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.
The image of ordinary fractions on 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.
Mathematics 5 "B" class
Date: 12/14/15
Lesson #83
Lesson topic: Display of common fractions and mixed numbers on the coordinate line.
The purpose of the lesson:
1. To form the concept of a coordinate beam among students.
2. To develop the ability and skills of the image of ordinary fractions on the coordinate beam.
3. To cultivate a sense of collectivism, the ability to listen to others.
Lesson type: generalization and systematization of the material covered.
Teaching methods: partially search, self-test method.
During the classes.
І. Organizing time.
“Here in Kazakhstan, life will be better than in other countries. I promise you this"
N.A. Nazarbayev
Dear students!
Our lesson is taking place on the eve of the Independence Day holiday. - But speaking about the state, it is impossible to remain silent about the head of state - the President of the Republic of Kazakhstan - N.A. Nazarbayev. The word president, translated from Latin, means "sitting in front"! The President ensures that the laws of the Constitution are not violated, the President protects the sovereignty of the state! December 1, 1991 N.A. Nazarbayev became the first President of sovereign Kazakhstan. And for many years Nazarbayev has been the first President of our state, thanks to this, the welfare of our country is growing, sports complexes, kindergartens, schools are being built, entertainment centers, health complexes.
And I propose to start our lesson with the following task.
Let's solve the problem:
1. Determine how old N. Nazarbayev is, if it is known that the President has ruled the country for 25 years, which is 1/3 of his age. How old is he?
25*3/1=75 years.
Checking homework. (tasks on cards)
correct and improper fractions
1. Select the whole part.
2. Write an improper fraction as a mixed number
Answers: A) 17; IN 1; C) 3;
3. Express the mixed number 5 as an improper fraction
Answers: A); AT) ; FROM) ;
4. Select the whole part.
a) 12 c) 25 c) 16 d) 15
5. Convert to an improper fraction.
6. Express an improper fraction as a mixed number as an improper fraction
Answers: A); AT) ; FROM) ; d)
Key (written on the board):
Oral account (on cards)
Math simulator ( Students have 5 minutes to complete their assignment. )
Explanation of the new topic
Let's move on to the main part of our lesson.
Write down the topic of the lesson.
coordinate beam. The image of ordinary fractions and mixed numbers on the coordinate beam.
Burkina S.
All sorts of shots are needed
Fractions are important
Learn the fraction
Then your luck will shine
If you know fractions
To understand their exact meaning
It will even become easy
Difficult task.
Let's go up the stairs step by step.
On the way up, we will repeat the past and learn new things.
Update basic knowledge
What are the elements of the fraction above and below the line called?
What action can replace the fractional line?
What is the division of the numerator and denominator by the same number called?
Work on the study of new material.
1. Flipchart ( repeating the definition of the coordinate ray )
2. Working with the reference diagram
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:
1. Divide a single segment into an equal number of parts corresponding to the number in the denominator.
2. From the origin, set aside the number of equal parts corresponding to the number in the numerator of the fraction.
For example:
Physical education minute
Dear Guys! We have already covered half of the way, but there are still many difficulties ahead, so it's time to take a break and spend some physical education.
We've done a good job
And have a good rest
We will recharge
And let's go on the road again.
Repeat all movements after me.
Hands behind your back, heads back
Let your eyes look at the ceiling.
Let's lower our eyes, look at the desk,
And up again - where is the fly flying?
Let's move our eyes, look for her,
And we decide again, a little more.
Now everyone is rested and you can continue on your way.
Solving tasks from the textbook.
Each of you has a task to solve. № 888, 889
. (the solution is carried out in notebooks).
The image of ordinary fractions on the coordinate beam.
Readers
Draw a coordinate ray, take 9 cells of the notebook as a single segment. Mark points on the coordinate beam: u 
Reshalkins
Draw a coordinate ray, take 10 cells of the notebook as a single segment. Mark on the coordinate beam the numbers:
Smekalkins
Draw a coordinate ray, take 12 cells of the notebook as a single segment. Mark point N on the coordinate ray, set aside segments on both sides of the point NA and NB with a length equal to a single segment. Find the coordinates of points A and B.
Lesson summary
Do you think fractions are fractions? small part something? which is not worth paying attention to.
And if, building your house, the one in which you live
The architect was wrong in the calculation by a small fraction.
To happen, you know?
The house would have turned into a pile of ruins.
You step on the bridge, it is reliable and durable.
Wouldn't an engineer be accurate in his drawings?
Three tenths - and the walls are erected obliquely,
Three tenths - and the cars will collapse from the slope.
Make a mistake only three tenths of a pharmacist,
It will become a poison, a medicine, it will kill a person.
Homework . Learn the theory from paragraph 5.6, solve No. 890, 891, 892
REFLECTION: And now you have to evaluate your work in the lesson.
Draw a face and rate yourself.
"5" "4" "3"
Back forward
Attention! Preview slides are for informational purposes only and may not represent the full extent of the presentation. If you are interested this work please download the full version.
Target: to form the ability to write and read fractions, to represent them as points on a coordinate line.
Type of lesson: lesson of acquaintance with new material.
Equipment: computer, projector.
Didactic support of the lesson: presentation power point, workbooks with a printed base (RT).
During the classes
I. Organizational moment.
Reporting the topic and setting the objectives of the lesson. (Slide 2)
The teacher also informs that “Smart Owl” will help in the lesson.
