Presentation of a coordinate on a straight line. Equipment and teaching materials
Coordinates on a straight line
Presentation for a 6th grade math lesson
math teachers
MBOU secondary school No. 86 named after Rear Admiral I.I. Verenikin
POSITIVE NUMBERS:
NEGATIVE NUMBERS:
POSITIVE NUMBERS:
Start point (or origin ) - point O represents 0 (zero). The number 0 itself is neither positive nor negative . It separates positive numbers from negative ones.
The straight line is vertical.
The positive direction is marked with an arrow.
The positive coordinates of the points are located above the O point, and the negative coordinates of the points are located below.
A STRAIGHT WITH A REFERENCE SELECTED ON IT, A SINGLE SECTION AND A DIRECTION IS CALLED A COORDINATE LINE.
A NUMBER SHOWING THE POSITION OF A POINT ON A DIRECT LINE IS CALLED THE COORDINATE OF THIS POINT.
- Where will the squirrel be located if it moves 3 m away from the hollow. How many answers can you give?
- Where will the squirrel be if it is located:
A) above the hollow by 2 m;
B) below the hollow by 3 m;
C) below the hollow by 1.5 m;
D) 2.5 m above the hollow.
Mound
Omsk
270 km
270 km
260 km
630 km
Chelyabinsk
Novosibirsk
Petropavlovsk
The train left the Petropavlovsk station and is moving at a speed of 90 km/h. Which city will the train arrive in 3 hours?
Where will the train be?
A) after 10 hours, if he goes to Novosibirsk;
B) in 5 hours if he goes to Chelyabinsk?
A group of tourists comes out of the sports camp and moves along the highway.
Show where the tourists will be:
A) after 3 hours, if they go at a speed of 3 km / h;
B) after 2 hours, if they go at a speed of 4 km / h.
What else do you need to know so that there is only one answer for each question?
While on a hike, tourists visited
at points K, M and R.
Where are these points in relation to the camp?
PRACTICAL
TASKS
Write down the coordinates of the points shown in the figure.
1. Draw points A(1), B(8.3), C(-6), D(6), M(-2.4), K(2.4) on the coordinate line.
2. Mark on the coordinate line a point that has the x coordinate, if x=-7; 3.3; -5.2; -1; 2; -1.8;
Name any three numbers located on the coordinate line:
A) to the right of the number 11;
B) to the left of the number -8;
C) to the left of the number -820;
D) to the right of the number -78.
QUESTIONS:
- What is a coordinate line?
- What is the coordinate of a point on a line?
- What numbers are the coordinates of points on a horizontal line located: a) to the right of the origin;
b) to the left of the origin?
4. What is the coordinate of the origin?
- What numbers indicate the coordinates of points on a vertical line located:
a) above the origin;
b) below from the origin?
This presentation is devoted to the second lesson in the study of the topic "Coordinates on a line". The presentation opens with oral work, which consists of ten tasks on different topics of the course: is the proportion correct, solve the proportion, make the proportion, etc. The material of this part of the presentation is taken from lesson developments in mathematics grade 6 (author V.V. Vygovskaya). The work also presents slides with pictures for problems No. 893, 894, 918,902 and 906 (according to the textbook "Mathematics. 6" by N. Ya. Vilenkin and others). Demonstration of drawings on a slide will draw students' attention to the problem being solved and will allow them to more effectively complete these tasks.
View document content
"Presentation. Line coordinates. 6th grade."
oral work
No. 1. Is the proportion correct:
Solution: 1 way (by determining the proportion)
2 way (according to the main property of proportion)
oral work
No. 2. Solve the proportion: 3.5: x = 0.8: 3.2.
No. 3 . Solve proportion:
oral work
No. 4. Make a proportion: 9 4 \u003d 3 12.
Solution: 9:3 = 12:4;
oral work
No. 6. What is the length on the plan of a distance of 200m, if the map scale is 1: 1000?
Solution: 200 m = 20,000 cm;
20,000: 1000 = 20 (cm) length on the map.
