Point, line, straight line, ray, segment, broken line. side AB and side BC are adjacent

We will look at each of the topics, and at the end there will be tests on the topics.

Point in mathematics

What is a point in mathematics? A mathematical point has no dimensions and is indicated by capital letters. with Latin letters: A, B, C, D, F, etc.

In the figure you can see an image of points A, B, C, D, F, E, M, T, S.

Segment in mathematics

What is a segment in mathematics? In mathematics lessons you can hear the following explanation: a mathematical segment has a length and ends. A segment in mathematics is the set of all points lying on a straight line between the ends of the segment. The ends of the segment are two boundary points.

In the figure we see the following: segments ,,,, and , as well as two points B and S.

Direct in mathematics

What is a straight line in mathematics? The definition of a straight line in mathematics is that a straight line has no ends and can continue in both directions indefinitely. A line in mathematics is denoted by any two points on a line. To explain the concept of a straight line to a student, you can say that a straight line is a segment that does not have two ends.

The figure shows two straight lines: CD and EF.

Beam in mathematics

What is a ray? Definition of a ray in mathematics: a ray is a part of a line that has a beginning and no end. The name of the beam contains two letters, for example, DC. Moreover, the first letter always indicates the starting point of the beam, so letters cannot be swapped.

The figure shows the rays: DC, KC, EF, MT, MS. Beams KC and KD are one beam, because they have a common origin.

Number line in mathematics

Definition of a number line in mathematics: a line whose points mark numbers is called a number line.

The figure shows the number line, as well as the OD and ED rays

Instructions

The sun can be drawn in the following way. First, draw a yellow circle on paper. Then draw triangular rays around it using rounded lines different shapes and different sizes.

The sun can also be drawn with even, identical rays in the shape of triangles with rounded sides.

The sun looks very unusual, the rays of which are braided into thin, neat braids with bright bows at the ends.

The sun with rays in the form of curved arrows looks quite peculiar.

Sources:

draw the sun

Many artists have created their works in which there are sunflowers. The most famous painting With same name belongs to the brush of Vincent Van Gogh. Sunflowers are very bright large flowers that are quite easy to draw. It is with them that you can begin to comprehend the art of drawing still lifes.

You will need

- Soft pencil.
- Round brush No. 6.
- Paints.
- Paper (preferably whatman paper) or canvas.

Instructions

Stretch the canvas or secure a sheet of whatman paper. First you need to outline general outlines compositions. If you draw in, then make a few strokes that will indicate the head of the flower, its stem and leaves, and in the background indicate a fence, a field, and a horizon line. If suggests a sunflower in flower arrangement, then draw the outline of a vase, table, drapery, and other flowers in the composition.

To make the star more interesting and shining, lengthen some of its rays a little (for example, through one). You can make the edges of the rays not straight, but figured, jagged.

Shade the outline Star of Bethlehem yellow paint warm shade. Give volume to the rays of the star: from its center, draw straight lines to each of the eight vertices and to the connecting points of the rays, dividing them into halves. Do this using a thin brush with yellow paint of a darker yellow-orange shade. Paint one of the resulting halves of each ray with the same paint.

Since the Star of Bethlehem mentioned in the Gospel moved, indicating the Magi, many are inclined to consider it a comet. Therefore, this star is often depicted with a long, arched tail. Draw the side of the star expanding towards the end, like a comet. The end of the tail can be shaped in a zigzag or wavy line, or you can smoothly reduce it to nothing when coloring the picture.

Paint the trail of the Star of Bethlehem with yellow paint, and use yellow-orange paint to make a few strokes along it, showing the movement of the extraordinary celestial body. Closer to the base of the star, you can make a texture from small, densely strewn dots, and towards the end of the tail - from more sparse ones.

Even in ancient times, people said that freckles- this is a sign of spring. Indeed, people with freckles on their faces seem more open, carefree and cheerful. But what about those who desperately want to have these red spots, but their skin, unfortunately, does not allow it?

You will need

foundation / self-tanner / henna

Instructions

The most in a simple way How to get freckles is to apply them with a special one, and its color should be as close as possible to the tone of your face. This way the hemp will look more natural. You can give painted spots a natural look by applying small layer foundation powder. The disadvantage of this method is that such freckles They wash off very easily and quickly, and you will have to reapply them every morning.

Another way is to create freckles using natural dye.
To do this, you need to buy a bag of henna at the nearest pharmacy (if you buy it at an oriental goods store, do not forget to specify to the seller that you need finely ground henna, since only such a mixture does not form lumps). Then mix the contents of the purchased sachet with warm or slightly hot water until a homogeneous mass is obtained. After this, cover the henna with plastic and place it in a warm place for at least 12 hours (this is necessary for the mixture to infuse and acquire a rich shade).

When the mixture is ready, apply it pointwise to those parts of your face where you would like to have freckles. Leave for a while and rinse with warm water. Remember that the longer you keep the mixture on your face, the darker your appearance will be. freckles.

To change the color of henna and, accordingly, freckles to a lighter or dark shade, add ground coffee, tea or lemon juice to the mixture. The content of sugar, essential oil or lemon juice in henna allows freckles to stay on the skin maximum amount time.

