Math lesson "movement along a coordinate ray". Video lesson “Movement along a number line. Simultaneous movement along the number beam

LESSON PLAN

Simultaneous movement along the number line

Basic goals:

1) to form in students an idea of simultaneous movement along a number line and its types: counter, in opposite directions, after, with removal;

2) train the ability to write formulas for coordinate dependence x moving points over time t ;

3) train the ability to solve word problems using the formula for the dependence of distance on speed and time of movement.

Mental operations required at the design stage:analysis, synthesis, generalization, analogy.

During the classes

ORGANIZING TIME.

Guys, let's start our next math lesson. The famous Russian mathematician and teacher Alexey Ivanovich Markushevich said:(SLIDE 3)

“Who has been studying mathematics since childhood,

he develops attention, trains his brain, will,

fosters perseverance and perseverance in achieving goals"

I propose to take these words as the epigraph of our lesson today.

II. KNOWLEDGE UPDATED.

1. Front work. "Mathematical dictation"

Dividend 300, divisor 60. Find the quotient. (5)
How much more is 200 than 197? (3)
How many times is 32 less than 320? (10)
How many hours is 1/3 of a day? (8)
What number should you multiply 12 by to get 72? (6)
3\5 numbers are equal to 9. Find the integer. (15)
The sum of 95 and 105 divided by 20. (10)
Find the difference between the numbers 130 and 124. (6)

(Check against standard.(SLIDE 4)

A word is encrypted in the answers to the mathematical dictation. To decipher it, the alphabet of the Russian language will help us. Each answer corresponds to the serial number of a letter in the alphabet. Write the letters on a line.

What did you get? What does this word mean?

Guys, now we know that any movement can be depicted on a coordinate ray.

Today you will evaluate your work yourself during the lesson. And you will do this using a coordinate beam. Each of you has such a ray. The division value is 1 point. Give yourself as many points as the number of correct answers in the mathematical dictation.(8 points)

2. Repetition of what has been learned.

Guys, what did we work with in previous lessons?? (We worked with a numerical and coordinate beam, learned to find the distance between points, considered the movement of objects on a numerical beam, learned to write down formulas for the dependence of a point’s coordinates on time.)

Today you will continue to study movement along the number line.

Now let's remember a little about what we have learned.(SLIDE 5)

Draw a number line with a division value of 2 cells.
Enter the numbers 0, 2, 4, 6, etc.
Listen to the problem and draw it on this ray:

Dunno left the point with coordinate 6 and headed towards Button, who lives at the point with coordinate 18. He walked at a speed of 4 units per minute. Show its movement on the beam.

(1 person at the board) – 2 points

At what distance were Dunno and Button at the beginning?(The distance between Dunno and Button was initially 12 units.)

How long will the journey take?(In 3 minutes Dunno will reach Button’s house).

At what point will Dunno be in 1 minute, 2 minutes?(10, 14)

Is it possible to create a formula for the dependence of the coordinates of a point on time?

(x = 6+4 t) – 1 point

What happens to the distance to Button's house?(Decreasing)

WORKING ON THE TOPIC OF THE LESSON.

1. Statement of the problem

Now let’s imagine that Button didn’t wait for Dunno and went to meet him. Can we picture her moving? What do we need to know?(At what speed did the Button go)

Button speed 2 units/min. Show her movement.

Is it possible to determine from the diagram how long after the heroes will meet?(in 2 minutes)

At what point will this meeting take place? (14) Check the box.

What happens to distance when objects move towards each other?(The distance decreases.)

How is this problem different from those we solved before?

How would you formulate the topic of the lesson? (Motion of two objects on a number line.)(SLIDE 6)

- Let's define the purpose of our lesson.

So, we have looked at movement when objects move towards each other. How else do you think objects can move?

Today we will look at different types of tasks.

2. Work in groups.(SLIDE 7)

Draw a diagram of the movement of objects:

From what points did you come from?

In what direction are they moving and at what speed?

Answer the questions:

How did the distance between objects change?

Did the objects meet and at what point?

What can you call this type of movement?

Create formulas for the dependence of object coordinates on time.

Guys, let's take a look next task(handout Appendix 3). Frontally on the board.(SLIDE 8)

3. Drawing up reference diagrams.(SLIDE 9)

To better remember all types of problems, try making a reference summary in your notebook. 4 points

IV. PRIMARY CONFIRMATION (followed by self-test).

S. 78 No. 2 – work in pairs(SLIDES 10-11)

Tasks are performed on printed basis with pronunciation. One student completes the task on the board using the finished drawing and table.

