X yak pobuduvat straight on the coordinate plane. Video lesson “Coordinate plane. Pose area straight

Distributed: Mathematics

Class: 6

lesson type: lesson uzgalnennya and systematization of knowledge.

Methods: verbal, academic, boys, independent work, frontal education, control and assessment

Ownership: interactive whiteboard, cards for independent work

Target: close the names of the coordinates of the assigned points and will be the points behind the given coordinates.

Lesson task:

Lighting:

uzgalnennya knowledge that vmіn uchniv on the topic "Coordinate plane";
intermediate control of knowledge and vmin uchniv.

Developing:

development of enumeration skills of students;
development of logical thought;
the development of mathematically literate language, the outlook of students;
development of smart independent work.

Vikhovny:

the development of discipline in the organization of work at the lesson;
vihovannya akuratnostі i pіd h pobudov.

Lesson structure:

Organizational moment.
Rechecking homework.
Actualization of basic knowledge.
Diagnostics acquired knowledge and learning.
Pіdbitya podsumkіv lesson.
Homework.

HID LESSON

1. Organizational moment

Today we will repeat with you that we have gone through a lot of lessons. Guess what we did with you in the lessons, like we talked about those that hit you the most, that you remember, that you lost your mind on the topic “Coordinate plane. Pobudov points behind її coordinates”. Our task: to repeat, study, systematize knowledge on the topic "Coordinate plane".

2. Homework revision

And at the same time, it’s reversible, as if you’ve done homework. Behind the given coordinates, you were to blame for the figure, one by one, at the world, wake up, sus_dni points one by one. As a result of the victorious work, you are guilty of bula viyti figure:

3. Actualization of basic knowledge

The task "Solve the crossword puzzle" will help you guess the basic concepts on the topic "Coordinate plane".
On the screen of the interactive board, a crossword puzzle is displayed and the students are taught the verses of yoga.

1. Two coordinate lines satisfy the coordinate ... (area)
2. Coordinate lines - ce coordinate ... (axis)
3. What kind of cut is established for the hour of the crossing of the coordinate lines? (straight)
4. What is the name of a pair of numbers that indicate the position of a point on a plane? (coordinate)
5. What is the name of the first coordinate? (abscissa)
6. What is another coordinate called? (ordinate)
7. What is the name of the child from 0 to 1? (alone)
8. How many parts is the coordinate plane divided by coordinate lines? (chotiri)

4. Diagnosis of acquired knowledge and learning

Points on the coordinate plane:

A(-3; 0); B(2; -3); Z(-4; 2); D(0; 4); E(1; 3); O(0; 0)

And now let's move on to figure out an additional point on the coordinate plane. Given coordinate points. Awaken the figure, wake up, wake up to the world, judgment points one with one.

Self-supporting robot.
(verification by the method of mutual verification)

Option 1.

(2; 9),
(3; 8),
(4; 9),
(5; 7),
(7; 6),
(6; 5),
(8; 3),
(8; 4),
(9; 4),
(9; -1),
(5; -2),
(5; -1),
(2; 2),
(4; -6),
(1; -6),
(0; -3),
(-4; -2),
(-4; -6),
(-7; -6),
(-7; 2),
(-8; 5),
(-5; 2),
(0; 2),
(2; 9).

Eye: (3; 5).

Option 2.

(2; 4),
(2; 6),
(0; 6),
(-1; 7),
(-1; 9),
(1; 11),
(2; 11),
(2,5; 12),
(3; 11),
(3,5; 12),
(5; 10),
(5; 9),
(8; 8),
(6; 8),
(4; 7),
(4; 5),
(5; 5),
(7; 3),
(7; -1),
(5; -3),
(0; -4),
(-3; -4),
(-9; -1),
(-9; 7),
(-6; 2),
(0; 2),
(2; 4).

Crilo:
(2; 2),
(2; -2),
(-4; 0),

Eye:
(2; 9).

5. P_dbitya p_dbag_v lesson

Nutrition teach:

1) What is the coordinate area?
2) How are the coordinate axes OX and OU called?
3) What kind of cut is established for the hour of the crossing of the coordinate lines?
4) What is the name of a pair of numbers that indicate the position of a point on the plane?
5) What is the name of the first number?
6) What is another number called?

