To mark a fraction on the coordinate beam you need. Image of ordinary fractions and mixed numbers on the coordinate beam

A number consisting of an integer part and a fractional part is called a mixed number.
In order to represent an improper fraction as a mixed number, it is necessary to divide the numerator of the fraction by the denominator, then the incomplete quotient will be the integer part of the mixed number, the remainder will be the numerator of the fractional part, and the denominator will remain the same.
To represent a mixed number as an improper fraction, you need to multiply the integer part of the mixed number by the denominator, add the numerator of the fractional part to the result and write it in the numerator of the improper fraction, and leave the denominator the same.

The fractional part means the division sign. In a column, divide the numerator 13 by the denominator 3. The quotient 4 will be the integer part of the mixed number, the remainder 1 will become the numerator of the fractional part, and the denominator 3 will remain the same.
Write the mixed number as an improper fraction:

The number 3 - the integer part of the mixed number is multiplied by the denominator 7 of the fractional part, the number 2 is added to the resulting product - the numerator of the fractional part of the mixed number; the result 23 will become the numerator of the improper fraction, while the denominator 7 will remain the same.

Image of ordinary fractions on the coordinate beam
For a convenient representation of a fraction on a coordinate ray, it is important to correctly choose the length of a unit segment.
The most convenient option to mark fractions on the coordinate ray is to take a single segment from as many cells as the denominator of the fractions. For example, if you want to depict fractions with a denominator of 5 on the coordinate ray, it is better to take a single segment with 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 it is required to mark fractions with different denominators on the coordinate ray, it is desirable that the number of cells in a single segment be divisible by 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 eight cells long. To mark the desired fraction on the coordinate ray, we divide the unit segment into as many parts as the denominator, and take as many such parts as the numerator. To represent the fraction 1/8, we divide the unit segment into 8 parts and take 7 of them. To depict the mixed number 2 3/4, we count two whole unit segments from the origin, and divide the third into 4 parts and take three of them:

Another example: a coordinate ray with fractions whose denominators are 6, 2 and 3. In this case, it is convenient to take a six-cell segment as a unit:

Questions for abstracts

Given points and . Find the length of segment AB.

The date: 13 /02/2017 ___________

Class: 5

Subject: maths

Lesson # : 129

Lesson topic: " Image of decimal fractions on the coordinate beam.».

Goals and objectives of the lesson:

Educational:

To form the ability to represent decimal fractions as points on the coordinate ray, to find the coordinates of the points depicted on the coordinate ray;

Developing:

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

Educational:

– to form the ability to express one's thoughts, listen to others, conduct dialogues, defend one's point of view; develop self-esteem skills.

During the classes

I. Organizational moment , greetings, wishes for fruitful work.

Check if you have prepared everything for the lesson.

II. Setting lesson goals.

Guys, look carefully at the topic of today's lesson. What do you think we are going to do in class today? Let's try to formulate the objectives of the lesson together.

III. Knowledge update. All students write in notebooks, one student behind a closed board. The teacher checks the work on the board, after which all students compare and correct the mistakes.

1) Mathematical dictation.

1. Three point one.

2. Five point eight.

3. One point five.

4. Zero point seventy.

5. Seven point twenty-five hundredths.

6. Zero point sixteen hundredths.

7. Three point one hundred and twenty-five thousandths.

8. Five point twelve.

9. Ten point 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 the decimals:

3) Let's remember!

To mark a point on a coordinate ray, you must ...

What letter marks a point on a coordinate ray?

How is the coordinate of a point written?

3. Learning new material.

Decimal fractions on the coordinate beam are depicted in the same way as ordinary fractions.

(2) 1)

The number 3.2 contains 3 whole units and 2 tenths of a unit. First, we mark a point on the coordinate ray corresponding to the number 3. Then we divide the next unit segment into ten equal parts and count two such parts to the right of the number 3. So we get point A on the coordinate ray, which represents the decimal fraction 3.2. The distance from the origin to point A is 3.2 unit segments. (A=3.2).

Let's draw the decimal fraction 3.2 on the coordinate ray.

2) Draw the decimal fraction 0.56 on the coordinate beam.

4. Consolidation of the studied material.

(3) 1. The road from Karatau to Koktal is 10 km. Petya walked 3 km. What part of the road did he walk?

1. How many equal parts is the whole path divided into? (for 10 parts )

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

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

1. What numbers are marked with dots on the coordinate line.

(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. Draw a coordinate line. For a single segment, take 5 cells of the notebook. Find points A (0.9), B (1.2), C (3.0) on the coordinate beam

(7) Working with the textbook

(8) 5. Physical education, attention exercise.

Differentiated work with students (work with gifted and low-achieving students).

6. Summing up the lesson.

Guys, what did you learn at the lesson today?

Do you think we have achieved our goals?

Reflection.

What do you guys think, have we achieved our goal?

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

What did you like about the lesson? What difficulties have arisen?

(9) 7. Homework :

Reference sheet for the lesson " Image of decimal fractions on the coordinate beam ».

1. Read the decimals:

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. Let's draw the decimal fraction 3.2 on the coordinate ray.

a) The number 3.2 contains 3 whole units and 2 tenths of a unit.

b)Let's draw the decimal fraction 0.56 on the coordinate beam.

3. The road from Karatau to Koktal is 10 km. Petya walked 3 km. What part of the road did he walk?

1. How many equal parts is the whole path divided into?

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

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

4. What numbers are marked with dots on the coordinate line.

5. On the coordinate line, some points are marked with letters. Which of the points corresponds to the number 34.8; 34.2; 34.6; 35.4; 35.8; 35.6?

