Mixed numbers. An image of ordinary fractions on the coordinate beam

For a convenient image, the fraction on the coordinate beam is important to choose the right length of the unit segment.

The most convenient option to mark the fractions on the coordinate beam - take a single segment from so many cells, what is the denominator of fractions. For example, if you want to portray the fractions with a denominator 5 on the coordinate beam, the unit cut is better to take a length of 5 cells:

In this case, the image of fractions on the coordinate beam will not cause difficulties: 1/5 - one cell, 2/5 - two, 3/5 - three, 4/5 - four.

If you want to mark the fractions with different denominants on the coordinate ray, it is desirable that the number of cells in a single section shall be divided into all denominators. For example, for the image on the coordinate ray of fractions with denominators 8, 4 and 2, it is convenient to take a single segment length in eight cells. To mark the desired fraction on the coordinate beam, a single segment is divided into as many parts, what is the denominator, and we take such parts as much as the numerator. To portray a 1/8 fraction, a single segment is divided into 8 parts and take 7 of them. To portray a mixed number 2 3/4, we count two whole single segments from the beginning of reference, and we divide the third parts and take three of them:

Another example: the coordinate ray with fractions, the denominators of which are 6, 2 and 3. In this case, in this case, it is convenient to take a length of six cells as a single thing:

Lesson plan

Ordinary fractions

date

Capesova A.A.

Class: 5.

Participated: everything

Did not participate: 0

Theme lesson:

An image of ordinary fractions and mixed numbers on the coordinate beam

Training goals achieved in this lesson (reference to the curriculum)

5.5. 2 .3

coordinateordinarye fractions, mixed numbers;

The purpose of the lesson:

Build a coordinate beam and choose an optimal single segment;

Picture ordinary fractions on the coordinate beam.

Evaluation criteria

Pictures ordinary fractions on the coordinate beam.

Builds the coordinate beam and selects a single segment;

Language objectives

part, beam, single segment, correct fraction, irregular fraction

Education of values

M. әngilіk ate: society of universal labor.

Intergovernmental communications

Artistic work. economy

Previous knowledge

Know the concept of the beam;

Can build a coordinate beam, choose a single segment;

Can be marked natural numbers on the coordinate beam;

During the classes:

Beginning of the lesson

Organizing time.

To create a psychological atmosphere, he holds the game "I like in you"

Children take each other by hands and smile, call good qualities of their classmates.

Combining into groups

"Magic Pouch"

Students from the bag get candy and sit in groups of candies.

Actualization of knowledge.

Exercise 1.

Oral work.

Work in pairs.

What are the elements of the fraction standing above the line, under the line?

What action can be replaced by a fractional line?

What part of the figure is painted?

Determine what part of the figure is painted with gray. Give several answer options.

Students work in a pair are then discussed in the group what is happening with the teacher.

Descriptors:

Calls the elements of the fraci

Understands that it shows the denominator and the numerator of the fraction;

Knows the main property of the fraction

Feedback: pupil - student, student - teacher.

Candy

Handout

Cards

Answers are shown by the teacher (interactive board)

interactive board

Middle lesson

Exit on the topic:

Guys are already known how natural numbers are depicted on the coordinate direct.

Is it possible to depict ordinary fractions on the coordinate direct? (Pupil Answer)

The teacher voiced the topic of the lesson "An image of ordinary fractions on the coordinate beam ».

Distributes the finished material, where students in the group are studying.

Definition. The number corresponding to the point of the coordinate beam is called the coordinate of this point.

To portray the correct fraction on the coordinate ray.

Split a single segment to an equal number of parts corresponding to the number in the denominator.

From the beginning of reference to postpone the number of equal parts corresponding to the number in the fractional numerator.

Sample: To portray a fraction on the coordinate beam, you need to divide a single segment to 9 equal parts and count 5 such parts.

About A.

0 1 H.

Task 2. . "Check yourself"

Mount the flashing point on the coordinate beam.

- Find the coordinates of the points

Descriptors:

Understands what the denominator of the fraction will mean;

Understands what the numerator of the fraction means;

Notes on the coordinate direct corresponding point;

Records its coordinate.