6. Homework

P(-1.5; 10),
(-1,5; 11),
(-2; 12),
(-3; 12),
(-3,5; 11),
(-3,5; 10),
(-5; 12),
(-9; 14),
(-14; 15),
(-12; 10),
(-10; 8),
(-8; 7),
(-4; 6),
(-6; 6),
(-9; 5),
(-12; 3),
(-14; 0),
(-14; -2),
(-12; -2),
(-7; -1),
(-3; 3),
(-4; 1),
(-3; 0),
(-4; -1),
(-2,5; -2),
(-1; -1),
(-2; 0),
(-1; 1),

(-2; 3),
(2; -1),
(7; -2),
(9; -2),
(9; 0),
(7; 3),
(4; 5),
(1; 6),
(-1; 6),
(3; 7),
(5; 8),
(7; 10),
(9; 15),
(4; 14),
(0; 12),
(-1,5; 10).
P(-3.5; 10),
(-4; 6),
(-3; 3),
P(-1.5; 10),
(-1; 6),
(-2; 3).

(-2; 11),
(-3; 11)

Two mutually perpendicular coordinate lines that intertwine at the point O - cob vіdlіku, utvoryuyut rectilinear coordinate system, which is also called the Cartesian coordinate system.
The plane, where the coordinate system is drawn, is called coordinate area. The coordinate lines are called coordinate axes. Horizontal - all abscissa (Ox), vertical - all ordinates (Oy).
Coordinate axes divide the coordinate plane into four parts - four. The ordinal numbers of the quarters are taken to rank against the year's arrow.
Whether a point in the coordinate plane is given by its coordinates - abscissa and ordinate. For example, A(3; 4). Read: point A with coordinates 3 and 4. Here 3 is the abscissa, 4 is the ordinate.

I. Pobudov points A (3; 4).

Abscissa 3 show that on the cob it is necessary - points 3 solitary vіdrіzka, and then vіdklademo uphill 4 single winders and put a speck.

Tse i є speck A(3; 4).

Pobudov points B (-2; 5).

Vіd zero vіdklademo left 2 solitary winds, and then uphill 5 single winds.

We put a spot AT.

Call for a single ticket to accept 1 cell.

II. Have points at the coordinate plane xOy:

A(-3;1);B(-1;-2);

C(-2:4);D(2;3);

F(6:4);K(4; 0)

III. Determine the coordinates of the triggered points: A, B, C, D, F, K.

A(-4; 3);IN 20);

Z(3; 4);D(6;5);

F(0;-3);K(5;-2).

Sterzhuvati, if you know mathematics, it is impossible, because you cannot draw graphs, depict irregularities on the coordinate line, and work with the coordinate axes. Visual storage in scientific life is necessary, even without scientific applications in formulas and calculations, you can get lost for an hour. We marvel at these statistics, how to practice with the coordinate axes and learn the simplest graphs of functions.

Zastosuvannya

The coordinate line is the basis of the simplest types of graphs, from which the schoolboy sticks to his primary path. It is practically victorious in the skin of mathematical topics: with the development of the speed of the hour, the design of the dimensions of the objects and the calculation of their areas, in trigonometry, the hour of work with sines and cosines.

The main value of such directness is value. Shards of mathematics are a science, demonstrating the high level of abstractness of thought, graphs help the subject of the world. How to behave? At some point in the space we will perebuvatim in a few seconds, hvilin, year? What can you say about the new thing in the region with other objects? Yaku shvidkіst vіn maє vіpadkovo vibranіy moment o'clock? How to characterize yoga roc?

And about the speed of the language, it’s not without reason - it’s most often used to display the graphs of the function. And the stench can also change the temperature or vice versa in the middle of the object, its expansion, orientation along the horizon. In this manner, it is often necessary to induce a coordinate line in physics.

Single-mode chart

Understanding richness. Just one number is enough to designate the place of rotting the point. Tse yakraz i є vypadok іz zastosuvannyam coordinate line. If the space is double, then two numbers are needed. Graphs of this type are written more often, and further in the articles, they are clearly visible.

What can you do to help a point on the axis, if there is only one? It is possible to expand the scope of the object, its position in the open space like a certain "zero", that is the point, which looks like an ear to the eye.

Changing the parameters of the hour is not to be given away, the shards of all the indications are adjusted for one specific moment. However, from what it is necessary to start! Otzhe, let's do it.

