Presentation: "Types of angles." Presentation: “Types of angles” Practical work to consolidate what has been learned

• Presentation for math lesson on this topic "Corner. Types of angles"

Presentation compiled

Soboleva L.G.,

primary school teacher

MBOU "Secondary School No. 3" Glazov

Game "Mathematical basketball"

Well done!

30 + 7 25 + 5 32 – 12 66 + 4 80 – 7

28 – 10 45 – 45 53 + 7 59 – 9 90 + 9

Game "Four Wheel"

Divide the shapes into two groups

LINES

POLYGONS

Crossword "Geometric"

Geometric figure shaped

elongated circle.

The smallest geometric figure.

A geometric figure that has no corners.

The part of a line that has a beginning

but there is no end.

L U H

K R U G

T ABOUT CH K A

O V A L

Corner is a geometric figure formed by two different rays

with a common beginning.

Angle designation

Dot ABOUT- vertex of the corner.

Rays OA And OB- sides of the angle.

Sharp corner is an angle that is less than a right angle.

Obtuse angle is an angle that is greater than a right angle.

Game “The corner gave them a name”

rectangle

____gon

triangle

____gon

____gon

pentagon

hexagon

____gon

____gon

polygon

____gon

quadrilateral

SINQWINE

• 1noun (What?)
• 2 adjectives (Which?)
• 3 verbs (what to do?)
• Offer
• Association (synonym)

Practical work

Build right angle

1. Take a square and a pencil.

2. Circle the corner as in my picture.

We are building sharp corner

Take a ruler and pencil.

Draw a straight line

And then another one like mine

Attach a square. What do you think?

Attach a square. What do you say?

Let's build

obtuse angle

Take a ruler and pencil.

Draw a straight line

And then another one like

I have.

• found out

• Understood

• learned

Homework

• Imagine and draw different objects using circles, ovals, dots, rays and angles

(complete the task on a landscape sheet)

THANK YOU for your work

I wish you creative success

Subject: Corner. Types of angles. (Textbook “Mathematics 2nd grade, part 2”

Goals: form an idea of ​​the types of angles; improve computational skills and problem solving abilities, develop logical thinking. To cultivate in students a relationship of business cooperation (benevolence to each other, respect the opinions of others, be able to listen to comrades), accuracy, and instill interest in the subject.

Planned results: Students will learn to determine the types of angles (acute, obtuse, straight) using a square model; recognize geometric shapes; check the correctness of addition and subtraction operations; explain and justify action to solve a problem; monitor and evaluate your work and its results.

Equipment: for children - a drawing square, a sheet for a right angle model, a card with angles, a counting book. For the teacher - Presentation, projector, document camera and a sample of solved examples, a square, plates “Types of angles”, “Parts of an angle”, drawing of a figure.

During the classes.

Stages:

Teacher activities

Student activities

Note

I. Organizational moment.

Creating conditions to maintain interest in learning.

The long-awaited call was given,

The lesson begins!

What qualities do we need in a math lesson?

You are still studying, but you can already be called experts, because you already know and can do a lot. And today you will have to answer many questions, as befits experts, and also learn something new, because a person lives while learning and learning something new. Guests came to our lesson. They want to see how you can work.

(children talk together with the teacher)

Children's answers

(children together with the teacher pronounce and perform actions)

I'll open my notebook

And I’ll put it on an angle.

I, friends, will not hide from you:

I'm holding my pen correctly!

I’ll sit straight and won’t bend over,

I'll get to work!

(Write the number. Cool job)

II. A minute of penmanship.

260 260

how to write 2 correctly? 6? 0? We write a line.

Let's talk about the resulting number

(children in a chain): this is the number two hundred and sixty; it is three-digit; it has 2 hundreds, 6 tens, 0 units; his neighbors, 259, 261; it can be obtained from neighbors if k 259+1 or 260-1; this number can be replaced by the sum of the bit terms 200 and 60; There are 26 dozens in this number; 260 units in total.

Cultivating neatness

II I. Updating knowledge. Self-determination for activity

Preparing and motivating students to introduce new material, develop rational and intuitive abilities

There's no point in standing still

Bored from idleness,

We'll try everything together

Learn something new.