Answer: 20 cm.
oral work
No. 9. Which is more: 5% of 80 or 80% of 5?
oral work
No. 10. There are 25 people in the class. Of these, 15 are boys. What percentage of students are girls?
Where is each bird in relation to the knot of the rope? (Cage side 1 dm)
Used Books.
- Mathematics. 6th grade. Textbook for educational institutions. N. Ya. Vilenkin, V. I. Zhokhov, A. S. Chesnokov, S. I. Shvartsburd.
2. Lesson development in mathematics. 6th grade. V.V. Vygovskaya.
The educational presentation for the topic "Coordinates on a straight line" has a clear structure, the presentation of the material takes place in a logical sequence and is supported by the necessary figures. The font size and color palette do not tire the eyes of students and allow you to clearly see the elements of the slides from all the learning places in the class. The presentation is not oversaturated with animation effects, so the students are as focused as possible on the teacher's explanation, and not on the animation.
slides 1-2 (Presentation topic "Coordinates on a straight line", examples)
The supply of new material begins with the consideration of the line AB and the point O, which divides the given line into two additional rays. After that, a single segment is chosen and agreed to be called the origin of coordinates. The students explain that the position of a point on each of the rays is given by a coordinate, and in order to distinguish the coordinates from each other on these rays, they put a “+” sign in front of the coordinate for one ray, and a “-” sign in front of the coordinate of the other ray. Thus, students are brought to the concepts of "positive" and "negative" numbers.
slides 3-4 (examples, definition of a coordinate line, coordinates of a point)
The whole explanation takes place in stages, each moment is shown on a slide, the necessary examples are given. Students' attention is drawn to the fact that, for brevity, writing positive numbers is usually omitted with the "+" sign. In addition, the presentation emphasizes that the point O represents zero, which in itself is neither a positive nor a negative number - it simply separates positive numbers from negative ones.
slides 5-6 (examples, questions)
The questions proposed on the last slide are designed to quickly control the acquired knowledge by students as a result of viewing the presentation with an accompanying teacher's explanation. This will make it possible to quickly identify students' misunderstanding of any points of the considered educational material. In turn, schoolchildren must demonstrate not only the reflex reproduction of the heard material, but also make an analysis of the necessary concepts of the topic, correctly formulate and express their thoughts.
The educational presentation to the topic "Coordinates on a straight line" can be used not only during school classes, but also for remote or independent study by schoolchildren.
Shvetsova T.S.
Coordinates on a straight line
(6th grade)
Shvetsova Tatyana Sergeevna, teacher of mathematics
Educational institution:
MOU Pavlovskaya secondary school
Item:
mathematics.
Classes:
6.
Equipment -
multimedia projector, screen, computer.
Form of use -
projection onto the screen during frontal work with the class.
Author's media product
:
presentation.
The presentation was developed to help the teacher conduct a math lesson in grade 6 on the topic: “Coordinates on a straight line.” The words of the teacher at such stages as oral counting, explanation new topic, oral consolidation of a new topic, historical background, summing up the lesson are visually accompanied by a presentation, which saves the teacher's time if he accompanied his words with other visualizations.
This presentation will make the lesson more interesting, new material more understandable. With oral counting and consolidation, students see confirmation of the correctness of their answers, which cannot be done when working with a textbook. When explaining a new topic, each word of the teacher is displayed on the screen, the teacher is facing the class, which cannot be achieved when working with the board. The main points of the historical background are displayed in the presentation, which will allow the visual perception of the report. When summing up the lesson, the teacher has the opportunity to return to the main points of the new topic, which will allow students to better absorb the new material.
Before working with the presentation, the teacher should study the lesson outline in detail in order to find out the main "subtleties" of each slide.
Literature:
1. Lesson plans according to the textbook by N.Ya. Vilenkin and others. Volgograd 2005
2. Textbook "Mathematics Grade 6" N.Ya. Vilenkin and others. M: Mnemosyne
Math lesson + presentation in grade 6 on the topic "COORDINATES ON A LINE"
Author: Shvetsova Tatyana Sergeevna
mathematic teacher
MOU Pavlovsk secondary school
Purpose: 1. To teach to mark a point on a coordinate line at given coordinates and to read the coordinates of a point marked on a coordinate line.