How to induce the coordinate system

For the cob, it is necessary to draw a horizontal line - this will be our whole. From the right side we “gostrim” її, so that the bula looked like an arrow. In this rank, we are meaningfully directly, for which the numbers will increase. At the bіk izmenshennya, the arrow is clearly set. Traditionally, everything is directed to the right, so we just follow this rule.

Let's put a zero sign, like a cob of coordinates. Tse those same place, in the form of which one is conducted, chi is rozmіr, vaga, shvidkіst, or else. Krіm zero, we obov'yazkovo owennі znachit so zvan tsіnu podіlu, to introduce the standard of unity, vidpovіdno to the extent possible on the axis of chi іnshi values. Tse obov'yazkovo is necessary to work, to be able to know the dozhina vіdrіzka on the coordinate line.

Through the rіvnu vіdstan one vіd one we put flecks or notches on the line, and under them we write like 1,2,3 and so on. І axis, everything is ready. Ale with the schedule, sho viyshov, you need to learn how to practice.

See a point on the coordinate line

From the first glance at the proponation of the handmaidens of the little one, I realized: the specks on the axis can be zafarbovani chi not zafarbovani. Do you think it's vipadkovist? Call me! “Successive” point wins out in case of non-suvorable unevenness - ty, as it is read as “more or less one”. Well, it’s necessary to fit the interval quite well (for example, “iks” can take values from zero to one, but do not include її), we speed up with an “empty” point, which, in fact, is a small circle on the axis. Significantly, that the learners do not love the suvori nerіvnostі, because it is more foldable to work with them.

Depending on the fact that the points you win on the chart will be named and prompted intervals. Even if the unevenness from both sides is not suvor, we take it into account. If from one side of the veins a “voice” appears, then it is called a napiv_interval. Nareshti, as part of the straight line is bordered on two sides by empty points, it is called an interval.

flat

With two straight lines, we can already see the graphs of functions. Let's say the horizontal line will be in the hour, and the vertical line will be in the middle. І axis is already possible for us to signify, as if we were to lift the object for the hvilina or the time of the way. In this rank, a robot with a flat area allows you to follow the snake of the object. Tse richly tsіkavіshe, nizh doslіdzhennya static camp.

The simplest graph on such a plane is straight, it looks like the function Y(X) = aX + b. Does the line bend? Tse means that the object changes its characteristics in the follow-up process.

See, you stand on the dahu, if you look at the stone with a twisted hand. If you let yoga in, you will fly down, raising your hand from zero windiness. And yet, in a second, we will add 36 kilometers per year. The stone continues to be quick and far away, and in order to paint this ruh on the graph, you will need to freeze the swirl at a moment’s notice, placing specks on the axle at the weather.

Notes on the horizontal coordinate line behind the lock mark the name X1, X2, X3, and the vertical one - Y1, Y2, Y3 is clear. Projecting them onto the plane and knowing the peretina, we know the fragments of the resulting little thing. By going through one line, we take away the schedule of the function. At the time of the fall of the stone, the quadratic function looks like: Y(X) = aX * X + bX + c.

Scale

Obviously, it’s not necessary to place an instruction from the subdivisions on the direct target of the meaning. As you can see the flow of the roller, which will take 0.03 meters per piece of fluff, put the value on the coordinate direct fraction. For this drop, set the price for the subdivision as 0.01 meters.

It is especially handy to tie such an armchair at the cage in a cage - here you can immediately see what to stitch a seat on the arch for your schedule, so you won’t go beyond the fields. It is not easy to develop one's own strength, even if the width of a cell in such stitching is 0.5 cm. I needed it - they changed the little ones. To change the scale of the schedule, do not waste and change your powers.

Point coordinates and vіdrіzka

If a mathematical task is given at the lesson, they can have the parameters of various geometric figures, such as looking at the sides, perimeter, area, and looking at the coordinates. And here you may need to induce a figure, and take away the tribute that is tied to it. Forecasting power: how to know on the coordinate line you need information? How to wake up a figure?

For example, go about the point. Todi for the mind of the head of the figure is a great letter, and the arms are worth a sprinkling of numbers, most often two (it means, we will be pleased with the two-world expanse). There are three numbers in the arches, written through a dot with whom or through whom, the whole space. Skin z value - the coordinate on the visual axis: horizontally (X), then - vertically (Y).