Feedback: "Traffic light"

Students show cards depending on the correctness of the answer:

Green color- Agree, right;

Yellow color - I doubt, there is a question;

Red color- do not agree, wrong

Fizminutka:

Once - bend, get risen

Two - burn, turn

Three three cotton bush

Head three nodies

Four hands wider

Five, six - sit quietly

Seven eight laziness throw.

Task 3.

Method "Jicks".

Position the point A () on the coordinate ray; IN(); FROM().

Draw a coordinate beam, take a section with a length of 1 cm for a single segment. Mark on it:

Point A (6). Set the right and to the left of it segments equal to 2 single segments. Record the coordinates of the points received.

Draw a coordinate beam, take 20 cells of the notebook for a single segment. Mark on it points with coordinates :; What numbers are depicted by the same point.

Descriptors:

Knows how to build a coordinate beam

Knows how to choose a single segment;

Knows how to record the coordinates of the points obtained

Performs a reduction of fractions

Found equal fractions.

Students evaluate the solution with the help sheet of answers

Feedback:

Green-faith

Yellow - need to refine (there are errors)

Red - not right

An inteese board.

Aktivstudio.

List of answers

Stickers (green, yellow, red)

End of the lesson

Lesson's activity reflection

At the lesson, I worked active / passively

I am satisfied with your work / unhappy

The lesson for me seemed short / long

For a lesson, I'm not tired / tired

My mood has become better / became worse

The lesson material was clear to me / incomprehensible

Useful / useless

Interesting / uninteresting

I know …….

I can…….

I need to learn ....

Homework.

differentiated tasks (students themselves choose tasks from the level of complexity).

Cards

With differentiation

tasks

Differentiation - What way do you want to provide more support? What tasks do you give students more capable compared to others?

Diffensed tasks cards

Evaluation - how do you plan to check the level of learning the material by students?

F.O. Corporative, competence

"Thumb up or down", fizminutka, traffic light,

Health and Compliance Property

security

Fizminutka, TB rules when working with an interactive board

The number consisting of an integer part and fractional part is called a mixed number.
In order for the wrong shot to imagine in the form of a mixed number, it is necessary to divide the fluster to the denomoter, then the incomplete private will be a whole part of a mixed number, the residue is a fractional part with a numerator, and the denominator will remain the same.
To present a mixed number as an incorrect fraction, you need to multiply a whole part of the mixed number to the denominator, to add a fractional parts numerator to the resulting result and write in the numerator of the wrong fraction, and the denominator leave the same.

The fractional part means the sign of the division. In the column, we divide the numerator13 to the denominator 3. Private 4 will be a whole part of a mixed number, the residue 1 will become the numerator of the fractional part, and the denominator 3 will remain the same.
Write a mixed number in the form of incorrect fraction:

Number 3 - the integer part of the mixed number is multiplied by the denominator 7 of the fractional part, the number 2- a large part of the fractional part of the mixed number is added to the resulting product; Result 23 will be a numerator of the wrong fraction, and the denominator 7 will remain the same.

An image of ordinary fractions on the coordinate beam
For a convenient image, the fraction on the coordinate beam is important to choose the right length of the unit segment.
The most convenient option to mark the fractions on the coordinate beam - take a single segment from so many cells, what is the denominator of fractions. For example, if you want to portray the fractions with a denominator 5 on the coordinate beam, the unit cut is better to take a length of 5 cells:

In this case, the image of fractions on the coordinate beam will not cause difficulties: 1/5 - one cell, 2/5 - two, 3/5 - three, 4/5 - four.
If you want to mark the fractions with different denominants on the coordinate ray, it is desirable that the number of cells in a single section shall be divided into all denominators. For example, for the image on the coordinate ray of fractions with denominators 8, 4 and 2, it is convenient to take a single segment length in eight cells. To mark the desired fraction on the coordinate beam, a single segment is divided into as many parts, what is the denominator, and we take such parts as much as the numerator. To portray a 1/8 fraction, a single segment is divided into 8 parts and take 7 of them. To portray a mixed number 2 3/4, we count two whole single segments from the beginning of reference, and we divide the third parts and take three of them:

Another example: the coordinate ray with fractions, the denominators of which are 6, 2 and 3. In this case, in this case, it is convenient to take a length of six cells as a single thing:

Questions to the abstract

Dana dots and. Find the length of the car cut.

