“What geometry studies” - Thales of Miletus (c. 625 – 547 BC), the first Greek geometer. Geometry in Ancient Greece. L=(P1+P2)/2 L – circumference P1 - perimeter of a large square P2 - perimeter of a small square. Muse of Geometry, Louvre. Geometry. Geometry in Ancient Babylon. The bodies that remind us of the Egyptian pyramids began to be called pyramids.

“The history of the emergence of geometry” - Herodotus (5th century BC). History of the emergence and development of geometry. Euclid - ancient Greek scientist (III century BC), "Principles". What does geometry study? (Plato). Thales of Miletus (639 - 548 BC). Geometric shapes. Lesson topic: “Introduction to geometry”. Geometry brings the mind closer to truth.

“Planes in space” - X. 0. y. z. Analytical geometry. n. x. An equation of the form is called general equation plane. Analytical geometry in space.

“Dihedral angle geometry” - Parallelism and the ratio of the lengths of parallel segments. Ac. angle RKV - linear for a dihedral angle with RSAV. A). (2) On the edge of the MTK. On the verge of DIA. angle RSV - linear for a dihedral angle with edge AC. On the verge of ASR. Find (see) the edge and faces of the dihedral angle. straight line MK is perpendicular to edge MT (by condition).

“Inscribed angle” - Constructing an angle equal to a given one. Presentation. S. E. Khasanova E.I., mathematics teacher, According to figure b). find the size of the external angle. 8th grade. A. O. The magnitude of the inscribed angle. 1 case. Definition: How are angles AOB and ACB similar and different? A). Introduction to the definition of inscribed angle. How quickly with a compass and ruler.

Direct coordinates

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 of counting (or origin ) – point O represents 0 (zero). The number itself is 0 is neither positive nor negative . It separates positive numbers from negative ones.

The straight line is located vertically.

The positive direction is marked with an arrow.

Positive coordinates of points are located above point O, and negative coordinates of points are located below.

A STRAIGHT WITH AN ORIGIN OF REFERENCE, A UNIT SEGMENT AND A DIRECTION SELECTED ON IT IS CALLED A COORDINATE STRAIGHT.

THE NUMBER SHOWING THE POSITION OF A POINT ON A LINE IS CALLED THE COORDINATE OF THIS POINT.

• Where will the squirrel be 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) 2 m above the hollow;

B) below the hollow by 3 m;

B) below the hollow by 1.5 m;

D) 2.5 m higher than the hollow.

Mound

Omsk

270 km

270 km

260 km

630 km

Chelyabinsk

Novosibirsk

Petropavlovsk

The train left the Petropavlovsk station and is traveling at a speed of 90 km/h. Which city will the train arrive in 3 hours?

Where will the train be located:

A) in 10 hours, if he goes to Novosibirsk;

B) in 5 hours, if he goes to Chelyabinsk?

From sports camp A group of tourists comes out and moves along the highway.

Show where the tourists will be:

A) after 3 hours, if they walk at a speed of 3 km/h;

B) after 2 hours if they are walking at a speed of 4 km/h.

What else do you need to know so that there is only one answer to each question?

While on a hike, tourists visited

at points K, M and R.

Where are these points located in relation to the camp?

PRACTICAL

TASKS

Write down the coordinates of the points shown in the figure.

1. Draw on coordinate line points A(1), B(8,3), C(-6), D(6), M(-2,4), K(2,4).

2. Mark a point on the coordinate line that has coordinate x, 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;

B) 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 called?
• 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 of coordinates?

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 the origin?

The lesson is developed taking into account a differentiated approach to teaching: the key points of the lesson are compiled on the basis of a lesson constructor, which takes into account the psychological characteristics of students - the type of thinking. Here you can see the organization of a situation of success, taking into account the psychophysiological characteristics of students, in stages, since learning, like any activity, can be represented in the form of the following sequence of actions: setting up an activity; ensuring the student’s activities taking into account his individual psychological characteristics; comparison of the obtained results with the expected ones. Therefore, at these stages of the lesson, work is distributed between right-hemisphere and left-hemisphere students.
The set of materials for left-brain and right-brain students is different.

Lesson type: lesson in learning new knowledge

Lesson type: explanatory and illustrative

Objective of the lesson:

• Educational aspect: further formation of the foundations of a functional line through the introduction of the concept of a coordinate line; creating an approximate basis for the ability to find the coordinates of a straight line and construct points according to given coordinates;
• Developmental aspect: creating conditions for developing the ability to transfer known methods of action to a new situation;
• Educational aspect: fostering a sense of responsibility for one’s actions (inaction), involvement in everything that happens in the classroom.