Test yourself - 8 points

V. RESULT OF THE LESSON. (SLIDE 12)

What new did you discover in class today?
Did you achieve the goal of the lesson?
What was important to you in the lesson? https://accounts.google.com
Slide captions:
math lesson “You can’t learn math by watching your neighbor do it”
“Whoever studies mathematics from childhood develops attention, trains his brain, will, cultivates perseverance and perseverance in achieving the goal” A. I. Markushevich
Warm-up for the mind 3 10 8 6 15 10 6 MOVEMENT 1 A 3 B 10 I 4 D 5 D 6 E 7 E 8 F 9 W 11 J 2 B 12 K 14 M 21 U 15 N 16 O 17 P 18 R 19 S 20 T 22 F 13 L 23 X 25 H 32 S 26 W 27 SCH 28 B 29 S 30 b 31 E 33 I 24 C
Let's remember what we know Draw a number line with a division value of 2 cells. Enter the numbers 0, 2, 4, 6, etc. Listen to the problem and draw it on this ray.
Lesson topic: “Simultaneous movement along coordinate ray» Goal: get to know different types simultaneous movement tasks; learn to build and read diagrams for problems.
Work in groups Draw on a diagram the movement of objects: - from which points they came - in what direction they are moving and at what speed Answer the questions: - how did the distance between objects change? - did the objects meet and at what point? - What can you call this type of movement? Create formulas for the dependence of object coordinates on time.
Presentation of works
Types of tasks
We fix it – p.78 No. 2
We fix it – p.78 No. 2
To summarize: What new did you discover in class today? Did you achieve the goal of the lesson? What was important to you in the lesson? Who has a good understanding of the topic of the lesson and can explain it to others? What can you praise yourself for?
Homework: Come up with 1-2 problems for simultaneous movement. Decide by choice: No. 3 or No. 4 p.79 Optional: p.80 No.8

§ 1 Movement along a number line. Simultaneous movement along the number beam
A number beam is a beam that is directed from left to right and has a marking scale, and the beginning of the beam coincides with the number 0.

Let's draw a number line. To do this, draw a ray that is located from left to right,

let us plot a unit segment e on it several times successively from the beginning of the ray, putting down the numbers 1, 2, 3, 4, etc., respectively. The beginning of the ray is denoted by the number 0.

Let us assume that a pedestrian walks 3 unit segments in 1 hour, starting his movement from the beginning of the coordinate ray. This means that the pedestrian speed is 3 units/hour. On the coordinate beam, the speed of movement is indicated by an arrow. The length of the arrow corresponds to the speed of movement. The arrow also shows where the movement started and in which direction it is happening.

Knowing the pedestrian’s speed is 3 units/hour, we can say that in 1 hour he will be at a point with coordinate 3 or in 1 hour he will cover a distance equal to three unit segments.

After 2 hours, a pedestrian, moving at the same speed, will end up at a point with coordinate 6, or in 2 hours he will cover a distance equal to six unit segments: 3 2 = 6.

After 3 hours the pedestrian will be at the point with coordinate 12, etc. The movement of a pedestrian can be shown by marking with an arc the path traveled by him for each unit of time and highlighting the points at which he ended up.

On a coordinate beam, using the rules of movement along a numerical beam, it is also possible to show the simultaneous movement of two objects, namely:

· from what points did the simultaneous movement begin?

· in what direction and at what speed did it occur;

· how the distance between two moving objects changed - decreased or increased, and by how much;

· at what distance from each other were the objects at a given point in time;

· where and when the meeting took place (if this meeting took place).

Consider the following coordinate ray, which shows the simultaneous movement of two pedestrians.

Based on this coordinate ray, we can say that two pedestrians simultaneously walked towards each other from two different points with coordinates 0 and 20. The speed of one pedestrian is 4 units/hour, and the speed of the other is 2 units/hour. Since the movement occurs towards each other, the distance between pedestrians is reduced. After two hours of travel it will be equal to 8 units. After the first pedestrian has walked a distance of 12 units, and the second pedestrian has walked a distance of 8 units, they will meet at coordinate 12. The meeting point on the coordinate ray is indicated by a flag.