Sections: Mathematics , Competition "Presentation to the lesson"

Class: 5

Presentation to the lesson

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purpose: To form the ability to record and read the fractions, depict their points on the coordinate direct.

Type of lesson: learning lesson with new material.

Equipment: computer, projector.

Didactic LESSONS: POWER POINT presentation, workbooks with printed basis (RT).

During the classes

I. Organizational moment.

Message Topics and setting lesson purposes. (Slide 2)

The teacher also reports that the "smart owl" will help in the lesson.

II. Oral work. (Slides 3-6)

1. Write down what part of all the figures are: a) one any figure, b) circles, c) squares, d) triangles?

2. What part of the figure is painted?

3. Determine which part of the figure is painted with gray. Try to give several answers options.

4. Read the fractions.

III. Mathematical dictation. (Slides 7-9)

The teacher welcomes all tasks, then students exchange notebooks and perform a check using slides 8-9. (Estimation criteria: 6 tasks - "5", 5 tasks - "4", 4-3 tasks - "3".)

(Tasks 1, 5, 6 - general, tasks 2-4 - by options).

1. Write down the fraci: two thirds, eleven twelve, seven fifths, one hundreds, fifteen sixth, eight seventh, twenty-three hundredths, nine ninth.
2. Which of these fractions are the correct (incorrect)?
3. Write down the three correct (incorrect) fractions with denominator 7.
4. Write down the three incorrect (correct) fractions with a numerator 5.
5. Record the fraction, the numerator of which is 5 units less denominator.
6. Write down the fraction, the denominator of which is 3 times the numerator.

IV. Formation of skills and skills.

1. Preparatory stage in the formation of a new skill. (Slides 10-12)

Correct parts from a log?

RT Part 1, No. 85. Write down with the help of a fraction, which part of the segment is highlighted in blue.

Performing this task, students are based on the meaning of the fraction: the denominator shows how the segments were divided, and the numerator shows how many such parts were taken.

W. No. 747 (executed by students on the board).

O. 748 (Perform independently followed by checking). (Slide 12)

2. Image of fractions of points on the coordinate direct. (Slides 13-17)

Mount the flashing point on the coordinate beam.

Find the coordinates of the points.

RT Part 1, No. 94, 95, 98. (Slide 18)

№ 94. Enter the appropriate fraction above each marked point.

No. 95. Note on the coordinate direct point corresponding to the specified fractions.

№ 98. Note on the coordinate direct number 1.

Fizkultminutka. (Slides 19-22)

W. No. 749 (orally), 750. (Slide 23)

Independent work. (Slide 24)

Dany points ... Which of them are the right (left) 1?

V. The outcome of the lesson.

There is a way to build a point with a given coordinate and once again the question of choosing a single segment convenient for the construction of these fractions is discussed.

Vi. Homework. (Slide 25)

P. 8.2. № 751, 752, 761, 765.

Date: 13 /02/2017 ___________

Class: 5

Thing: mathematics

Lesson number : 129

Theme lesson: " An image of decimal fractions on the coordinate beam.».

Objectives and objectives of the lesson:

Educational:

To form the ability to depict decimal fractions on the coordinate beam, find the coordinates of the points depicted on the coordinate beam;

Developing:

– continue to work on development: 1) to observe, analyze, compare, prove, draw conclusions; 2) mathematical and general horizons; 3) evaluate their work;

Educational:

– to form the ability to express your thoughts, listen to others, to conduct dialogues, defend your point of view; Shape self-esteem skills.

During the classes

I. Organizational moment , greeting, wishes of fruitful work.

Check if you have prepared everything for a lesson.

II. Setting the goals of the lesson.

Guys look carefully on today's lesson. What do you think, what will we do with you today in the lesson? Let's try to formulate the objectives of the lesson.

III. Actualization of knowledge. All students are written in notebooks, one student behind a closed board. The teacher checks the work on the board, after which all students compare and correct errors.

