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23.01.2024

Presentations 6 coordinates on a straight line. Coordinate line

Direct coordinates

Presentation for a 6th grade math lesson

math teachers

MBOU Secondary School No. 86 named after Rear Admiral I.I.Verenikin


POSITIVE NUMBERS:

NEGATIVE NUMBERS:


POSITIVE NUMBERS:

Start of counting (or origin ) – point O represents 0 (zero). The number itself is 0 is neither positive nor negative . It separates positive numbers from negative ones.


The straight line is located vertically.

The positive direction is marked with an arrow.

Positive coordinates of points are located above point O, and negative coordinates of points are located below.


A STRAIGHT WITH AN ORIGIN OF REFERENCE, A UNIT SEGMENT AND A DIRECTION SELECTED ON IT IS CALLED A COORDINATE STRAIGHT.

THE NUMBER SHOWING THE POSITION OF A POINT ON A LINE IS CALLED THE COORDINATE OF THIS POINT.





  • Where will the squirrel be located if it moves 3 m away from the hollow? How many answers can you give?
  • Where will the squirrel be if it is located:

A) 2 m above the hollow;

B) below the hollow by 3 m;

B) below the hollow by 1.5 m;

D) 2.5 m higher than the hollow.


Mound

Omsk

270 km

270 km

260 km

630 km

Chelyabinsk

Novosibirsk

Petropavlovsk

The train left the Petropavlovsk station and is traveling at a speed of 90 km/h. Which city will the train arrive in 3 hours?

Where will the train be located:

A) in 10 hours, if he goes to Novosibirsk;

B) in 5 hours, if he goes to Chelyabinsk?


A group of tourists leaves a sports camp and moves along the highway.

Show where the tourists will be:

A) after 3 hours, if they walk at a speed of 3 km/h;

B) after 2 hours if they are walking at a speed of 4 km/h.

What else do you need to know so that there is only one answer to each question?


While on a hike, tourists visited

at points K, M and R.

Where are these points located in relation to the camp?




PRACTICAL

TASKS


Write down the coordinates of the points shown in the figure.


1. Draw points A(1), B(8,3), C(-6), D(6), M(-2,4), K(2,4) on the coordinate line.

2. Mark a point on the coordinate line that has coordinate x, if x = -7; 3.3; -5.2; -1; 2; -1.8;


Name any three numbers located on the coordinate line:

A) to the right of the number 11;

B) to the left of the number -8;

B) to the left of the number -820;

D) to the right of the number -78.


QUESTIONS:

  • What is a coordinate line?
  • What is the coordinate of a point on a line called?
  • What numbers are the coordinates of points on a horizontal line located: a) to the right of the origin;

b) to the left of the origin of coordinates?

4. What is the coordinate of the origin?

  • What numbers indicate the coordinates of points on a vertical line located:

a) above the origin of coordinates;

b) below the origin?

This presentation is devoted to the second lesson in the study of the topic "Coordinates on a straight line." The presentation opens with oral work, which consists of ten tasks on different topics of the course: is the proportion correct, solve the proportion, make a proportion, etc. The material for this part of the presentation is taken from lesson developments in mathematics grade 6 (author V.V. Vygovskaya). The work also presents slides with drawings for problems No. 893, 894, 918,902 and 906 (based on the textbook “Mathematics. 6” by N. Ya. Vilenkin and others). Showing pictures on a slide will attract students' attention to the problem being solved and will allow them to complete these tasks more effectively.

View document contents
"Presentation. Direct coordinates. 6th grade."


Oral work

No. 1. Is the proportion correct:

Solution: 1 way (by determining the proportion)

Method 2 (according to the main property of proportion)


Oral work

No. 2. Solve the proportion: 3.5: x = 0.8: 3.2.

No. 3 . Solve the proportion:


Oral work

No. 4. Make up a proportion: 9 4 = 3 12.