The most radical and most durable way is to draw funny spots in a tattoo parlor. The essence of this procedure is as follows: paint of a certain color is selected to match the color of the skin (usually a golden hue), which is subsequently thin needles applied under the skin. Yes, this procedure is not very pleasant, and it costs a lot of money, but final result, rest assured, will exceed all your expectations. Freckles made in the salon look very natural and beautiful. They usually last from a year to several years, after which they fade painlessly in the sun.

Video on the topic

You will get an even five-pointed star only by using drawing tools - a ruler, a protractor and a compass, and the last two items are equally interchangeable.

You will need

A sheet of paper, a simple pencil, an eraser, a ruler, a protractor or a compass.

Instructions

Prepare the necessary tools and a sheet of paper for the job. If you don't have a compass, then use a protractor. on paper with a simple pencil circle. To do this, use any round object - a cup, wide tape, plate, recording disk, etc. On the resulting circle, draw a ruler horizontal line, dividing the circle in half. Then draw in the middle of the horizontal line vertical line, dividing the circle into four even parts.

Place a protractor on the horizontal line so that the vertical line passes through the ninety-degree mark. Mark an angle of seventy-two degrees and place a dot on the circle. Then turn the protractor counterclockwise and position it so that it lies on the vertical line and the horizontal line passes through the ninety-degree mark. Again mark the angle of seventy-two degrees and place a point on the circle. Next, mark the remaining points.

Use a ruler to construct a five-pointed star, connecting the dots. Use an eraser to erase unnecessary lines. The straight star is ready.

Rovna star can be constructed using a compass. To do this, use a ruler to draw a horizontal line. Then build a vertical line that intersects the horizontal line at right angles at point O. From point O, using a compass, draw a circle of arbitrary radius. Mark the intersection points of the circle and lines with points V and D.

Using a ruler, divide the segment DA in half and mark its middle with point A. Around point A, draw an arc through point V so that the arc intersects the horizontal line. Designate the intersection point as point B. The segment VB will be the side of the pentagon into which you inscribe star.

Starting from point V, mark the points of a regular pentagon on the circle. Having placed five points, connect them using a ruler in the shape of a five-pointed star. Use an eraser to erase unnecessary lines.

Rays the suns passing through the clouds give the landscape a picturesque look. Unfortunately, such a scene is not always possible to capture with a camera. However, you can draw rays in Photoshop program and overlay them on the photo.

You will need

- Photoshop program;
- photo.

Instructions

Open a photo suitable for applying lighting effects in Photoshop editor. Rays you will need to edit without affecting the photo. To get this opportunity, add a new layer on top of it using the combination Ctrl+Shift+N.

Many perceive the Sun not only as an object for the study of astronomy, the source of life on Earth in the most pragmatic sense, but also as a symbol of goodness, joy, and sincerity. It’s not in vain that the good ones good people often affectionately called "sunshine". Now we will look at several options for how to draw the sun.

Sunny with a cheerful face

First, let's draw a cute, cartoon version of the sun with a smiling face. Of course, this option is more suitable for children - it will perfectly teach the child how to draw the sun beautifully. But such sunshine will also certainly give an adult a boost of positivity.

First, let's outline the main figure - a circle.

Then we will depict the details of the face - large shiny eyes, a smile, small eyebrows and blush on the cheeks.

And, of course, you need to draw the rays. They will form a single figure, similar to a crown.

Now let's color our masterpiece - the circle will be yellow, the rays will be orange, and the eyes will be soft blue.

That's all, the sun is drawn.

The sun with big eyebrows

Let's continue the theme of cartoon suns. This time our celestial body will not only have big eyes and a dazzling smile, but also thick dark eyebrows. And also freckles. This is a very fun example of how to draw a sun step by step.

Like last time, let's start with a circle. This will be the most basic figure.

Then we outline the angular rays different sizes. This way they will look more natural.

After this, we will begin to depict the face: the eyes will be elongated and dark, the mouth will be large, and the eyebrows, as we agreed, will be thick and dark. And don't forget about freckles!

Sun with little eyes

Time to try out another style - although in this case the sun’s “face” features will be very small, it will look incredibly cute. You can see this for yourself if you try to learn how to draw a sun with a pencil.

The beginning, according to tradition, will consist of the image of a circle. Try to make the figure as even and correct as possible. Don't worry if you don't succeed the first time: it's lovely pencil technique is that all shortcomings can be quickly corrected.

Now the rays. Here they will be smooth, triangular, curly.

Time to do some face work. Small dotted eyes, a shy smile, circles of blush - isn’t it adorable?

On this note we will finish - the drawing is ready.

Widely smiling sun - recharge yourself with positivity

What could be more positive than the sun literally beaming with joy? This can cheer up even the gloomiest and most stressful day. So if you want to always maintain an upbeat mood, you should learn how to draw the sun with a smile. The children's song spoke the truth - it really makes things brighter.

As in all other cases, our sun will be round. The circle should be smooth and beautiful.

