develop practical skills in constructing geometric figures using knowledge about them;
  • consolidate skills in solving word problems on proportional division, comparing named numbers.

2. Developmental:

  • develop students’ spatial imagination;
  • develop students’ communication skills during pair work, the ability for mutual control and self-control.

3. Educators:

  • cultivate accuracy when performing formations;
  • awaken in the student a sense of pride in his personal achievements and the successes of his comrades.

Lesson type: learning new material.

Lesson format: practical work.

Equipment:

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

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

During the classes

1. Organizational moment.

2. Oral counting.

– Find errors in calculations on the board.

Correct answers: 100 024; 12,548; 6,504.

 3. Checking homework.

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

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

 4. Updating students’ knowledge about the rectangle.

– In the last lesson, we learned how to build a rectangle using a compass and a ruler. Please remember what kind of geometric figure this 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 lesson topic: “Constructing a rectangle on unlined paper.”

– What tools will be needed for practical work? (square, pencil)

SLIDE 2. Goal: Learn how to build a rectangle on unlined paper using a square.

SLIDE 3. Objectives: 1. To develop practical skills in constructing geometric figures, using knowledge about them.

2. Develop spatial imagination.

3. Cultivate accuracy when performing formations.

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

SLIDE 5. Draw an arbitrary ray AD. 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, point A. We drew the beam AB with a pencil along the second side of the square. We received one right angle VAD.

SLIDE 6. One of the sides of the square was applied to the ray AB so that the vertex of the right angle coincided with point B. The ray BC was drawn 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 ray AD so that the vertex of the right angle coincided with point D. The ray DS was drawn with a pencil along the second side of the square. We obtained the third right angle ADS.

SLIDE 8. Students are asked a problematic question - whether the result is a rectangle.

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

SLIDE 9. Checking students' assumptions.

It is necessary to find out whether the VSD angle is right. If yes, then the result is a rectangle (since, by definition, a rectangle is a quadrilateral with all right angles). If not, then the figure ABCD is not a rectangle.

The check is carried out using a square. One of its sides must be applied to beam BC so that the vertex of the right angle coincides with point C. Next, we look to see whether 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 right and the quadrilateral ABCD is a rectangle.

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

At this time, the teacher controls the construction process and provides individual assistance to students.

 6. Exercise for the eyes(using SLIDES 10-12 of the presentation)

7. Working with the textbook.

– Open the textbook on page 7. Task No. 33. (Work on options. There are 2 students at the board.)

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

Compare named numbers.

(6 km 5 m = 6 km 50 dm 2 days.20 hours = 68 hours
3 t 1 c > 3 t 10 kg 90 cm 2< 9 дм 2)

2 students are tested. At the desks there is mutual checking.

– Task 34. Calculate the value of the first expression. There is 1 student at the board.

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

1 student checks.

– Task 30. A table has been prepared on the board for short recording. Let's fill it all out together. What should we call the columns of the table? (Per 1 page/Number of pages/Total)

On the board, 1 student solves the problem.

1) 90: 6 = 15 (p.) – on one page

2) 75: 15 = 5 (page)

Answer: 5 pages will be required.

1 student checks.

*Additional task – No. 31.

8. Lesson summary.

– What new did you learn?

– What have you learned?

– What tools can you use to build a rectangle on unlined paper? (Using a compass and ruler, using a square)

– Where in our lives can the ability to construct a rectangle or square on unlined paper come in handy?

What remains unclear?

Giving marks to students who are actively working in class.

9. Homework.

1. Construct a square on unlined paper using a square and a ruler.

-What is a square? (A rectangle with all sides equal.)

Use this definition in your homework.

– How to make a short recording? (In table form.)

– How many days did it take for the jackets to be sewn in the studio? (Two days.)

– What would you name the columns of your table? (Consumption per 1 jacket/number of jackets/total meters)

First, let's remember what kind of figure 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 whether 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. By applying the square to all the corners of the first figure, we see that it coincides with all the 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 No. 2 is not a rectangle.

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

Figure No. 4. We apply a right angle of the square, and it coincides with the angle 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 angle is also the same. The fourth corner is also the same. This means that figure No. 4 is a rectangle.

Figure No. 5. 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 No. 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 constructing angles. 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. And figure No. 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 construct a rectangle using a square and a ruler.

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

Rice. 5. Point - vertex of the corner

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

Rice. 6. Sides of the corner

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

Rice. 7. Sides of two corners

Now we will 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 of the sides of the figure

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

Rice. 9. Designation of the vertices of a rectangle

We constructed 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 construct a rectangle on a piece of paper using a square and a ruler.

Bibliography

  1. Alexandrova E.I. Mathematics. 2nd grade. - M.: Bustard - 2004.
  2. Bashmakov M.I., Nefedova M.G. Mathematics. 2nd grade. - M.: Astrel - 2006.
  3. Dorofeev G.V., Mirakova T.I. Mathematics. 2nd grade. - M.: Education - 2012.
  1. Proshkolu.ru ().
  2. Social network of educators Nsportal.ru ().
  3. Illagodigardaravista.com ().

Homework

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

Rice. 10. Drawing for the assignment

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

Rice. 11. Drawing for the assignment

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

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

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

5. Provide specific and convincing examples of different types of 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 dividing polygons into parts.

Indicate the equipment that is useful to provide a lesson on familiarization with the types of angles.

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

a) essential features of 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 technique of their comparison (contrast or contrast):

Create an algorithm for constructing a rectangle with given sides using a compass, ruler, and square.

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

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 tasks for recognizing geometric shapes.

Provide three geometric proof problems accessible to primary school students. When can younger students be given proof problems? Why?

