Values ​​on the scale of a single view and the coordinates of the point. Video lesson “Coordinate line. Values ​​on the scale of a single view of the coordinates of the Pobudov point of the coordinate exchange

§ 1 Coordinate area

In this lesson you will learn how to use a coordinate system, as well as how to identify the coordinates of a point on a new place.

In order to get the coordinates cleared, we will need to do this first, first of all.

Significantly yogo OX, point O is the cob of exchange.

Getting ahead of ourselves, let's say that point O is called the cob for the coordinate exchange.

The line can be drawn straight at any time, but in many cases the line can be drawn horizontally and right-handed towards the cob.

Now, let’s cross it horizontally with your left hand and, significantly, straight ahead with your arrow. It is important to change point E.

We write 0 above the cob (dot), and the number 1 above point E.

The OE block is called single.

So, piece by piece, adding one piece at a time, an endless scale is created.

The numbers 0, 1, 2 are called coordinates points O, E and A. Write point O and in the arms indicate coordinate zero - O (o), point E and in the arms indicate coordinate one - E (1), point A and at the arms її coordinate two is A(2).

In this manner, in order to prompt the coordinate exchange, it is necessary for me:

1. cross the line OX horizontally with your left hand and mark it straight with an arrow, write the number 0 above the point O;

2. It is necessary to put the titles of a single section in this way. To do this, you need to mark a point that is subordinate to point O (in which place it is customary to put not a dot, but a stroke), and write the number 1 above the stroke;

3. at the end of a single section, you need to insert another single section, equal to the single one, and also put a stroke, then at the end of that section you need to add another single section, also means with a stroke and so on;

4. So that the coordinate memory is completed, you need to write down the numbers from the natural series of numbers above the strokes to the right: 2, 3, 4 and so on.

§ 2 Values ​​of coordinates of a point

Let's look at the history:

On the coordinate exchange, mark the following points: point M with coordinate 1, point P with coordinate 3 and point A with coordinate 7.

Let's create a coordinate line with the cob at point O. A single section of this line is selected 1 cm, then 2 cells (after 2 cells we put a stroke and the number 1 from zero, then after two more lines - a line and the number 2; then 3; 4 ; 5) 6; 7 and so on).

Point M will be positioned to the right of zero by two margins, point P will be positioned to the right of zero by 6 margins, so 3 multiplied by 2 will be 6, and point A will be to the right of zero by 14 margins, so 7 multiplied by 2 will be 14.

The future will come:

Find and write down the coordinates of point A; IN; і 3 values ​​​​on this coordinate exchange

This coordinate line contains a single section, which is relative to one panel, meaning the coordinate of point A is 4, the coordinate of point 8, the coordinate of point C is 12.

When choosing a pouch, pass OH with the cob at the point O, where a single cut and straight line are indicated, called a coordinate exchange. The coordinate range is nothing more than an endless scale.

The number that indicates the point of the coordinate system is called the coordinate of the point.

For example: And at the arms 3.

Read: point A at coordinate 3.

Note that often the coordinate line is shown in exchange with the cob at point O, and place a single section on the cob, at the ends of which write the numbers 0 and 1. At which section it is important that If necessary, we can easily continue the daily scale, sequentially placing single slices on the exchange.

In this way, at this point you learned to create a coordinate line, as well as to designate the coordinates of points that are located on the coordinate line.

List of Wikoritan literature:

1. Mathematics 5th grade. Vilenkin N.Ya., Zhokhov V.I. ta in. 31st view., Ster. - M: 2013.
2. Didactic materials for 5th grade mathematics. Author - Popov M.A. - 2013.
3. We will calculate without pardons. Works from self-testing in mathematics grades 5-6. Author - Minaeva S.S. - 2014.
4. Didactic materials for 5th grade mathematics. Authors: Dorofev G.V., Kuznetsova L.V. - 2010.
5. Control and independent robots in 5th grade mathematics. Author: Popov M.A. – 2012.
6. Mathematics. 5th grade: nav. for students backlighting. installation/І. I. Zubareva, A. G. Mordkovich. - 9th view, Ster. – K.: Mnemosina, 2009.