6. Draw a coordinate ray. For a single segment, take 5 cells of the notebook. Find points A (0.9), B (1.2), C (3.0) on the coordinate beam

7. Working with the textbook : open in the textbook on p. 89, perform the number: No. 1254 (task for ingenuity).

8. Count the shapes like this: "First triangle, first corner, first circle, second corner, etc."

9. Homework :

1. Task number on the board

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

For a convenient representation of a fraction on a coordinate ray, it is important to correctly choose the length of a unit segment.

The most convenient option to mark fractions on the coordinate ray is to take a single segment from as many cells as the denominator of the fractions. For example, if you want to depict fractions with a denominator of 5 on the coordinate ray, it is better to take a single segment with 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 it is required to mark fractions with different denominators on the coordinate ray, it is desirable that the number of cells in a single segment be divisible by 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 eight cells long. To mark the desired fraction on the coordinate ray, we divide the unit segment into as many parts as the denominator, and take as many such parts as the numerator. To represent the fraction 1/8, we divide the unit segment into 8 parts and take 7 of them. To depict the mixed number 2 3/4, we count two whole unit segments from the origin, and divide the third into 4 parts and take three of them:

Another example: a coordinate ray with fractions whose denominators are 6, 2 and 3. In this case, it is convenient to take a six-cell segment as a unit:

Lesson Plan

Common fractions

the date

Kapezova A.A.

Grade:5

Participated: all

Did not participate:0

Lesson topic:

Image of ordinary fractions and mixed numbers on the coordinate beam

Learning Objectives Achieved in This Lesson (link to syllabus)

5.5. 2 .3

draw on a coordinate linecommone fractions, mixed numbers;

The purpose of the lesson:

Build a coordinate ray and choose the optimal unit segment;

Draw ordinary fractions on a coordinate line.

Evaluation criteria

Depicts ordinary fractions on a coordinate beam.

Builds a coordinate ray and selects a single segment;

Language tasks

part, ray, unit segment, proper fraction, improper fraction

Value Education

M әngіlіk el: The Society of General Labor.

Interdisciplinary communication

Artistic work. economy

Previous Knowledge

Know the concept of a beam;

They can build a coordinate ray, choose a single segment;

They can mark natural numbers on the coordinate beam;

During the classes:

Lesson start

Organizing time.

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

Children take each other's hands and smile, name the good qualities of their classmates.

Grouping

"Magic bag"

Students take out candy from the bag and sit in groups according to the color of the candy.

Knowledge update.

Exercise 1.

oral work.

Work in pairs.

What are the elements of the fraction above and below the line called?

What action can replace the fractional line?

What part of the figure is shaded?

Determine which part of the figure is shaded in gray. Give multiple answers.

The students work in pairs, then discuss as a group and check with the teacher.

Descriptors:

Names the elements of a fraction

Understands that shows the denominator and numerator of the fraction;

Knows the basic property of a fraction

Feedback: student - student, student - teacher.

Candies

Handout

Cards

Answers shown by the teacher (interactive whiteboard)

interactive board

Middle of the lesson

Output on the topic:

Guys, you already know how natural numbers are depicted on a coordinate line.

Is it possible to represent ordinary fractions on a coordinate line? (Students answer)

The teacher announces the topic of the lessonImage of ordinary fractions on the coordinate beam ».

Distributes finished material, where students in a group study it.

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

To depict a proper fraction on a coordinate ray, you need:

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

From the origin, set aside the number of equal parts corresponding to the number in the numerator of the fraction.

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

O A

0 1 x

Task 2 . "Check yourself"

Mark a blinking point on the coordinate beam.

- Find coordinates of points

Descriptors:

Understands what the denominator of a fraction means;

Understands what the numerator of a fraction means;

Marks the corresponding point on the coordinate line;

Records its coordinate.

Feedback: "Traffic light"

Students show cards depending on the correct answer:

Green color - agree, correct;

Yellow color - I doubt there is a question;

Red color - disagree, wrong

Fizminutka:

One - bend, unbend

Two - bend down, turn around

Three in a lodoshi three claps

Three head nods

Four arms wider

Five, six - sit quietly

Seven eight laziness discard.

Task 3

Jixo method.

Draw points A () on the coordinate ray; AT(); FROM().

Draw a coordinate ray, take a segment 1 cm long as a single segment. mark on it:

Point A (6). Set aside to the right and left of it segments equal to 2 single segments. Write down the coordinates of the obtained points.

Draw a coordinate ray, take 20 cells of the notebook as a single segment. Mark points on it with coordinates: ;. What numbers are represented by the same dot.

Descriptors:

Able to build a coordinate beam

Able to select a single segment;

Able to record the coordinates of the received points

Performs fraction reduction

Finds equal fractions.

Students evaluate the solution using the answer sheet

Feedback:

green-correct

Yellow - needs to be finalized (there are errors)

Red is wrong

Interactive board.

Aktivstudio

Answer sheet

Stickers (Green, Yellow, Red)

End of the lesson

Reflection of activities in the lesson

During the lesson, I worked actively / passively

I am satisfied / dissatisfied with my work

The lesson seemed short / long for me

For the lesson I was not tired / tired

My mood got better/worse

The material of the lesson was clear / incomprehensible to me

Useful / useless

Interested / uninteresting

I know …….

I can…….

I need to learn....

Homework.

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

Cards

With differential

fixed tasks

Differentiation – how do you want to be more supportive? What tasks do you give students who are more capable than others?

Cards with differentiated tasks

Assessment - how do you plan to check the level of mastery of the material by students?

F.O. Mutual appraisal, self-appraisal

"thumb up or down", physical minute, traffic light,

Health and safety

security

Fizminutka, safety rules when working with an interactive whiteboard