§ 2 Brief summary of the lesson topic
1. On a coordinate beam you can show and determine: the beginning of the movement of objects, the direction and speed of movement, the distance between them at different time intervals, the place and time of meeting of objects.

2. On the coordinate beam, the speed of movement is shown by an arrow. The length of the arrow corresponds to the speed of movement. The arrow also shows where the movement started and in which direction it is happening.

3. The movement of objects along a coordinate ray can be shown by marking with an arc the path they travel for each unit of time and highlighting the points at which they find themselves.

List of used literature:
1. Peterson L.G. Mathematics. 4th grade. Part 2 / L.G. Peterson. – M.: Yuventa, 2014. – 96 p.: ill.
2. Mathematics. 4th grade. Guidelines to the mathematics textbook “Learning to Learn” for 4th grade / L.G. Peterson. – M.: Yuventa, 2014. – 280 pp.: ill.
3. Zach S.M. All tasks for the mathematics textbook for grade 4 by L.G. Peterson and a set of independent and tests. Federal State Educational Standard. – M.: UNWES, 2014.
4. CD-ROM. Mathematics. 4th grade. Lesson scripts for the textbook for part 2 Peterson L.G. – M.: Yuventa, 2013.
Images used:

Okay guys. Now open your textbooks to page 69. Let’s read the text “in the frame”( one of the students is reading)
To consolidate our knowledge, let's do task 1 on page 69. Read the task. (One student reads the assignment) Look at the board, in front of you is an action plan with which we will complete this task.( A plan appears on the board: - Determine where Winnie the Pooh, Piglet, Eeyore came from?

-Where and at what speed are they going?

- How long will it take them to go all the way?

- At what point will they be 3 hours after leaving?)

Which one of you is ready to work on your first drawing? (one of the students goes to the board)

Draw the ray as shown in the textbook and mark all the data.( student draws a ray on the board)

Where did Winnie the Pooh come from?( from the point with coordinate (0), i.e. from the beginning of the ray)

goes to the right to the potty, 8 units per hour)

56:8=7 hours)

At what point will he be 3 hours after leaving?( at point 24)

Well done, we figured out the first drawing.

Let's work with the second drawing. Who will go to the board?

Where did Piglet come from?( Piglet left point 45)

Where and at what speed is it going?( moves to the beginning of the beam, where his house is located, at a speed of 5 units. in 1 hour.)

How long did it take him will pass all path?( He will cover the entire route in 9 hours.)

Where will he be in 3 hours?( In 3 hours Piglet will be at point 30.)

Well done, now we are working on the third drawing. Who will come to the board?( 3rd student comes out)

Where did Eeyore come from?( Eeyore left point 20)

Where and at what speed is it going? ( moves along the number beam to the right at a speed of 10 units. in 1 hour.)

How long will it take him to go all the way?( He will cover the entire route in 6 hours.)

Where will he be in three hours? (In 3 hours, Eeyore will be at point 50.)

We continue to work further. I suggest you work in rows. Open the textbooks on page 70 and read task 2. Complete this task yourself in rows, 1st row completes the task under the letter a, 2nd row completes the task under the letter b, 3rd row completes the letter c. Get to work, I give you 5 minutes for this task.

Look at the board and compare your solution with the standard. Row 1, check your solution.( children compare with the standard)

There are mistakes?

Where is the mistake?

Correct the mistakes.

Row 2, check your solution. (children compare with the standard)

There are mistakes?

Where is the mistake?

Correct the mistakes.

Row 3, check your solution.( children compare with the standard)

There are mistakes?

Where is the mistake?

Correct the mistakes.
Liya Nasyrova
Mathematics lesson according to the program L. G. Peterson in 4th grade “Simultaneous movement along a coordinate ray”

SUBJECT:

date: 02/09/17

Class: 4 V

Type lesson: lesson discovery of new knowledge.

Basic goals:

1) to form in students an idea of simultaneous movement along the number line and its types: counter, in opposite directions, after, with removal;

2) train the ability to write down dependency formulas x coordinates of moving points versus time t;

3) train the ability to solve word problems using the formula for the dependence of distance on speed and time movement.

Equipment: textbook, presentation, handout material.