Ticket number 24

Solving problems using equations

When solving problems using equations, the following must be observed: first, write down the condition of the problem in algebraic language, i.e. so as to obtain the equation; secondly, simplify this equation to a form in which the unknown quantity will be on one side, and all known quantities will be on the opposite side. Ways to do this have already been discussed earlier. One of the basic principles of algebraic solutions is that magnitude must be present in the equation. This will allow us to write down the conditions as if the problem had already been solved. After this, all that remains is decide equation and find the common value of all known quantities. Since these quantities 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.

Problem 1. A man, when asked how much he paid for a watch, answered: “If you multiply the price by 4, add 70 to the result, and subtract 50 from this amount, 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 problem statement as an algebraic expression, that is, as an equation. Let the price of the watch be xx
This price was multiplied by 4, that is, we get 4x4x
70 was added to the product, that is, 4x+704x+70
We subtracted 50 from this, that is, 4x+70−504x+70−50. Thus, we have written down the condition of the problem using numbers in algebraic form, but we do not yet have equations. However, according to the last condition of the problem, all previous actions ultimately led to a result that equals 220220.Therefore, this equation looks like this: 4x+70−50=2204x+70−50=220
After performing operations with the equation, we find that x=50x=50.

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

2) QUANTITY is a special property of real objects or phenomena, and the peculiarity is that this property can be measured, that is, the number of quantities that express the same property of objects are called quantities same kind or homogeneous quantities. For example, the length of a table and the length of a room are homogeneous quantities. Quantities - length, area, mass and others have a number of properties. Methods for studying the area of ​​a 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, area is distinguished 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 objects being compared are sharply different from each other or completely identical. In this case, children use overlapping objects or compare them by eye, matching objects according to the space they occupy on the table, on the ground, on a sheet of paper, etc. however, when comparing objects whose shapes are 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 the length or width of objects, i.e. switch to linear extension, especially in cases where objects differ greatly from each other in one of the dimensions.

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. The understanding that figures can be different and identical in area becomes clearer. This is facilitated by exercises such as cutting out figures from paper, drawing and coloring them in notebooks, etc. In the process of solving problems with geometric content, students become familiar with some properties of 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 entire figure and its parts (the part is smaller than the whole), and practice constructing figures of different shapes from the same given parts (i.e., constructing equally composed figures). Students gradually accumulate ideas about dividing figures into unequal equal parts, comparing the resulting parts by superimposing, comparing the resulting parts by superimposing. Children acquire all this knowledge and skills in a practical way along with the study of the figures themselves.

You can get acquainted with the area like this:

"Look at the pieces attached to the board and say which one takes up the most space on the board (the AMKD square 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 the CDMB square. Compare area of ​​triangle ABC and square AMKD (the area of ​​the triangle is less than the area of ​​the square).

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

Other figures, as well as surrounding objects, are similarly compared in area.

Ticket number 25

Lesson 1. SUBJECT “MATHEMATICS”. COUNTING OBJECTS

Lesson objectives: to introduce students to the subject “Mathematics”; introduce the educational set “Mathematics”; identify students’ ability to count objects.

During the classes

I. Organizational moment.

II. Introduction to the subject "Mathematics" and the educational set "Mathematics".

The teacher, talking with the children, tells them in an accessible form about what they are studying in the subject “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?

Next, the teacher informs the children that a textbook consisting of two books will help them in mastering mathematics; it was written for first-graders by 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, paint, write, but only in specially designated areas.

The concepts of “perpendicular lines”, “perpendicular”. Constructing a right angle on unlined paper (using a compass).

Constructing symmetrical figures using a square, ruler and compass.

Constructing symmetrical segments and figures using drawing tools on checkered and unlined paper.

Parallelism of lines.

Constructing parallel lines using a square and ruler.

Construction of rectangles.

Repetition of the basic properties of opposite sides of a rectangle and square. Constructing drawings using a ruler and square on unlined paper.

Measuring time.

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

Project “How time was measured in ancient times”

Examples of subtopics: ancient calendar, sundial, water clock, flower clock, measuring instruments in ancient times.

Solving logical problems. Text encryption.

Logical problems related to measures of length, area, time. Graphic models, diagrams, maps. Modeling from paper supported by a graphic card with instructions.

Project "Location Encryption" (or "Transmission of Secret Messages")

Examples of subtopics: methods of encrypting texts, devices for encryption, location encryption, signs in encryption, the game “Treasure Hunt”, competition of decryptors, creating a device for encryption.

Class (34 h)

Decimal number system.

The meaning of a digit depending on its place in the number record. 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 different professions.

Coordinate angle.

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



Charts. Diagrams. Tables. Constructing charts, graphs, tables using MS Office.

Use of graphs, tables, diagrams in reference literature and the media. Collecting information using tables, graphs, diagrams. Types of charts (bar, pie). Creation of charts, graphs, tables using MS Office.

Project "Strategies".

Examples of subtopics: games with winning strategies, strategies in games, strategies in sports, strategies in computer games, strategies in life (strategies of behavior), combat strategies, strategies in ancient times, strategy in advertising, championship in a computer game in the “Strategy” genre, a collection of games with winning strategies, an album with diagrams of battles won thanks to correctly chosen strategies, sports team games, commercials and posters.

Polyhedron.

The concept of a “polyhedron” as a figure whose surface 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 of ​​a rectangular parallelepiped.

Cube Development of a cube.

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

Frame model of a parallelepiped.

Making a frame model of a rectangular parallelepiped and a cube from wire. Solving practical problems (material calculations).

Dice. Games with dice.

Making dice for board games. Collection of dice games.

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. Game "Battleship", "Tic Tac Toe" (including on an endless board)

A new type of visual relationship between quantities. Constructing coordinates 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. Comparison of angles.

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

Types of angles.

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

Classification of triangles.

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

Constructing a rectangle using a ruler and protractor.

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

Plan and scale.

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