So, a single fraction and a tenth, a hundred and so on parts allow us to place them at the points of the coordinate line, which will be like the end tens fractions (as in the first butt). However, there are points on the coordinate line that we cannot locate, but which we can get as close as possible, and the coordinates are smaller and smaller to an infinitesimal part of a single section. These points represent numerous periodic and non-periodic tens fractions. Let's bring a bunch of butts. One of these points on the coordinate line represents the number 3.711711711…=3,(711) . To get to this point you need to add 3 single units, 7 tenths, 1 hundredths, 1 thousandths, 7 ten thousandths, 1 hundred thousandths, 1 millionths of a single unit, and so on. And another point on the coordinate line confirms pi (π = 3.141592 ...).

Since the elements of faceless real numbers include all the numbers that can be written in the form of finite and continuous tens fractions, then all the information contained in this paragraph allows us to confirm that each point of coordinates Now we have assigned a specific operational number to the line, which makes it clear that the different points represent different active numbers.

It is also obvious that this similarity is one-to-one. Then, we can indicate a specific point on the coordinate line that corresponds to the actual number, and we can also follow this active number by indicating a specific point on the coordinate line that matches this actual number. For this reason, we have to insert a number of single cuts, as well as tens, hundreds, and so on, of a single cut, from the cob to the required direction. For example, the number 703.405 is indicated by a point on the coordinate line, from which a cob can be drawn by putting 703 single units in a positive direction, 4 units to become a tenth of a unit, and 5 units Izkiv, which becomes a thousandth part of a single.

Also, the skin point on the coordinate line corresponds to the effective number, and the skin point number is located in the same place as the point on the coordinate line. Why is the coordinate axis often called the straight line? number line.

Coordinate point on the coordinate line

The number that represents a point on a coordinate line is called coordinate of the point.

At the previous point, we were told that each effective number is indicated by a single point on the coordinate line, so the coordinate of the point uniquely indicates the position of that point on the coordinate line. In other words, the coordinate of a point uniquely specifies that point on the coordinate line. On the other hand, the skin point on the coordinate line is represented by a single active number - the coordinate of that point.

There is nothing more to say about the accepted appointments. Write down the coordinate of the point in the round arms of the right hand in the letter with which the point is designated. For example, if point M has coordinate -6, we can write M(-6), and the notation means that point M on the coordinate line has coordinate .

List of literature.

• Vilenkin N.Ya., Zhokhov V.I., Chesnokov A.S., Shvartsburd S.I. Mathematics: handbook for 5th grade. counter-lighting installations.
• Vilenkin N.Ya. ta in Mathematics. 6th grade: hand-held tool for fire-lighting deposits.
• Makarichev Yu.M., Mindyuk N.G., Neshkov K.I., Suvorova S.B. Algebra: handbook for 8th grade. counter-lighting installations.

The coordinate of a point is the same as the “address” on the number exchange, and the number exchange is the “place” in which the number and any number can be found behind the address.

More lessons on the website

Guess what, it’s a natural series. These are all the numbers that can be selected for the order of objects so that they stand strictly in order, one by one, in a row. This series of numbers begins with 1 and continues until infinity with equal intervals between the adjacent numbers. Add 1 - and the next number is removed, another 1 - and again. I, although we didn’t take any number from this row, there are natural numbers on 1 on the right and 1 on the right. It’s more important to blame the number 1: the next one is the natural number є, and the one before it is not. 1 is the least natural number.

And one geometric figure that has a lot of color in its natural surroundings. If you are wondering about the topic of the lesson written down in school, you won’t be able to figure out what to do with it. And it’s true, the cob is washed, but the end axis is not. And it would be possible to continue chewing and continue chewing it, but the axis only seems like it would just end, and there would be nowhere else to chew it.

Vikorist and similar powers of power, together with a natural series of numbers and a geometric figure - promen.