Solution: 9:3 = 12:4;


Oral work

No. 6. What is the length of a distance of 200 m on the plan if the map scale is 1: 1000?

Solution: 200 m = 20,000 cm;

20,000: 1000 = 20 (cm) length on the card.

Answer: 20 cm.


Oral work

No. 9. Which is greater: 5% of 80 or 80% of 5?


Oral work

No. 10. There are 25 people in the class. Of these, 15 are boys. What percentage of students are girls?



Where is each bird located in relation to the knot in the rope? (Cage side 1 dm)




Used Books.

  • Mathematics. 6th grade. Textbook for educational institutions. N. Ya. Vilenkin, V. I. Zhokhov, A. S. Chesnokov, S. I. Shvartsburd.

2. Lesson developments in mathematics. 6th grade. V.V. Vygovskaya.

The educational presentation on the topic “Coordinates on a Line” has a clear structure, the material is presented in a logical sequence and is supported by the necessary drawings. The font size and color palette are easy on students' eyes and allow them to clearly see slide elements from all areas of the classroom. The presentation is not oversaturated with animation effects, so students are maximally concentrated on the teacher’s explanation, and not on the animation.

slides 1-2 (Presentation topic "Coordinates on a straight line", examples)

The presentation of new material begins with the consideration of straight line AB and point O, which splits this straight line into two additional rays. After which they select a unit segment and agree to call it the origin of coordinates. Students are explained that the position of a point on each of the rays is specified by a coordinate, and in order to distinguish the coordinates from each other on these rays, they put a “+” sign in front of the coordinate for one ray, and a “-” sign in front of the coordinate of the other ray. In this way, students are introduced to the concepts of “positive” and “negative” numbers.

slides 3-4 (examples, definition of a coordinate line, point coordinates)

The entire explanation occurs in stages, each moment is depicted on the slide, and the necessary examples are given. Students' attention is drawn to the fact that for the sake of brevity, the “+” sign is usually omitted when writing positive numbers. In addition, the presentation emphasizes that point O represents zero, which in itself is neither a positive nor a negative number - it simply separates positive numbers from negative ones.

slides 5-6 (examples, questions)

The questions proposed on the last slide are intended to quickly monitor students' acquired knowledge as a result of viewing the presentation with an accompanying explanation from the teacher. This will make it possible to quickly identify students’ misunderstanding of any aspects of the educational material discussed. In turn, schoolchildren must demonstrate not only reflexive reproduction of the material they heard, but also analyze the necessary concepts of the topic, correctly formulate and express their thoughts.

An educational presentation on the topic “Coordinates on a Line” can be used not only during school classes, but also for distance learning or independent study by schoolchildren.

The lesson is developed taking into account a differentiated approach to teaching: the key points of the lesson are compiled on the basis of a lesson constructor, which takes into account the psychological characteristics of students - the type of thinking. Here you can see the organization of a situation of success, taking into account the psychophysiological characteristics of students, in stages, since learning, like any activity, can be represented in the form of the following sequence of actions: setting up an activity; ensuring the student’s activities taking into account his individual psychological characteristics; comparison of the obtained results with the expected ones. Therefore, at these stages of the lesson, work is distributed between right-hemisphere and left-hemisphere students.
The set of materials for left-brain and right-brain students is different.

Lesson type: lesson in learning new knowledge

Lesson type: explanatory and illustrative

The purpose of the lesson:

  • Educational aspect: further formation of the foundations of a functional line through the introduction of the concept of a coordinate line; creating an approximate basis for the ability to find the coordinates of a straight line and construct points according to given coordinates;
  • Developmental aspect: creating conditions for developing the ability to transfer known methods of action to a new situation;
  • Educational aspect: fostering a sense of responsibility for one’s actions (inaction), involvement in everything that happens in the classroom.