All attentive, inquisitive

Important discoveries await.

On the road of school knowledge

We will lead everyone to success!

This is the motto that we will conduct this lesson under. Let's start with mental counting

A)- Fill the table

Minuend

Subtraction

Difference

What is unknown in the first column? How did you find it?

What is unknown in the second column? How did you find it?( To find the minuend, you need to add the difference to the subtrahend. To find the subtrahend, you need to subtract the difference from the minuend.)

B)– Solve problems

There were 2 birch trees, 4 apple trees, 5 cherries growing in the garden. How many fruit trees were there in the garden? (9)

My sister is 9 years old, my brother is 3 years old. How much older will your sister be than her brother in 5 years? (6)

IN)

How to call it in one word: What is it? (geometric figures). What two groups can they be divided into?(Group I - there are angles; Group II - no corners.)

Say the name and which group it should be assigned to.( The first group includes figures 1, 3, 5; in the second - figures 2, 4.)

What is the name of the science that studies geometric shapes?(GEOMETRY)

Today we are invited by the Queen of Mathematics on a journey through the field of Geometry. To find out the purpose of the trip, you need to solve the “Geometric” crossword puzzle.

G) 1) Part of a line that has a beginning but no end. (Ray).

2) A geometric figure that has no corners. (Circle).

4) A geometric figure in the shape of an elongated circle. (Oval).

Children calculate and show the answer with a counting book.

explain and justify action to solve a problem

Children's answers.

Improving computing skills

Development of logical thinking

IV. Setting a learning task

Development of ability to plan activities

What do you think: what is the topic of our lesson? What learning objectives will we set for the lesson?

Children answer what they want to know: What is an angle. Types of angles.

V. Discovery of new knowledge

Development of activity abilities

Primary consolidation of the concept of “angle”

Summing up (intermediate)

A) How many of you have heard the word corner in everyday life? Angles surround us in everyday life. Give your own examples of where there are corners around us. (Look at the screen). Shown here is a metal corner for connecting pipes, a stationery corner, drawing squares, corner furniture: table, sofa.

Let's start discovering new knowledge.

B)- Think about what tools we will need in the lesson? (ruler, triangle, pencils)

In your notebook, mark a point and label it with the letter O. Draw two rays from point O. How many parts did the rays divide the plane into? Shade the smaller part with a colored pencil.

What shape did you shade? (Corner).

Formulate a definition.

A figure that consists of a point and two rays emanating from this point is called an angle.

An angle is a geometric figure formed by two different rays with a common origin.

Point O is the vertex of the angle. An angle can be called by one letter written near its vertex. Angle O. But there can be several angles that have the same vertex. What to do then?

In such cases, if you call different angles with the same letter, it will not be clear which angle you are talking about. To prevent this from happening, you can mark one point on each side of the angle, put a letter next to it and designate the angle with three letters, while always writing in the middle the letter indicating the vertex of the angle. Angle AOB.

What are the rays emanating from a point called? (Sides.) State the definition and show the sides in the picture. The rays that form an angle are called sides. Rays OA and OB are the sides of the angle.

IN) Do you see the same angles on the screen?(No.) It's time to learn the types of angles.

1 2 3 4 5

6 7 8

Practical work. Construction of a right angle model.

There are different angles, but first we will get acquainted with the most important angle. Take a piece of paper. Fold the sheet in half, and then in half again. Trace the fold lines with a pencil. How many parts do straight lines divide the plane into? (For four).

How many angles did you get? (Four).

These are special angles. Maybe someone knows the name of these corners? (These angles are right).

Place a dot at the intersection of the fold lines. Label one right angle with letters. Shade the inside of it with a colored pencil.

It is not always convenient to determine a right angle by eye. To do this, use a ruler-square. To determine whether an angle is right or not, you need to align the vertex and one side of the angle with the vertex and side of the right angle on a straight edge. Find a right angle on it using your model. If the sides of the model coincide with the sides of the square, then this is a right angle.

Exercise: Using the right angle model, find right angles in the picture and write down their numbers.

The figure shows that there are other angles - not right angles. Is it possible to compare angles by magnitude? Each of the corners has its own name.

