For a convenient image of a fraction on a coordinate ray, it is important to choose the correct length of a unit segment.
The most convenient way to mark fractions on a coordinate ray is to take a single segment of as many cells as the denominator of the fractions. For example, if you want to depict fractions with a denominator of 5 on a coordinate ray, it is better to take a unit segment 5 cells long:
In this case, depicting fractions on a coordinate beam will not cause any difficulties: 1/5 - one cell, 2/5 - two, 3/5 - three, 4/5 - four.
If you need to mark fractions on the coordinate ray with different denominators, it is desirable that the number of cells in a unit segment is divisible by all denominators. For example, to depict fractions with denominators 8, 4 and 2 on a coordinate ray, it is convenient to take a unit segment eight cells long. To mark on a fiducial line the required fraction, 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 segment six cells long as a unit:
A number consisting of an integer part and a fractional part is called a mixed number.
To represent an improper fraction as a mixed number, you need to divide the numerator of the fraction by the denominator, then the partial quotient will be whole part mixed number, the remainder is the numerator of the fractional part, and the denominator remains 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 resulting result and write it in the numerator of the improper fraction, leaving the denominator the same.
The fractional part means the division sign. In a column, we 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 a mixed number as an improper fraction:
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 of 23 will become the numerator of the improper fraction, but the denominator of 7 will remain the same.
Image ordinary fractions on the coordinate ray
For a convenient image of a fraction on a coordinate ray, it is important to choose the correct length of a unit segment.
The most convenient way to mark fractions on a coordinate ray is to take a single segment of as many cells as the denominator of the fractions. For example, if you want to depict fractions with a denominator of 5 on a coordinate ray, it is better to take a unit segment 5 cells long:
In this case, depicting fractions on a coordinate beam will not cause difficulties: 1/5 - one cell, 2/5 - two, 3/5 - three, 4/5 - four.
If you want to mark fractions with different denominators on a coordinate ray, it is desirable that the number of cells in a unit segment be divided by all denominators. For example, to depict fractions with denominators 8, 4 and 2 on a coordinate ray, it is convenient to take a unit 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 segment six cells long as a unit:
Questions for notes
Points and are given. Find the length of segment AB.
Date: 13 /02/2017 ___________
Class: 5
Item: mathematics
Lesson No. : 129
Lesson topic: " Image decimals on the coordinate ray.».
Goals and objectives of the lesson:
Educational:
Develop the ability to represent decimal fractions with points on a coordinate beam, find the coordinates of points depicted on a coordinate beam;
Educational:
– continue work on developing: 1) skills to observe, analyze, compare, prove, and draw conclusions; 2) mathematical and general outlook; 3) evaluate your work;
Educational:
– develop the ability to express one’s thoughts, listen to others, conduct dialogues, defend one’s point of view; develop self-esteem skills.
Lesson progress
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 will do in class today? Let's try to formulate the goals of the lesson together.
III. Updating knowledge. 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 mistakes.
1) Mathematical dictation.
1. Three point one tenth.
2. Five point eight.
3. One point five.
4. Zero point seven.
5. Seven point twenty-five hundredths.
6. Zero point sixteen.
7. Three point one hundred twenty-five thousandths.
8. Five point twelve.
9. Ten point twenty four hundredths.
10. One point three.
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. Studying new material.
Decimal fractions on a coordinate ray 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, mark a point on the coordinate ray corresponding to the number 3. Then divide the next unit segment by ten equal parts and count two such parts to the right from 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 equal to 3.2 unit segments (A = 3.2).
Let us depict the decimal fraction 3.2 on the coordinate ray.
2) Let us depict the decimal fraction 0.56 on the coordinate ray.
4. Consolidation of the studied material.
(3) 1. The road from Karatau to Koktal is 10 km. Petya walked 3 km. How far along the road did he walk?
1. How many equal parts is the entire path divided into? (into 10 parts )
2. What will one part of the path be equal to? (1/10 or 0.1)?
3. What will the three parts of such a path be equal to? (0.3)?
1. What numbers are marked by 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 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 ray
(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 new did you learn in class today?
Do you think we managed to achieve 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 did you encounter?
(9) 7. Homework :
Support sheet for the lesson " Image of decimal fractions on a coordinate ray ».
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 us depict 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 us depict the decimal fraction 0.56 on the coordinate ray.
3. The road from Karatau to Koktal is 10 km. Petya walked 3 km. How far along the road did he walk?
1. How many equal parts is the entire path divided into?
2. What will one part of the path be equal to?
3. What will the three parts of such a path be equal to?
4. What numbers are marked by dots on the coordinate line.
5. On a coordinate line, some points are designated by 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 ray
7. Working with the textbook : open the textbook on page 89, perform the number: No. 1254 (ingenuity task).
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 called the “State of Numbers,” there lived fractions: ordinary and decimal
Sections: Mathematics, Competition "Presentation for the lesson"
Class: 5
Presentation for the lesson
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Target: develop the ability to write and read fractions, depict them as points on a coordinate line.