Lesson structure:

Stage 1: Statement of educational task
Stage 2: Updating knowledge
Stage 3: Introducing new concepts and ways of doing things
Stage 4: Primary consolidation
Stage 5: Lesson summary
Stage 6: Homework instruction

Basic methods: conversation, demonstration

Equipment and teaching materials:

  • Computer,
  • Projector,
  • Magnets
  • Presentation on the topic “Coordinates on a straight line”,
  • Didactic materials: card for determining the coordinate line,
  • A set of cards with test tasks for “left-hemisphere” students.

DURING THE CLASSES

Teacher activities

Student activities

 Features of using tasks for students with different functional brain asymmetries
Left hemisphere Right hemisphere
Organizational tap Write down the number
Classwork
Stage 1

Stage objectives:

  • Prepare for the upcoming work
  • Ensure understanding and acceptance of the learning task for the lesson and for the future.
You have six equations in front of you, your task is to solve them and say which action helped you find the roots. (Let left-hemisphere students solve equation 6 on their own). Solve equation No. 6 independently, participate in solving equations. Orally solve equations 1-5 Slide 2 For left-hemisphere people, a task aimed at depth of knowledge. High need for mental activity. To develop the need for further education. For right-hemisphere creative tasks (make a sentence)
While the guys are finding the roots of equation No. 6, make up a sentence from these words that will be the epigraph of today's lesson Solve an equation, participate in making a proposal Make a proposal, express your versions Slide 3
This statement belongs to the ancient Greek scientist Pythagoras. I suggest writing the epigraph in your notebook Write down in notebooks Slad 4
Let's go back to the equations and solve the last one.
What equations could we not solve in elementary school, and why?		 They offer their own answers.
Answer questions		 Write down in notebooks.
Answer questions		 Slides 5-6
So, since we did not come to a common answer, we had difficulties. Maybe there are new numbers that will help you find the root of the equation. And what is the task in class today? Get acquainted with new numbers that you have not studied before.
Stage 2

Stage objectives:
Create conditions for

  • Reproduction of the concepts of coordinate ray;
  • reproducing the general scheme of actions when determining the coordinates of a given point and when constructing a point according to given coordinates on a coordinate ray.
And in order to learn new numbers, let’s remember where you can place all the numbers that you have studied. What is the "home" for all numbers? Coordinate beam. Left hemisphere - tasks related directly to theory.
Construct a coordinate ray. What is needed to build it? Constructing a coordinate ray
Unit segment, beginning, direction.
Challenge the student to mark points with coordinates 5; 3.5; 1/2 Mark the points
Stage 3

Stage objectives:
Create conditions for

  • analysis of a new situation;
  • motivation for introducing a coordinate line;
  • transferring known methods for determining the coordinates of a point and constructing a point from its coordinates on a ray to the situation of a coordinate line;
  • introducing an indicative framework for new actions.
What happens if we continue the ray and build an additional ray to this one? Do it.
Will it be a simple straight line?

The result will be straight.
They build an additional beam to this one.
No.
They express their ideas.
It turns out that there are also numbers on the left.
Do you think the number 5 has the same meaning for winter and summer? They come to new numbers with a minus sign.
Maybe you know what these numbers with a minus sign are called? Where do these numbers exist? They express their versions.
These numbers are located to the left of 0.
So what numbers is the lesson dedicated to? (if they can’t, then name these numbers).
Let's write down the topic of the lesson.		 Negative.

Write down the topic of the lesson.
Let's analyze how we got negative numbers, a new straight line. All actions are reproduced.
Name all the elements.
They go out onto the coordinate line.		 Slide 7
Who can formulate the definition of a coordinate line.
So, what do we call the numbers on the left? On right?		 Formulate a definition.

On the left are negative numbers.
On the right are positive ones.