An acute angle is an angle that is less than a right angle. An obtuse angle is an angle that is larger than a right angle.

Using the right angle model, find out whether the remaining angles of the square will be right. We see that the angle of the square is less than a right angle, so what is it?

Let's check the third corner. Let's apply the model of a right angle to the angle of a square and compare. So what is it called? (sharp) So, the drawing square has 1 right angle and 2 acute angles.

G) Let's determine the types of angles using the right angle of the drawing square. If the sides of an angle and a right angle of a square coincide, then what angle is it? (right angle) If the angle is less than the right angle of the triangle, then it is...? (acute angle) If the angle is greater than the right angle of the triangle, then it is an obtuse angle.

What types of angles are there? (hang up a sign) Name the acute angles. Name obtuse angles.

Children's answers

Practical work

(Children do task in pairs, then one student names his answer, everyone checks the work).

Fostering in children an attitude of business cooperation (being kind to each other, respecting the opinions of others, being able to listen to comrades),

VI. Fizminutka

Health-saving technology

(children speak and do exercises) All the guys stood up together

And they walked on the spot.

Stretch on your toes

And they turned to each other

We sat down like springs,

And then they sat down quietly.

VII. Consolidation.

A) According to the textbook p.9 No. 2 . What do the examples have in common?

What two groups can all examples be divided into? (Group I examples on addition, Group II - on subtraction.)

B) Solving problems No. 5, 6(orally)

B) Test. reading on the screen

3) 3.

Solve examples 1 and 2 with comments. 3 - 5 examples on your own. Mutual verification - according to the standard (projected through a document camera)

the student reads.

Show: How many actions does the task take?

Show the answer.

Explain the solution

Day-night game: children show the answer with their fingers

Improving written calculation skills,

check the correctness of addition and subtraction operations

Explain and justify action to solve a problem

Monitor and evaluate their work and its results

VIII. Reflection

What new did you learn in the lesson? What elements does an angle consist of?What angles are there?

WhichDid you set learning objectives for the lesson?

Our journey through the country of Geometry ends

What can you say at the end of the lesson? Evaluate your work: if you are satisfied with your work, everything worked out for you, then the yellow circle. If you made a little mistake, but realized your mistakes. It's a green circle. If you need help understanding new material, raise the red circle.

In the future, in mathematics and geometry lessons, we will learn a lot about different geometric shapes.

Children's answers

self-esteem

Evaluate their work and its results

I X . D/Z

p.8 (pr.) p.9 No. 1, 3.

Ratings. Thanks for the work.

• Development of logical thinking, attention, memory, spatial imagination;
• Development of creative skills on the topic for successful completion of tasks;
• Development of the culture of speech and emotions of students.

3. Educational:

• In order to solve the problems of moral education, promote the cultivation of humanity and collectivism, observation and curiosity, the development of cognitive activity, and the formation of independent work skills;
• In order to solve the problems of aesthetic education, to promote the development of a sense of beauty in students.

DURING THE CLASSES

I. Organizational moment.

Well, check it out, my friend,
Are you ready to start the lesson?
Is everything in place?
Is everything alright?
Pen, book and notebook?
Is everyone sitting correctly?
Is everyone watching carefully?
Everyone wants to receive
Only a “5” rating.

Guys, today we will again go on a journey through the kingdom of Geometry.

3. Oral counting.

2 slide

At the gate we are met by King Dot and his daughter, Princess Straight. Before the king and princess introduce us to the inhabitants of their kingdom, they want to test you.

II. Verbal counting.

(Slide 3)

1) Game “Confused Caterpillar”.

The caterpillar has lost the numbers, look at the remaining ones, guess what rule can be used to continue the series of numbers. (Children say the rule: these are even numbers; each subsequent number is 2 more than the previous one).

What numbers did the caterpillar lose? (2,4,6,8,10,12,14,16)

(Slide 4)

2) Game “Mathematical Basketball”.

Basketball- a team sports game, the goal of which is to throw a ball into a suspended basket with your hands.

Any of you will score a goal if you solve the example correctly. (Children solve examples in a chain). 30 + 7 25 + 5 32 - 12 66 + 4 80 - 7 28 - 10 45 - 45 53 + 7 59 - 9 90 + 9

Slide 5

Logic task

How many spots do 15 piglets have? (15)

When a goose stands on two legs, it weighs 4 kg. How much will a goose weigh when it stands on one leg?