1) Mathematical dictation.

1. Three integer one tenth.

2. Five as much as eight tenths.

3. One whole five tenths.

4. Zero as seventy hundredths.

5. Seven whole twenty five hundredths.

6. Zero to sixteen hundredths.

7. Three whole hundred twenty-five thousandths.

8. Five whole twelve hundredths.

9. Ten whole twenty-four hundredths.

10. One whole three tenths.

Answers:

1. 3,1

2. 5,8

3. 1,5

4. 0,75

5. 7,25

6. 0,16

7. 3,125

8. 5,12

9. 10,24

10. 1,3

2) oral work

(1) Read decimal fractions:

3) Let's remember!

To mark the point on the coordinate beam, you need ...

What letter is the point on the coordinate beam?

How does the point coordinate record?

3. Studying a new material.

Decimal fractions on the coordinate beam are also depicted as ordinary fractions.

(2) 1)

The number 3.2 contains 3 entire units and 2 tenths of the unit shares. First, note on the coordinate beam, the point corresponding to the number 3. Then the next single segment is separated by ten equal parts and count the two parts to the right of the number 3. So we get a point A on the coordinate beam, which depicts a decimal fraction 3.2. The distance from the beginning of the reference to the point A is 3.2 single segments. (A \u003d 3.2).

Pictures on the coordinate ray decimal fraction 3.2.

2) depict the decimal fraction 0.56 on the coordinate ray.

4. Fastening the material studied.

(3) 1. The road from Karatau to Cocktal is 10 km. Petya passed 3 km. What part of the road he passed?

1. How many equal parts is divided all the way? ( on 10 pieces )

2. What will one part of the path be equal? (1/10 or 0.1)?

3. What will be the three parts of such a path? (0.3)?

1. What numbers are noted by points on the coordinate direct.

(4) 2.

A (0.3); B (0.9); C (1,1); D (1.7).

A (6.4); B (6.7); C (7.2); D (7.5); E (8,1).

A (0.02); B (0.05); C (0.14); D (0.17).

(5) 3.

E.

(6) 4. Instruct the coordinate beam. For a single segment, take 5 cells of the notebook. Find on the coordinate ray of points A (0.9), in (1,2), C (3.0)

(7) Working with a textbook

(8) 5. Fizkultminutka, exercise for attention.

Differentiated work with students (Work with gifted and weakly speaking students).

6. Summing up the lesson.

Guys What new did you know today at the lesson?

Do you think we managed to achieve your goals?

Reflection.

What do you think guys have reached the goal?

What did you know in the lesson? - What did you learn in the lesson?

What did you like in the lesson? What difficulties arose?

(9) 7. Homework :

The reference sheet to the lesson " An image of decimal fractions on the coordinate beam ».

1. Read decimal fractions:

0,2 1,009 3,26 8,1 607,8 0,2345 0,001 3,07 27,27 0,24 100,001 3,08 3,89 71,007 5,0023

2. Pictures on the coordinate ray decimal fraction 3.2.

a) The number 3.2 contains 3 entire units and 2 tenths of a single share.

b)Pictures on the coordinate ray decimal fraction 0.56.

3. The road from Karatau to Cocktal is 10 km away. Petya passed 3 km. What part of the road he passed?

1. How many equal parts is divided all the way?

2. What will one part of the path be equal?

3. What will be the three parts of such a path?

4. What numbers are noted by points on the coordinate direct.

5. On the coordinate direct, some points are denoted by letters. Which point corresponds to the number 34.8; 34.2; 34.6; 35.4; 35.8; 35.6?

6. Instruct the coordinate beam. For a single segment, take 5 cells of the notebook. Find on the coordinate ray of points A (0.9), in (1,2), C (3.0)

7. Working with a textbook : Open in the textbook on page89, perform the number: No. 1254 (task for the smelter).

8. Calculate the figures like this: "First triangle, first angle, first circle, second angle, etc."

9. Homework :

1. Task number on the board

2. Come up with a fairy tale, which should begin like this: in some kingdom, in some state, which called the "State of Numbers" lived - there were fractions: ordinary and decimal