2. Development of attention and accuracy when performing tasks.
3. Development of interest in the study of the subject.
☺ - click the left mouse button.
During the classes:
| № | Name of the lesson | Stage content | slide number |
| 1 | Lesson organization. 3 min. | Teacher: “Today we will learn how to show the position of a point on a line, what a coordinate line is, learn how to mark a point on a coordinate line at given coordinates and read the coordinates of a point marked on a coordinate line.” | slide 1 |
| 2 | Verbal counting | Teacher: "Before we start learning a new topic, let's practice mental counting" The first example is ☺ , students answer, ☺ (answer check), etc. | slide 2.3. |
| 3. | Formation of new knowledge of students. | 1. Positive and negative numbers. Teacher: “Let us have some straight line AB☺,. Point O divides this line into two additional rays - OA and OB☺ , . We choose a unit segment ☺ and take the point O as the origin. Then the position of the point on each of the rays is given by the number ☺ . To distinguish the coordinates on these rays from each other, it was agreed to put the +☺ sign before the numbers on one ray, and the -☺ sign before the numbers on the other ray. Numbers with a + sign are called positive☺ . Signed numbers are called negative numbers. For brevity, the notation usually omits the + sign before a positive number ☺ . The reference point - point O represents 0 (zero☺). The number 0 itself is neither positive nor negative.☺ . It separates the positive from the negative. The positive direction is marked with an arrow ☺ . | slide 4. |
| The lines can be in different positions. For example, a thermometer scale - it also shows positive and negative numbers. Positives are above zero☺, negatives are below☺. | slide 5 |
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| So, what is called the coordinate line and the coordinate of the point? A straight line with a reference point selected on it☺ , the unit segment ☺ and the direction ☺ is called the coordinate line. The number showing the position of a point on a straight line ☺ is called the coordinate of this point ☺ . They write☺ : С(-4)" | slide 6 |
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| 4. | Performing oral tasks to consolidate a new topic. | Students orally perform the tasks shown on the slides. | slide 7.8 |
| 5. | Solving problems from the textbook. | № 895, № 896, № 897,№ 898. | |
| 6. | Summing up the lesson. | Teacher: “1) What line is called the coordinate line? (hereinafter the oral answer of the student) ☺ by hyperlink 2) In which direction from zero are positive numbers when the coordinate line is horizontal; vertical? | Slide 9,15 |
| 3) What number is neither positive nor negative? 4) What is the coordinate of a point? (further students answer) ☺ by hyperlink | slide 10.16 |
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| And now we will make a report "From the history of the emergence of negative numbers" Negative numbers appeared much later than natural numbers and ordinary fractions. The first information about negative numbers is found among Chinese mathematicians in2nd century BC.☺ Positive numbers were then interpreted as property, and negative numbers as debt, shortage.☺ But neither the Egyptians, nor the Babylonians, nor the ancient Greeks knew negative numbers.☺ Only inYII century. Indian mathematicians began to make extensive use of negative numbers, but regarded them with some distrust. In Europe, negative numbers began to be used fromXII-thirteenth century, but beforeIn the 16th century, as in antiquity, they were understood as debts, most scientists considered them "false", in contrast to positive numbers - "true". The recognition of negative numbers was promoted by the works☺ French mathematician, physicist and philosopher René Descartes (1596-1650). He proposed a geometric interpretation of positive and negative numbers - he introduced the coordinate line. The final and universal recognition as really existing negative numbers was received only in the first half ofXYIII in. At the same time, the modern designation for negative numbers was established. |
slide 11 |
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| 7. | Homework. | item 26, no. 918, no. 909 (a) | |
| Teacher: “Thank you for the lesson and I ask you to draw your mood in a notebook with a pencil” | Slide 14 |