6 slide

You have passed all the tests. The king and princess are very pleased with you and are ready to introduce you to the inhabitants of the kingdom of “Geometry”!

(When you click, the gate leaves open.)

(Slide 7)

Guys, before you are the inhabitants of the kingdom “Geometry”.

Look at the shapes in each frame. Which one is the odd one out? Why?

(Students name the extra figures and justify their choice).

Divide all remaining figures into two groups. How can I do that? (The remaining shapes can be divided into two groups: lines and polygons.)

Name the types of lines and polygons that you know. (Lines: straight, broken, curved. Polygons: square, trapezoid, rectangle, quadrangle, pentagon, hexagon, polygon).

IV. Working on new material.

(Slide 8)

1) - The crossword puzzle will tell you the topic of the lesson. Crossword “Geometric”.

1) Part of a line that has a beginning but no end. (Ray).

2) A geometric figure that has no corners. (Circle).

4) A geometric figure in the shape of an elongated circle. (Oval).

The topic of our lesson is hidden vertically. Find her. (Corner). (click, geometric shapes fly out).

Please formulate the topic of our lesson.

Guys, why are we going to study angles?

Do you think this knowledge will be useful to you?

(Children's answers)

Angles surround us in everyday life. Give your own examples of where you can find angles around us.

Guys, maybe someone knows what an angle is? (children's opinions are listened to)

We will check the correctness of our formulation a little later.

People of what professions are most likely to encounter angles? (constructor, engineer, designer, builder, architect, sailor, astronomer, architect, tailor, etc.)

Slide 9.

Look at the pictures: a connecting corner for pipes and a stationery corner for papers; carpenter's square and drafting square; corner table and corner sofa.

Guys, now the King and Princess offer to play a little.

Slide 10.

Game “The corner gave them a name.”

The angle is an important figure. He helped give names to many figures. Name the figures.

What do the names of the figures have in common? (that they have a square - a common part)

Why is the first part of the words different everywhere? (because there are different numbers of angles)

Fizminutka 11-16 slides

Slide 18.

Guys, now step back one cell from the red fields and place point O. Draw two rays from this point.

Draw point O (4-5) on the board in advance. Call 4-5 children to draw rays on the board.

What kind of figures did we get? (corner)

Look how different these angles are.

Guys, now put together a rule from words.

Work in pairs.

(Conclusion: an angle is a geometric figure formed by two different rays

with a common beginning).

Guys, now look at the figure that I drew.

Is it an angle or not.

(The children say - no, we return to the rule again, after which we conclude that this is also an angle - a reversed one)

Slide 19. (output by angle)

Poster on blackboard

Point O is the vertex of the angle. An angle can be called by one letter written near its vertex. Angle O. But there can be several angles that have the same vertex. What to do then? (On the sheet there is a drawing of such angles)

Children's answers.

In such cases, if you call different angles with the same letter, it will not be clear which angle you are talking about. If this does not happen, you can mark one point on each side of the angle, put a letter near it and designate the angle with three letters, while always writing in the middle the letter indicating the vertex of the angle. Angle AOB. Rays AO and OB are the sides of the angle.

Poster on blackboard

Slide 20.

Guys, you have different types of corners on your tables. Please find the same types of angles.

How will you search? (Children's answers)

One person on my models is looking for the same angles.

Guys, look, numbers 6 and 7 matched completely, but 1 and 5 did not. No. 5 is bigger.

What can be concluded? After the children answer, a slide appears.

CONCLUSION: slide 21

• Equal angles coincide when superimposed
• If one angle is superimposed on another and they coincide, then these angles are equal

Slide 22.

Making a right angle model.

Slide 23

It is not always convenient to determine a right angle by eye. To do this, use a ruler-square.

What color is used to highlight an angle greater than a right angle? (Blue).

Less direct? (Green).

Which of the three proposed angles is a straight line?

Why did you decide so? (The vertex and sides of the angle coincide with the right angle on the square ruler).

How to determine the type of angle?