Stages:

1. Motivation to educational activities (1-2 min)

2. Updating knowledge and trial educational action (4-5 min)

3. Identifying the location and cause of the difficulty (3-4 min)

4. Construction of a project for getting out of a difficulty (4-6 min)

5. Implementation of the completed project (5-8 min)

6. Primary consolidation with commenting in external speech (4-5 min)

7. Independent work with self-test against standard (3-5 min)

8. Inclusion in the knowledge system and repetition (5-8 min)

9. Reflection on learning activities lesson(2-3 min)

During the classes

Stages Teacher activities Student activities

Motivation for learning activities

(2 minutes) Hello guys. My name is Liya Linarovna. Today I'll give you a math lesson.

Look at the slide. Read this statement.

"Victory is where it is forward movement»

Do you agree with this statement?

You are absolutely right.

Conclusion: The main thing is to move forward towards your goal, and then victory will definitely be your reward.

Because you must always move. Strive for something and then everything will work out.

Updating knowledge and trial learning activities

(5 minutes)- Guys, what did you work with in the past? lessons?

When solving what problems did you use your number beam skills?

Today you will continue studying movement along the number line.

Before you start new topic, what should we do?

What can I offer you for this?

Right. Each of you has card number 1 on the tables.

Depict winnie the pooh movement.

The number line shows the circuit movement Winnie the Pooh to a pot of honey. Your task is to show Winnie the Pooh movement.

1) From what point did it start? movement?

2) In what direction and at what speed object is moving?

3) What happens to the distance?

Now fill out the table.

I'll give you a minute to complete the task.

Pick up a red pencil and check your answers against the standard.

What did you repeat now?

Now take card number 2.

Read the assignment. What's in it

task new?

What is the key word?

(simultaneously)

How would you formulate the topic of our lesson?

Right. The topic of our lesson« Simultaneous movement along a coordinate beam» .

Complete the task. Takes 2 minutes to complete.

(If possible, prove that the objects move like this, and how it changes movement) We worked with numerical and coordinate beam, learned to find the distance between points, considered movement objects on the number line, learned to write dependence formulas coordinates of a point versus time.

When solving problems on movement.

Repeat completed material.

Repetition task.

To repeat.

From point s coordinate 8.

Right. 4. units min

It increases

Fill out the diagram.

Self-test against the standard.

Movement along the number line.

Read the assignment.

It is necessary to depict and describe movement of two objects.)

-Simultaneous movement along a coordinate beam.

Identifying the location and cause of the problem

(4 min)- Who didn’t have time to complete the task?

What is your problem?

Please clarify what task you had to complete?

What skills did you use to complete the task?

Where did the problem arise?

Why do you think there is a difficulty?

They raise their hands.

It was necessary to depict movement, after 5 minutes the drawings collide with each other.

It was necessary to depict and describe movement two objects on the number line

Ability to describe movement objects on the number line

When pictured and described movement two objects on the number line

We do not have a rule for the case when movement two objects are involved.

Building a project to get out of a problem

(4 min)- What needs to be done to solve this problem?

What goal will you set for yourself?

What do you think will help you achieve your goals (Diagram, rules for depicting objects by numerical beam, table)

Choose a rule, a standard.

Find image method simultaneous movement of two objects along a coordinate ray and a method for analyzing the results obtained.

Knowledge, tables, diagrams, rules.

Fizminutka

(1 min)-There’s a lot ahead of us interesting discoveries. But first, let's rest.

They stood up one after another,

Raise your hands up quickly!

Rise up on your toes,

Stretch well!

Hands to the sides now

We keep our backs straight.

Let's jump once, again.

Stomp once and twice, once and twice

And now we sat down at our desks

And we will continue our lesson

Execute movement.

Implementation of the completed project

(8 min)-Take card number 3.

But before you get started, I suggest you familiarize yourself with and remember the image rules movement.

(standard on the board)

You can begin the task.

Who wants to present the result of their work?

Describe movement.

1) From what points did it start? movement.

How many minutes later did they meet (I post a support diagram movement towards each other D-8)

What happens to distance when objects moving towards each other?

What can you say about movement after the meeting and what happened to the distance between Dunno and Button?

Will objects always move closer to each other? Will it always be like this movement?

Now I will ask two students to leave. Stand with your backs to each other. Now you will move away from each other.

What happens to distance?

What is this called? movement?

Now there are two more students. One of you goes ahead, and the other catches up with him.

What happened to the distance?

How can you call this movement?

Whose should be bigger soon?

Now one of you will go in front, the other behind. Your task is not to overtake him.

What happened with the breakup?