Lesson type: lesson on introducing new material.
Equipment: computer, projector.
Didactic support for the lesson: Power Point presentation, workbooks with a printed base (PT).
Lesson progress
I. Organizational moment.
Communicating the topic and setting lesson goals. (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 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 several answer options.
4. Read fractions.
III. Mathematical dictation. (Slides 7-9)
The teacher talks through all the tasks, then the students exchange notebooks and complete the 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 – variants).
- 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 proper (irregular)?
- Write down three proper (irregular) fractions with a denominator of 7.
- Write down three improper (proper) fractions with numerator 5.
- Write down a fraction whose numerator is 5 units less than the denominator.
- Write down a fraction whose denominator is 3 times the numerator.
IV. Formation of skills and abilities.
1. Preparatory stage for the formation of a new skill. (Slides 10-12)
How to cut 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. Representation of fractions by points on a coordinate line. (Slides 13-17)
Mark a flashing dot on the coordinate ray.
Find the coordinates of the points.
RT part 1, No. 94, 95, 98. (Slide 18)
No. 94. Write the corresponding fraction above each marked point.
No. 95. Mark the points on the coordinate line corresponding to the indicated fractions.
No. 98. Mark the number 1 on the coordinate line.
Physical education minute. (Slides 19-22)
U. No. 749 (oral), 750. (Slide 23)
Independent work. (Slide 24)
Given points... Which of them are located to the right (left) 1?
V. Lesson summary.
The method for constructing a point with a given coordinate is generalized and the issue of choosing a unit segment convenient for constructing the indicated fractions is discussed again.
VI. Homework.(Slide 25)
Section 8.2. No. 751, 752, 761, 765.
Name of the institution State Institution “Secondary school-
gymnasium No. 9"
Position: mathematics teacher
Work experience 8 years
Subject mathematics
Topic Image of ordinary fractions and mixed numbers
on the coordinate ray.
Topic: Representation of ordinary fractions and mixed numbers on a coordinate ray.
Target:
1. educational: generalize and systematize students’ knowledge and skills on this topic; to form subject and mathematical functional literacy;
2. developing: develop memory, logical thinking, attention and mathematical speech;
3. educational: develop teamwork skills, a sense of teamwork, the ability to listen to comrades, and work in a group.
Lesson type: consolidation of learned knowledge.
Lesson equipment: 16 laptops, interactive whiteboard.
We need all sorts of fractions,
Different fractions are important to us.
Study them diligently
And good luck will come to you.
If you know the fractions
And understand their exact meaning,
It will become easy
Even a difficult task.
Lesson progress
I.Organizational moment. Psychological mood of the class. (1 min.)
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(testing the theory learned in the previous lesson):
1) Oral survey. (7 min.)
1. What is a coordinate ray called?
(A ray with a given unit segment is called coordinate beam.)
2. What is a unit segment?
(A segment whose length is taken as one is called single segment.)
3. What is the coordinate of a point?
(The number corresponding to a point on a coordinate ray is called coordinate of this point.)
4. What numbers can be depicted on a coordinate ray?
(On the coordinate ray you can depict with dots natural numbers, number o, ordinary fractions and mixed numbers.)
5. How to depict a proper 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 beginning of the count, set aside the number of equal parts corresponding to the number in the numerator of the fraction.
6. At what intervals are proper and improper fractions found?(Proper fractions are represented by dots in the range from 0 to 1, and improper fractions to the right of 1 or coinciding with it.)
2) Completing tasks. (5 min.)
1. Children from each group paint the number of squares
corresponding to each fraction on the interactive whiteboard.
Determine the largest and smallest fractions.
2. (the drawing of the task is done on the board. Explain why? (5 min.)(NOK).
3.Interactive simulator (10 min.)
Now go ahead and sit down at your laptops. Open the interactive simulator.
https://pandia.ru/text/80/343/images/image004_29.jpg" align="left" width="225" height="67 src=">A section is highlighted on the coordinate ray by hatching. Find out which of the numbers written in the table will be represented by dots in this area. Color the cell in the bottom row of the table if the number falls on the selected area of the ray.
6. Children complete the task on an interactive board (optional).
(5 min.)
7. Homework (children receive on cards - individually)
7. Summing up the lesson. Grading. (2 min.)
For each correct answer, children receive emoticons and attach them to their achievement sheet. Then they are attached to a magnetic board, where the result of each group’s work is visible. The teacher gives marks.
8. Reflection (2 min.)
What did you like best about the lesson?
What difficulties did you encounter?
How did you overcome them?
In what mood do we end the lesson?
I ask you to rate using various stickers:
learned - green sticker,
help needed - blue sticker,
did not understand - pink sticker.