• To determine the type of angle, you need to combine its vertex and side, respectively, with the vertex and side of the right angle on the square.

Slide 24

Each of the corners has its own name. An acute angle is an angle that is less than a right angle. An obtuse angle is an angle that is greater than a right angle.

(Tables with the names of the angles appear on the board)

My mother took the piece of paper
And folded the corner
This is the angle for adults
It's called DIRECT.
If the corner is already SHARP,
If wider, then - DUMB.

Slide 25.

Guys, is it always possible to overlap the angles?

No. (If drawn in a notebook...)

For this purpose, there is a protractor with which angles are measured. Angles are measured in degrees. Look at the types of protractors.

Slide 26.

Very often we can observe angles on the clock. The angles are formed by the hour hands.

Work according to the textbook.

Exercise: Using the right angle model, find right angles and write down their numbers. (Children complete the task independently, then one student names his answer, everyone checks the work).

With the help of a square it is convenient not only to determine right angles, but most importantly - to build them. Let's build a right angle, everyone will name it with one or three letters.

Slide 27-29 (The teacher is on the board, and the children are building a right angle in their notebooks. Mutual testing is carried out in pairs).

I'm SHARP - I want to draw,
Now I’ll take it and draw it.
I lead two straight lines from a point,
It's like two rays
And we see an ACUTE ANGLE,
like the edge of a sword.

And for an obtuse ANGLE
We repeat everything again:
From a point we draw two straight lines,
But let's spread them wider.
Look at my drawing,
He's like scissors inside
If there are two rings
We'll push it all the way.

Practical work to consolidate what has been learned.

There is wire on your desks. Make a right angle out of it and test it with a square, then make it sharp and obtuse.

7. Lesson summary.

Tell me, using a diagram, what did you learn from today's math lesson?

8. Homework.

One day point

I went hunting

She took the bow

Two straight arrows.

Thought period:

"What will happen when I

I'll let you in on my own

Are two stronger arrows?

I thought period

And she did it

And now we have a corner.

Handsome, cheerful,

Has two beams

And playful to the point,

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Slide captions:

1 2 3 4 Unit of measurement of time 2. Unit of measurement of mass 3. Hundredth part of a number 4. Instrument for measuring the length of segments MIN U T A G R A M M P R O T C E N T L I N E I C IIII I IIII I IIII I IIII I IIII I IIII I IIII I IIII I IIII I IIII I IIII I IIII I IIII I 0 1 2 3 4 5 6 7 8 9 10 11 12 Gram

straight ray segment

How was this figure formed?

An angle is a figure formed by two rays emanating from one point. O A B AOB Side of corner Vertex of corner

The sign for denoting an angle was introduced in the 18th century by the French mathematician Pierre Erigon Erigon used the sign to denote a right angle

Write down the depicted angles using the “” sign, indicate their sides and vertices. M O K A V S If you completed the task correctly, then you have written down:  KOM: OK and OM - sides  KOM O - top  KOM  VAS: AB and AC - sides  VAS A - top  VAS

Look carefully at the drawing. It shows points that belong to  ABC and do not belong to  ABC. So, points P, E, D, K belong to  ABC, points M, O do not belong to  ABC, and points P, K lie on the sides of  ABC. A B S R K E D M O

Look carefully at the picture and name the points that belong to  GENUS and do not belong to  GENUS. If you completed the task correctly, then you have named points: Points T, A, B, C, K belong to  GENERAL. Points M, H do not belong to  ROD. R O D T S V A N K M

A= B A B A S A

Equal angles coincide when superimposed. If one angle is superimposed on another and they coincide, then these angles are equal or

SHARP DULL STRAIGHT DEVELOPED

O A B Two complementary rays form an unfolded angle

Look carefully at the drawing. Write the angles in increasing order of their magnitudes. If you completed the task correctly, then you have written down:  AED,  ROS,  MKE K M E R O S V A D

Hour 1 2 3 4 5 6 7 8 9 10 11 Angle O O P T T R T T P O O 12 3 9 6 1 2 11 10 5 4 7 8 Determine the type of angles that the hands of the clock form. CHECK O - SHARP R - STRAIGHT T - DULL R - REVEALED

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