Unusually on the cob, I am deprived of an empty place: the instruction from natural numbers can be written down and the well-known number 0. Now every natural number, which is in the natural series, can be found in the exchange of two vessels - the smaller and the larger. Having removed from zero more than one digit +1, you can subtract the number 1, and having completed the next digit +1 - the number 2... Keeping this up, we can then subtract all the natural numbers. The axis of such a view, representations on the surface, is called a coordinate dimension. We can say it more simply – in numerical terms. The smallest number is the number 0, which is called cob , every day there is a number distant from the front to the other side, and there is no greatest number, as there is no end either in exchange or in the natural series. I’ll emphasize once again that you stand between the ear of the cob and the number 1 that follows it, as well as between any other two constant numbers of the numerical exchange. This is called in a single burst . In order to calculate such a change as a number, it is necessary to place exactly the same number of separate slices from the cob.

For example, to count the number 5 on the exchange, we put 5 single cuts on the cob. To calculate the number 14 on the exchange, add 14 single cuts from zero.

As you can do in these butts, on different seats one by one the cut-outs can be different (), and on the same exchange all the same cut-outs () are equal to each other (). (Perhaps there will be a change of slides in the pictures, which will confirm pauses)

As you know, on geometric chairs it is customary to name points by the great letters of the Latin alphabet. This rule is established until the chair is on the back. The same coordinate line marks the cob point, on the numerical scale this point is represented by the number 0, and this point is called the letter O. In addition, it is significant that the point is located in places corresponding to any numbers of this bar. Now the point on my skin exchanges its song to the address. A(3), ... (5-6 point on both exchanges). The number that represents a point on the exchange (that’s the name of the point’s address) is called coordinate points. And the promin itself is a coordinate promin. Coordinate and numeric values ​​– the sense of which changes.

It is indicated that it is given – it is significant in the numerical exchange of the point behind their coordinates. Raju you will retire from this place independently from the sewer. M(3), T(10), U(7).

For this purpose we will need to use a coordinate system. Tobto -promin, cob of yakko - point O (0). Now you need to select a single section. You need it yourself vibrate so that all the necessary points fit on the chair. The highest coordinate is 10. If you place the cob in 1-2 cells on the left edge of the side, it can last longer than 10 cm. Then we take a single cut of 1 cm, which is significant on the exchange, and 10 cm from the beginning of the exchange there is the number 10. The T point corresponds to this number. (...)

And if you need to identify point H (15) on the coordinate exchange, you need to select another single section. Even so, as with the previous butt, it will no longer work, because the sewing will not fit in between the necessary visible clothing. You can select a single cut for 1 cut, and from zero to the desired point, cut 15 clicks.

Subject: "Coordinate memory."

Goals:

learn to designate coordinates and points on a numerical line, orientate yourself on a coordinate line, repeat the concept of “coordinate line”;

close your mind independently analyze and discover different types of information;

develop skills in learning and writing, calculation, logical thinking, expansiveness.

HIGH LESSON

I. Organizational moment

II. Updating knowledge

There is a place on the back of the head with a cob at the pointAbout .

Rozmova's nutrition:

What's on the back? (Promin)

What is the coordinate exchange? (No. )

Why? (No vicinity selected. )

How is a single section indicated? (learn to go to school, which means a single lesson )

Why is it called that?

How to understand the entry:U (3)?

What is the name of the number 3?

How many pointsU (3) what can be determined by the coordinate exchange? (One. )

Points C(7), E(4), M(8), T(10) are indicated. Name the coordinates of the point C, E, M, T.

She has 6 hours of students working on cards

Option I

Option II

1. Write the coordinates of the pointD , E , T іBefore

A (8), Before (12), R (1), M (9), N (6), S (3).

1. Write the coordinates of the pointM , N , Z іR , marked on the coordinate exchange.

2. Place the coordinate bar on a new pointA (6), U (5), Z (3), D (10), E (2), F (1).

III. ZUN secured.

Zavdannya 1

Sew the coordinates with a single cut of 1 cell. On your entry, enter the letters corresponding to the numbers of this key, and read the word that came out.