Whose speed was greater?

Let's check if we answered the questions correctly. Let's open the textbooks on page 78. Game

« Moving dots» .

Read the assignment.

What should be done?

Let's look at the picture under letter a).

How many objects are there on the number line?

From what point did it start? movement of the first object?

From what point did it start? movement of the second object?

In what direction and at what speed did it happen?

How did the distance between the two change? moving objects, and for how long?

How far apart were the objects at a given point in time? (initial distance between objects)

Where and when did this meeting take place?

Now let's fill out the table.

Initial coordinate of point A 2. Points B 22. After 1 minute, how long will it travel? Point A 4. Point B 19.

In 2 minutes?

Now let's write the dependency formula.

How do we find the path traveled?

Let's look at all the other tables.

Objects moving in opposite directions at speeds of 6 units. /min and 9 units. /min.

The first object comes out from point 30, and the other from point 42. At first the distance between them was 12 units.

Read the rules.

Complete the task.

Anyone who wishes comes to the board.

Dunno begins movement from 0, moves to the right at a speed of 4 units. /min, after 1 minute it will be at point 4, after two minutes - 8, after 3 minutes - 12, after 4 minutes - 16, after 5 minutes - 20. Start button movement at point 40, moves to the left at a speed of 6 units/min, in 1 minute it will be at point 34, in two minutes - 28, in 3 minutes - 22, in 4 minutes - 16, in 5 minutes - 10. At the beginning of the journey, the distance between them was 40 units ., after 1 minute – 30 units, after 2 minutes – 20 units, after 3 minutes – 10 units, after 4 minutes – 0 units, after 5 minutes – 10 units)

In 4 minutes.

The distance decreases.

Dunno and Button began to move in opposite directions, and the distance between them began to increase.)

It is increasing.

-Movement in opposite directions. -

It is decreasing.

- Moving to catch up.

The second one.

It was increasing.

The speed of the first one was greater.

Depict simultaneous movement.

There are two objects on the number line.

First object moves from point A with coordinate 2.

From point B from coordinate 22.

First object moves to the right at a speed of 2 units. min

Second object moves to the left at a speed of 3 units. min

The distance between objects decreased. Decreased by the distance traveled.

The initial distance between objects is 20 units.

The meeting took place in coordinate 10.

Fill out the diagram.

Point A will be at coordinate 6 a, V in coordinate 16.

Need speed * time

Primary consolidation with commenting in external speech

(5 minutes)-Using these formulas, you need to draw a number ray and show movement of objects.

A)Ha = 16+4*t (16 original point)

They draw a beam and show movement of objects.

Independent work with self-test according to the standard

(5 minutes)- Now your task is to complete the task yourself.

Using these formulas, depict movement objects on the number line.

A) X a= 40- 4хt

B) Хz= 20 +10хt

How many rays should you get?

Pick up pencils and test yourself against the standard.

A) 4 units 5 units

Inclusion in the knowledge system and repetition

(7 min)- Let’s solve problem number 3 on page 79

Let's read the problem, what do we need to find?

To solve this task what formula will we use?

To solve the problem you need to use the formula movement:

Car 450 km 90 5 h

Cyclist 36 km 18 2 h

To answer the question in the problem, you need to know the speed of the car and the speed of the cyclist. To find the speed you need to divide the distance by time:

1) 450 : 5 = 90 (km/h) car speed

2) 36 : 2 = 18 (km/h) cyclist speed

3) 90 : 18 = 5 (once.)

Answer: the speed of the car is 5 times the speed of the cyclist

Summarize. With what types movements you met?

At what movement Will the distance between objects increase? At what point will it decrease?

Have you achieved your goal? lesson?

Speed of car and cyclist, and compare them

To solve the problem you need to use the formula movement:

Solve the problem

WITH movement towards, in opposite directions, after, behind

The distance will increase as movement in opposite directions, with a lag, and decrease - with movement towards and after

They answer.

Reflection of educational activities on lesson

(2 minutes) "Fists"

So the first statement

1)Theme I understand the lesson.

2) I achieved my goal lesson.

3) I know what types there are movements

4) I can portray simultaneous movement

5) I can fill out the table based on the picture.

Whoever has all their fingers open, give each other a high five. And those who have other fingers that are not open, don’t be upset. At home you will consolidate your knowledge.

Evaluate their activities on lesson.

Slide captions:

During the classes