Now - oval eyes with highlights and a wide smile.

After this we will draw the rays. They will be very peculiar, curved, like tongues of flame. Moreover, short rays will alternate with long ones.

Now let’s carefully draw all the contours. It is best to do this with a felt-tip pen or marker.

Now everything is ready - smile at your sunshine. And no rain is scary now!

The sun doesn't care about rain - draw the sun with an umbrella

In autumn the sky is often cloudy. Many people do not like this, because gray, rainy weather causes despondency and sadness. But our sun is not afraid of either clouds or rain, because for such cases he has a wonderful umbrella. Let's depict it - at the same time we will learn how to draw the sun with paints.

First of all, let's draw a cloud, soft and fluffy in appearance.

Now there is a round sun with an open mouth in a smile, a funny button nose and cute eyes. True, for now it will be somewhat similar to Kolobok.

Now let’s depict our main weapon in the fight against clouds - a folded umbrella. By the way, our shining character will have gloves on his hands.

Time to draw the rays - writhing, uneven, almost alive. And we’ll make polka dots on the umbrella.

Time to start painting. Let's make the “Taurus” yellow, the rays and nose red, the umbrella pink, and the cloud blue. You can use any paints - watercolor, gouache, acrylic or even oil.

Now ours bright drawing finished.

Goals:

Introduce students to the concept of a ray as endless figure;
Learn to show the beam using a pointer;
Continue building computing skills;
Improve problem solving skills;
Develop the ability to analyze and generalize.

During the classes

I. Organizing time.

Guys, are you ready for the lesson? ( Yes. )
I count on you, friends!
You are a good friendly class.
Everything will work out for you!

II. Motivation for learning activities.

I really want the lesson to be interesting, informative, so that together we repeat and consolidate what we already know and try to discover something new.

III.Updating knowledge.

Read the numbers and name the “extra” number in each row:
a) 90, 30, 40, 51.60;
b) 88, 64,55,11, 77, 33;
c) 47, 27, 87, 74, 97, 17;
List the numbers in order:
a) from 20 to 30;
b) from 46 to 57;
c) from 75 to 84;
Do you think these texts will be tasks?

Change the question in the second text so that it becomes a task.

Change the condition so that the text becomes a task.

Solve the given problems.

IV. Primary assimilation of new knowledge.

Draw a line like this.

What is it called?

Draw a line like this.

What is it called? What is the difference between a segment and a straight line?

Draw a line like this.

Who knows what it's called?

Look at the picture, you see similar lines, what is it?

This line is called a ray. How does it differ from a straight line and a segment?

This is very interesting figure: It has a beginning and no end.

And this is how they portray her. ( Work on the board and in notebooks.) Mark a point, apply a ruler to it and draw a line along the ruler.

No matter how long the ruler is, we still won’t be able to draw the entire beam. In the figure we have depicted only part of the beam, which shows the direction of the beam.

The beam can be drawn in any direction:

Draw three different rays in your notebook.

To distinguish one ray from another, we will agree to denote the ray with two letters of the Latin alphabet in the same way as we denoted segments. The letters must be written in a strictly defined order: the first letter is written that indicates the beginning of the beam, the second is written above or below the beam.

Look at the picture in the textbook. The red beam is indicated by two letters. What letter indicates the beginning of the ray?

Let's read the entry together: “Beam AB”

Now read the following entries: beam BC, beam MK, beam BA, beam OX.

It is important to learn how to show the beam correctly. We will do this with the end of the pointer. ( Demonstration by the teacher.)

Now look at the poster. ( Prepared in advance, it has 3 rays.) It shows 3 rays. Read the title of each one. When naming a beam, show it with a pointer.

Fizminutka

1, 2, 3, 4, 5
We all know how to count.
We also know how to relax:
Let's put our hands behind our backs,
Let's raise our heads higher
And let's breathe easily.
One, two - head up,
Three, four - the legs are wider,
Five, six - quiet network.
Once - get up, stretch.
Two – bend over, straighten up.
Three - three claps of your hands,
Three nods of the head.
By four – your arms are wider.
Five - wave your arms.
Six - sit quietly at your desk.

V.Initial check of understanding.

1) Working with the textbook.

Is it possible to draw the entire beam?

In what direction can the ray be drawn?

Students name each ray by first reading the letter corresponding to the beginning of the ray.

Students draw a ray in their notebooks and label it with letters.

Place point O in your notebook. Draw a straight line through it. How many rays did you get?

Draw another straight line through this point. How many rays are there now?

VI. Organization of mastering methods of activity.

1) Work in a printed notebook.

Differentiated task.

1st group - No. 19

2nd group - No. 20

3rd group - No. 21

2) Fizminutka - ophthalmic simulator.

3) Working from the textbook

Read what addition methods did Znayka come up with?

Find the results of addition using the same methods.

What is known about the problem?

What do you need to know?

In short – is it more or less?

How to find out the length of a pencil?

Write down your answer.

VII. Reflection.

What new did you learn in the lesson?

What is a beam?

How to draw a ray?

How many rays can be drawn through one point?

Today in class they helped me.....

VIII. Homework.