Remember how to wake up the wind? You passed all the geometries. If there are two points, you can draw a straight line between them. Their coordinates are indicated in the arches, as in the problem the figure of the arches. For example: A(15, 13) - B(1, 4). In order to induce such a straight line, it is necessary to know those points on the coordinate plane, and then we will find them. From i all!

And be-yakі bugatokutniki, as you know, you can paint for help vіdrіzkіv. The task is over.

Rozrakhunki

It is possible that the first object, the position of which along the X axis is characterized by two numbers: starts at the point with the coordinate (-3) and ends (+2). If we want to recognize more than one item, then we can recognize less from a larger number. Give respect to the fact that a negative number gloats a sign of recognition, to that a minus by a minus gives a plus. Then, we add up (2 + 3) and take 5. Tse i є nebhіdny result.

Another example: we are given the last point of that object, but we are not given a post (it is necessary to know). Let the position of the home point be (6), and the size of the object that is twisted - (4). Vіdnіmayuchi dovzhina z kіntsevoї coordinates, we take into account vіdpovіd. Together: (6 - 4) = 2.

Negative numbers

It is often necessary to practically deal with negative values. In this direction, we move along the coordinate axis to the left. For example, the object of the eyelid 3 centimeters floats near the water. For a third of the wines, we are bored by the motherland, for two thirds we are resting at the front. Then, turning the surface of the water like an axis, we can calculate two numbers with the help of the simplest arithmetic: the upper point of the object is the coordinate (+2), and the lower one - (-1) centimeter.

It is not important to remember that at the slope with the flat we have settled down four coordinate lines. The skin of them may have a master number. In the first (upper right) part, the points are rotting, which form two positive coordinates, in the other - evil to the beast - the values along the "ix" axis will be negative, and along the "graves" - positive. The third and fourth wind up in the distance against the year's arrow.

Power is important

You know what can be directly represented as an impersonal point. We can look over the skils in advance, respectfully whether the skin has a small number of values, but not repeating them. Tse zdaєtsya naїvnim and zrozumіlim, but vinikaє those firm s important fact: the skin number shows one or more than one point on the coordinate line.

Visnovok

Remember that be-like wasps, figures that, according to the possibility of graphics, must be behind the line. The loners of the world were invented by a person not in a vipadkovo way - having succumbed to the chair, you look at the wrong images, it’s not enough to walk.

Be respectful and careful with prompt schedules and charges. Like and be-like a science that develops in schools, mathematics loves accuracy. Apply a little effort, and do not get good grades.

§ 1 Coordinate system: choice and method

At this level, we know the concepts "coordinate system", "coordinate plane", "coordinate axes", learn to find points on the coordinate plane.

Let's take the coordinate line x from the cob of coordinates with the point O, the positive straight line and the single vіdrіzk.

Through the cob of coordinates, the point of the coordinate line x is drawn by one coordinate line y, perpendicular to x, the positive direction is given uphill, the single line is the same. Otzhe, mi pobuduvali coordinate system.

Damo's appointment:

Two mutually perpendicular coordinate lines, which intertwine in points, as a cobweb of skin coordinates from them, establish a coordinate system.

§ 2 Coordinate all that coordinate plane

Straight lines, as if they establish a coordinate system, are called coordinate axes, for some reason they can have their own name: the coordinate line x - all abscissa, the coordinate line y - all ordinates.

The plane, where the coordinate system is chosen, is called the coordinate plane.

The described coordinate system is called rectangular. Often called the Cartesian coordinate system in honor of the French philosopher and mathematician Rene Descartes.

The skin point of the coordinate plane has two coordinates, which can be determined by dropping the perpendicular points on the coordinate axis. The coordinates of a point on the plane are a pair of numbers, for that number the first number is the abscissa, the other number is the ordinate. The abscissa shows the perpendicular to the x-axis, the ordinate - the perpendicular to the y-axis.

Significantly on the coordinate plane point A, we draw perpendiculars from it to the axes of the coordinate system.

Along the perpendicular to the abscissa axis (vіs x), the abscissa of point A is indicated, it is 4, the ordinate of point A is along the perpendicular to the ordinate axis (vіs y) - ce 3. The coordinates of our point are 4 і 3. A (4; 3). In this way, coordinates can be known whether there are points in the coordinate plane.

§ 3 Pobudov points on the plane

How to induce a point on the plane with given coordinates, tobto. behind the coordinates of the point of the plane is the її position? In this way, we vikonuemo in the reverse order. On the coordinate axes, we know the points that correspond to the given coordinates, through which we draw straight lines perpendicular to the x and y axes. Krapka peretina perpendicularіv i will be shukano, tobto. point іz given coordinates.