Lesson structure:

Stage 1: Statement of educational task
Stage 2: Updating knowledge
Stage 3: Introducing new concepts and ways of doing things
Stage 4: Primary consolidation
Stage 5: Lesson summary
Stage 6: Homework instruction

Basic methods: conversation, demonstration

Equipment and teaching materials:

• Computer,
• Projector,
• Magnets
• Presentation on the topic “Coordinates on a straight line”,
• Didactic materials: card for determining the coordinate line,
• Set of cards with test tasks for left-brained students.

PROGRESS OF THE LESSON

4 1:6

Let us choose a unit segment AB O C

Numbers with a “+” sign are called positive Numbers with a “-” sign are called negative positive negative The “+” sign in front of positive numbers is usually omitted for brevity, and instead of +2 they write 2, so +2=2 i.e. this is the same the same number, just marked differently. A B O

The starting point is the number 0 (zero). Origin of reference Is it negative or positive? The number 0 (zero) itself is neither positive nor negative. It separates positive numbers from negative numbers positive negative ABO

Historical information. Negative numbers first appeared in Ancient China approximately 2100 years ago. In Europe, negative numbers began to be used in the centuries. The recognition of negative numbers was facilitated by the work of the French mathematician, physicist and philosopher René Descartes (). He proposed a geometric interpretation of positive and negative numbers - he introduced the coordinate line (1637).

Above zero - positive, Below zero - negative. Vertical position of the line.

Read the readings of the thermometers shown in the figure:

We meet the coordinate line in history lessons (“time line”) years years 1000 years 2000 years

1. Read the numbers: 14; -1.5; 3.86; 0; -577; -1/5; 237. Test yourself! 14; 3.86; ,5; -577; -1/5

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Slide captions:

Find the value of the expression a) 3.5 – 2.8 b) 10 – 7.5 c) 8.4 – 9.5

Solve the equation: a) 15 – x = 12 b) 12 – y = 15

Cool work Coordinates on a straight line 02/09/15

What temperature does each thermometer indicate? -3°С -2.5°С 0°С +1.5°С +3°С

Where are negative numbers used? Why do we need such numbers? A negative number is expressed by a number zero is expressed Positive number is expressed as Expense (of money, water, fuel, etc.) Expense (of money, water, fuel, etc.) Loss (in rubles, kopecks) Profit (in rubles, kopecks) Temperature below zero degrees (freezing point of water or ice melting point) Temperature of ice melting (water freezing) Temperature above zero degrees Depth below ocean level Ocean level Ocean level Time BC (in years, centuries) Beginning of Christian chronology (beginning of AD) Time AD (in years, centuries)

History of negative numbers Negative numbers appeared much later than natural and ordinary numbers. The first information about negative numbers was found by Chinese mathematicians in the 2nd century BC. Positive ones are like property, and negative ones are like debt, shortage. In Europe, negative numbers began to be used in the 12th and 13th centuries. The recognition of negative numbers was facilitated by the work of the French mathematician René Descartes (1596 – 1650). He introduced the coordinate line (1637). Negative numbers received final recognition as truly existing only in the 18th century.

Practical work 1. Draw a horizontal line. 2. Mark point O on it (approximately in the middle). We will call it the reference point or the origin of coordinates. 3. Take 1 cell as a unit segment. 4. Continue the coordinate ray from point O to the right. Numbers located to the right of the reference point are called positive. Now continue the coordinate ray from point O to the left, maintaining a unit segment. Those numbers that are located to the left of the reference point are called negative.

A straight line with a reference point, a unit segment and a direction chosen on it is called a coordinate line.

Task: name a line among these lines that is a coordinate line.

Coordinate of point A (2); C (- 4). They read: “Point A with coordinate 2”; “Point C with coordinate – 4”, etc. The number showing the position of a point on a line is called the coordinate of this point.

No. 1 Write down the coordinates of points A, B, C, E, K, O, M. A (-5) B (0.5) C (1) E (-2.5) K (4) O (0) M (7)

No. 2 “Find the error” Points A, B, C, D are marked on the coordinate line. Are their coordinates written down correctly? A (2), B (- 3), C (- 2), D (- 4).