II. oral work. (Slides 3-6)
1. Write down what part of all the figures are: a) any one figure, b) circles, c) squares, d) triangles?
2. What part of the figure is shaded?
3. Determine which part of the figure is shaded in gray. Try to give multiple answers.
4. Read the fractions.
III. Mathematical dictation. (Slides 7-9)
The teacher says all the tasks, then the students exchange notebooks and check using slides 8-9. (Evaluation criteria: 6 tasks - “5”, 5 tasks - “4”, 4-3 tasks - “3”.)
(Tasks 1, 5, 6 - general, tasks 2-4 - by option).
- Write down the fractions: two thirds, eleven twelfths, seven fifths, one hundredth, fifteen sixths, eight sevenths, twenty three hundredths, nine ninths.
- Which of these fractions are correct (improper)?
- Write down three proper (improper) fractions with a denominator of 7.
- Write down three improper (proper) fractions with the numerator 5.
- Write a fraction whose numerator is 5 less than the denominator.
- Write a fraction whose denominator is 3 times the numerator.
IV. Formation of skills and abilities.
1. Preparatory stage to the development of a new skill. (Slides 10-12)
How to saw parts from a log?
RT Part 1, No. 85. Using a fraction, write down which part of the segment is highlighted in blue.
When completing this task, students rely on the meaning of the fraction: the denominator shows how many equal parts the segment was divided into, and the numerator shows how many such parts were taken.
U. No. 747 (performed by students on the board).
U. 748 (perform independently with subsequent verification). (Slide 12)
2. The image of fractions with dots on the coordinate line. (Slides 13-17)
Mark a blinking point on the coordinate beam.
Find the coordinates of the points.
RT part 1, No. 94, 95, 98. (Slide 18)
No. 94. Write the corresponding fraction over each marked point.
No. 95. Mark on the coordinate line the points corresponding to the indicated fractions.
No. 98. Mark the number 1 on the coordinate line.
Fizkultminutka. (Slides 19-22)
U. No. 749 (oral), 750. (Slide 23)
Independent work. (Slide 24)
Given points ... Which of them are located to the right (to the left) 1?
v. Summary of the lesson.
The method for constructing a point with a given coordinate is generalized and the question of choosing a unit segment convenient for constructing the indicated fractions is discussed once again.
VI. Homework.(Slide 25)
Clause 8.2. No. 751, 752, 761, 765.
Name of the institution GU "Secondary school-
gymnasium No. 9 "
Position math teacher
Work experience 8 years
Mathematics subject
Topic Image of common fractions and mixed numbers
on the coordinate line.
Topic: The image of ordinary fractions and mixed numbers on the coordinate beam.
Target:
1. educational: generalize, systematize the knowledge and skills of students on this topic; to form subject and mathematical functional literacy;
2. developing: develop memory, logical thinking, attention and mathematical speech;
3. educational: develop the skills of joint activities, a sense of collectivism, the ability to listen to comrades, work in a group.
Lesson type: consolidation of learned knowledge.
Lesson equipment: 16 laptops, interactive whiteboard.
We need all sorts of fractions,
Fractions are important to us.
Study them diligently
And luck will come to you.
Kohl fractions, you will know
And understand their exact meaning,
That will be easy
Even a difficult one.
During the classes
I.Organizing time. Psychological mood of the class. (1 minute.)
Guys, I smile at you, you smile at me. They say that a smile and good mood always helps to cope with any task and achieve good results.
Let's try to test this wonderful rule in today's lesson.
II.Pinning a new topic(checking the theory learned in the previous lesson):
1) Oral survey. (7 min.)
1. What is a coordinate line?
(A ray with a given unit segment is called coordinate beam.)
2. What is a single segment?
(A segment whose length is taken as a unit is called single cut.)
3. What is a point coordinate?
(The number corresponding to the point of the coordinate ray is called coordinate of this point.)
4. What numbers can be drawn on the coordinate line?
(On the coordinate ray can be represented by points integers, number o, common fractions and mixed numbers.)
5. How to depict a proper ordinary fraction on a coordinate ray?
A. Divide the unit segment into an equal number of parts corresponding to the number in the denominator of the fraction.
b. From the origin, set aside the number of equal parts corresponding to the number in the numerator of the fraction.
6. What intervals are regular and improper fractions?(Proper fractions are depicted as dots between 0 and 1, and improper fractions are to the right of 1 or coinciding with it.)
2) Completing tasks. (5 minutes.)
1. Children from each group fill in the number of squares,
corresponding to each fraction on the interactive whiteboard.
Determine the largest and smallest fractions.
2. (the task drawing is made on the board. Explain why? (5 minutes.)(NOC).
3. Interactive simulator (10 min.)
Now go ahead and sit down at your laptops. Open the interactive trainer.
https://pandia.ru/text/80/343/images/image004_29.jpg" align="left" width="225" height="67 src=">Hatched area on the coordinate ray. Find out which of the numbers , written in the table, will be represented by points in this section.Color the cell in the bottom line of the table if the number falls on the selected section of the beam.
6. The task is performed by children on an interactive whiteboard (optional).
(5 minutes.)
7. Homework (children receive on cards - individually)
7. Summing up the lesson. Grading. (2 minutes.)
Children receive emoticons for each correct answer and attach them to the achievement sheet. Then they are attached to a magnetic board, where the result of the work of each group is visible. The teacher gives marks.
8. Reflection (2 min.)
What did you like most about the lesson?
What difficulties did you have?
How did you overcome them?
How do we end the lesson?
I ask you to evaluate with the help of various stickers:
learned - green sticker,
help needed - blue sticker,
didn't get it - pink sticker.
The date: 13 /02/2017 ___________
Class: 5
Subject: maths
Lesson # : 129
Lesson topic: " Image decimal fractions on the coordinate line.».
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