21

9

27

3

0

24

15

12

6

18

A

R

A

about

before

T

і

d

about

n

The concept appears - “coordinate”.

Zavdannya 2

Yaka point on Does ZM move to coordinate 5? 7? What is the coordinate of the cob of mine? Vicenach Other points of the baby.

Zavdannya 3

Name the coordinates of the point identified: telephone, medical aid point, distance, gas station.

b) Let there be one unit on the promenade 5 km away.

Yake How far is it to the phone?

How far is the gas station from the first aid station?

Zavdannya 4

Draw on the coordinate plane points A (1) and B (7), where: a) e = 2 cm; b) e = 5 mm. Find the distance between points A and B in single sections, centimeters, millimeters.
Name the three numbers that appear on the coordinate bar:
a) to the right of point A (25);b) left-handed from point B (118);c) to the right of point C (2), and to the left of point D (15);d) to the right of point E (7), and to the left of point F (8).

Zavdannya 5

Murakha spoke along the coordinate menu from point A (9) three units to the right. At what point did you get drunk? Then he preached 5 units left-handed. Is it now? How many units and in what direction did you need to get a shiver in order to immediately reach this point?

b) Murakha vyishov from point B (4) of the coordinate exchange, making two displacements of the exchange and ending at point C (7). How could there be displacement?

IV. Lesson bag

– Students name the key words of the lesson, comment on what new things they learned in the lesson.

.– The work of the class is assessed in class.

V. Homework.

Zavdannya 6

The car passed from point A of the coordinate change 6 one right-handed and stopped at point (17). Which point did you go to? How is he responsible for moving to get from point A to point C (8)?

Zavdannya 7

How many units do you need to move in order to move from point M (16) to point with coordinate: a) 14; b) 22; o 12; d) 6; e)21; e) 0; g)16?

The name is the part of the straight line that contains the cob and does not have the end (mind the sun, minus the light from the lekhtarik). Take a look at the little ones and see what the figures are, how they are similar, how they look different, how they can be called. http://bit.ly/2DusaQv

The picture shows the straight parts that form the cob and do not form the end, but in exchange, which can be called about x.

• one line of designations by great writers Oh, and the name of the other, one letter is great, and the other is small Oh;
• the first one is clean, and the other one looks like a ruler, so there is a new number on it;
• on the other side there is the letter E, and below it the number 1;
• at the right end of this line there is an arrow;
• Perhaps it can be called a numerical promin.

Another variable can be called the numerical variable Ox:

• About - the cob in front and has coordinate zero;
• write O (0); point 3 is read as coordinate zero;
• It is customary to write the number zero (0) under the dot indicated by the letter;
• section OE - single section;
• point E is coordinate 1 (indicated by a dash on the chair);
• write E(1); read point E with coordinate one;
• the arrow at the right end of the line indicates directly from whom the work is being carried out;
• We introduced a new concept of coordinates, so the concept can be called coordinate;
• Since the coordinates of various points are indicated on the exchange, then the right hand is written in the name of the exchange to a small letter x.

Pobudova coordinate exchange

We have discovered the concept of coordinate exchange and the terminology associated with it, so we can learn how to be:

• we will remember and mean Oh;
• indicated by a straight arrow;
• The number 0 means the ear of the cob;
• means a single section of OE (it may be of different lengths);
• The coordinate of point E is indicated by the number 1;
• Other points of the same type will be located on the same distance, but they are not usually placed on the coordinate line, so as not to harm the position.

For the scientific manifestation of numbers, it is customary to vikorize the coordinate line, for which number the order of growth of evil is to the right. In this way, the number rotated with the right hand is always greater than the number rotated with the left hand on the straight line.

The coordinate system starts from a point, which is called the cob of coordinates. From this point, the right hand is drawn and the right hand arrow is painted at the end. The point is coordinate 0. At the end of a single segment, a single segment is laid out, the end of which is coordinate 1. At the end of a single segment, a rotor equal to the end is placed, at the end of which we place coordinate 2 and so on. d.