 Slide 7
Take card number 1. ( Annex 1 ) You can make explanations for yourself so as not to forget how the definition is formulated. Add the necessary information for the formulation Formulated according to the card
In what location did you meet the coordinate line? Give examples from life and solve the problem. In vertical Give examples. Slide 8
Check whether the points on the coordinate line are marked correctly? Raise your hands if you agree. Name the points, tell you at what distance from the origin these points should be marked Those who agree raise their hands. Slide 9.
Determine the temperature, name the coordinate. Write down the answers in your notebook.
(independent work)		 Slide 10. Right-hemisphere tasks that demonstrate a connection with life.
Test yourself! They check and correct errors. Slide 11.
Stage 4

Stage objectives:
Creating conditions for students to carry out new actions:

  • determining the coordinate of a point on a coordinate line;
  • constructing a point on a coordinate line at a given coordinate.
Guys, do you like to travel? I propose to take a journey for positive and negative numbers “Across the Mountains and Oceans” Right-hemisphere and left-hemisphere students work in pairs, since each has their own way of conveying information to the other, which benefits both participants in the educational process.
Complete the task from textbook No. 902, page 151. Fill out card No. 2 ( Appendix 2 ) You work in pairs. Fill out the table. Slide 13.
Now let's take a trip and check how you coped with the task. Check and correct errors Name the answers. Slides 14-24
The next trip will be to cities in different countries. Take card number 3. ( Appendix 3 ). I will show you a city with the corresponding temperature at the time of January 10, and your task is to mark the values ​​of the corresponding temperature and the name of the city on the coordinate line. (ask right-brain people) Marked on the coordinate line. Read the name of the city and the temperature.
Marked on the coordinate line.		 Slides 25-32
I hope you completed this task successfully, please check. Check Slide 34 Commitment to theory.
Establishing coordinates The next journey is “On the Temperature Scale”. Looking at the slide
Slide 35 Take card number 4 ( Appendix 4 ). Fill it out yourself, using knowledge from the field of geography, your own intuition, since not all values ​​are given, and the entire table must be filled out Fill out the table
Slide 36 Which one of you has perfect knowledge? Raise your hands who filled out the entire table correctly? They check the answers.
Slides 37-38 The journey is not over, now you will find yourself in the role of a submariner or a sniper. And who is who, you will find out on card No. 5 ( ). Complete the task. Establish a correspondence between a point and its coordinate. Decipher the word. Solve the problem and write it down in your notebook.
We check the snipers. Name points and coordinates. Decrypted word They look and check.
Slides 38-40 Checking submariners They look, listen, check. Give the answer to the problem Slide 41
Commitment to practice. A challenge from life. The journey ends at the Olympic Games. What can the table tell us? Answer questions. They give an answer.
Stage 5

Stage objectives:
Slides 42-44
organize primary reflection of the results of students’ own activities in the lesson. So, a lot of work has been done. Let's go back to the beginning of the lesson, what was the problem? They couldn't solve the equation.
Slide 45 -1
Maybe we can solve this equation now? How do we write the solution to the equation? They dictate the decision.
Slide 46 You will get acquainted with solving equations later, but now everyone will check how they worked in the lesson. Take card number 6 ( Appendix 6 ) (left-hemisphere), and the rest work orally. Perform the test They answer the question. They tell everything about numbers. Slide 47
For right-hemisphere students, oral type tasks and open-ended questions (own detailed answer) are required. For left-hemisphere people – closed-type questions (select a ready-made answer option) Let's check those who performed the test. Read the question and give your answer. They look, listen, and object if the answer is wrong.
Slides 48-52 What's great about what you discovered in this lesson? Share their own impressions.
Stage 6

Stage objectives:

  • Slide 53
  • formulate the purpose (learning task) of homework;
indicate possible means of support to achieve the goal Homework:
№898, №897

learn to build points with given coordinates, set the coordinates of points. Your assistants:

read the text on pp. 147 -148, answer the questions after the paragraph.

 Write down the task in your diary.
Slides 54-55
You did a great job today.		 Thank you for the lesson! Take colored magnets and place them on the coordinate line in that part of your mood from the lesson (negative or positive)
Attach magnets to the board where the coordinate line is depicted.

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