Let's take a look at the task: move the point M (2; -3) on the coordinate plane.

For qiu on the abscissa axis, we know the point z with coordinate 2, through the qiu point is a straight line perpendicular to the x axis. On the y-axis, we know the point with the coordinate -3 through it we draw a straight line perpendicular to the y-axis. The crossing point of the perpendicular lines i will be the given point M.

And now let's look at a sprat of okremikh vipadkіv.

Significantly on the coordinate plane of the point A (0; 2), (0; -3), C (0; 4).

The abscissas of these points are equal to 0. You can see on the small scale that all points are on the y-axis.

Later, the points, the abscissas of which equal to zero, lie on the y-axis.

We remember the coordinates of these points by points.

Viide A (2; 0), B (-3; 0) C (4; 0). In this direction, all ordinates are equal to 0 and the points are on the abscissa.

So, the points, the ordinates of which are equal to zero, lie on the abscissa axis.

Let's take two more falls.

On the coordinate plane, the points M (3; 2), N (3; -1), P (3; -4) are significant.

It is easy to remember that all abscissa points are the same. Like the z'edna points, the width is straight, parallel to the ordinate axis and perpendicular to the abscissa axis.

We ask for visnovok: the points that make the very abscissa lie on the same straight line, as if parallel to the ordinate axis and perpendicular to the abscissa axis.

If you change the coordinates of the points M, N, R by the points, then you will see M (2; 3), N (-1; 3), P (-4; 3). Ordinate points become single-mandate. In times, yakscho qi points of z'єdnati, viide straight line parallel to the abscissa axis and perpendicular to the y-axis.

In this order, the points that form that very ordinate lie on one straight line parallel to the abscissa axis and perpendicular to the ordinate axis.

At this level, you have learned the concepts of "coordinate system", "coordinate plane", "all coordinates - all abscissa and all ordinates". They learned how to know the coordinates of a point on a coordinate plane and learned how to find points on a plane behind її coordinates.

List of victorious literature:

Mathematics. Grade 6: lesson plan to assistant I.I. Zubarevoi, A.G. Mordkovich // author-sergeant L.A. Topilin. - Mnemosyne, 2009.
Mathematics. Grade 6: tutor for uchnіv zagalnosvіtnіh zakladіh. I.I. Zubarev, A.G. Mordkovich. - M.: Mnemozina, 2013.
Mathematics. Grade 6: assistant for zagalnosvitnіh zakladіv / G.V. Dorofiev, I.F. Sharigin, S.B. Suvorova and in/edited by G.V. Dorofeva, I.F. Sharigina; Russian Academy of Sciences, Russian Academy of Sciences. - M: "Osvita", 2010
Expert in mathematics - http://lyudmilanik.com.ua
Advice for students at secondary school http://shkolo.ru

Zastosuvannya

Single-mode chart

Understanding richness. In the one-world space, just one number is enough to designate the place of rotting the point. Tse yakraz i є vypadok іz zastosuvannyam coordinate line. If the space is double, then two numbers are needed. Graphs of this type are written more often, and further in the articles, they are clearly visible.

Changing the parameters of the hour is not to be given away, the shards of all the indications are adjusted for one specific moment. However, from what it is necessary to start! Otzhe, let's do it.

How to induce the coordinate system

See a point on the coordinate line

flat

With two straight coordinate planes, we can see the graphs of functions. Let's say the horizontal line will be in the hour, and the vertical line will be in the middle. І axis is already possible for us to signify, as if we were to lift the object for the hvilina or the time of the way. In this rank, a robot with a flat area allows you to follow the snake of the object. Tse richly tsіkavіshe, nizh doslіdzhennya static camp.

The simplest graph on such a plane is straight, it looks like the function Y(X) = aX + b. Does the line bend? Tse means that the object changes its characteristics in the follow-up process.

Scale

Point coordinates and vіdrіzka

And be-yakі bugatokutniki, as you know, you can paint for help vіdrіzkіv. The task is over.

Rozrakhunki

Negative numbers

Power is important

Visnovok

Be respectful and careful with prompt schedules and charges. Like and be-like a science that develops in schools, mathematics loves accuracy. Apply a little effort, and do not get good grades.