Ray: starting point, symbol of rays. Point, line, straight line, ray, segment, broken line

A point is an abstract object that has no measuring characteristics: no height, no length, no radius. Within the scope of the task, only its location is important

The point is indicated by a number or a capital (capital) Latin letter. Several dots - different numbers or in different letters so that they can be distinguished

point A, point B, point C

A B C

point 1, point 2, point 3

1 2 3

You can draw three dots “A” on a piece of paper and invite the child to draw a line through the two dots “A”. But how to understand through which ones? A A A

A line is a set of points. Only the length is measured. It has no width or thickness

Indicated by lowercase (small) Latin letters

line a, line b, line c

a b c

The line may be

1. closed if its beginning and end are at the same point,
2. open if its beginning and end are not connected

closed lines

open lines

You left the apartment, bought bread at the store and returned back to the apartment. What line did you get? That's right, closed. You are back to your starting point. You left the apartment, bought bread at the store, went into the entrance and started talking with your neighbor. What line did you get? Open. You haven't returned to your starting point. You left the apartment and bought bread at the store. What line did you get? Open. You haven't returned to your starting point.

1. self-intersecting
2. without self-intersections

self-intersecting lines

lines without self-intersections

1. direct
2. broken
3. crooked

straight lines

broken lines

curved lines

A straight line is a line that is not curved, has neither beginning nor end, it can be continued endlessly in both directions

Even when a small section of a straight line is visible, it is assumed that it continues indefinitely in both directions

Indicated by a lowercase (small) Latin letter. Or two capital (capital) Latin letters - points lying on a straight line

straight line a

a

straight line AB

B A

Direct may be

1. intersecting if they have common point. Two lines can intersect only at one point.
   • perpendicular if they intersect at right angles (90°).
2. Parallel, if they do not intersect, do not have a common point.

parallel lines

intersecting lines

perpendicular lines

A ray is a part of a straight line that has a beginning but no end; it can be continued indefinitely in only one direction

The ray of light in the picture has its starting point as the sun.

Sun

A point divides a straight line into two parts - two rays A A

The beam is designated by a lowercase (small) Latin letter. Or two capital (capital) Latin letters, where the first is the point from which the ray begins, and the second is the point lying on the ray

ray a

a

beam AB

B A

The rays coincide if

1. located on the same straight line
2. start at one point
3. directed in one direction

rays AB and AC coincide

rays CB and CA coincide

C B A

A segment is a part of a line that is limited by two points, that is, it has both a beginning and an end, which means its length can be measured. The length of a segment is the distance between its starting and ending points

Through one point you can draw any number of lines, including straight lines

Through two points - an unlimited number of curves, but only one straight line

curved lines passing through two points

B A

straight line AB

B A

A piece was “cut off” from the straight line and a segment remained. From the example above you can see that its length is the shortest distance between two points. ✂ B A ✂

A segment is denoted by two capital (capital) Latin letters, where the first is the point at which the segment begins, and the second is the point at which the segment ends

segment AB

B A

Problem: where is the line, ray, segment, curve?

A broken line is a line consisting of consecutively connected segments not at an angle of 180°

A long segment was “broken” into several short ones

The links of a broken line (similar to the links of a chain) are the segments that make up the broken line. Adjacent links are links in which the end of one link is the beginning of another. Adjacent links should not lie on the same straight line.

The vertices of a broken line (similar to the tops of mountains) are the point from which the broken line begins, the points at which the segments that form the broken line are connected, and the point at which the broken line ends.

A broken line is designated by listing all its vertices.

broken line ABCDE

vertex of polyline A, vertex of polyline B, vertex of polyline C, vertex of polyline D, vertex of polyline E

broken link AB, broken link BC, broken link CD, broken link DE

link AB and link BC are adjacent

link BC and link CD are adjacent

link CD and link DE are adjacent

A B C D E 64 62 127 52

The length of a broken line is the sum of the lengths of its links: ABCDE = AB + BC + CD + DE = 64 + 62 + 127 + 52 = 305

Task: which broken line is longer, A which has more vertices? The first line has all the links same length, namely 13 cm. The second line has all links of the same length, namely 49 cm. The third line has all the links of the same length, namely 41 cm.

A polygon is a closed polyline

The sides of the polygon (the expressions will help you remember: “go in all four directions”, “run towards the house”, “which side of the table will you sit on?”) are the links of a broken line. Adjacent sides of a polygon are adjacent links of a broken line.

The vertices of a polygon are the vertices of a broken line. Adjacent vertices are the endpoints of one side of the polygon.

A polygon is denoted by listing all its vertices.

closed polyline without self-intersection, ABCDEF

polygon ABCDEF

polygon vertex A, polygon vertex B, polygon vertex C, polygon vertex D, polygon vertex E, polygon vertex F

vertex A and vertex B are adjacent

vertex B and vertex C are adjacent

vertex C and vertex D are adjacent

vertex D and vertex E are adjacent

vertex E and vertex F are adjacent

vertex F and vertex A are adjacent

polygon side AB, polygon side BC, polygon side CD, polygon side DE, polygon side EF

side AB and side BC are adjacent

side BC and side CD are adjacent

CD side and DE side are adjacent

side DE and side EF are adjacent

side EF and side FA are adjacent

A B C D E F 120 60 58 122 98 141

The perimeter of a polygon is the length of the broken line: P = AB + BC + CD + DE + EF + FA = 120 + 60 + 58 + 122 + 98 + 141 = 599

A polygon with three vertices is called a triangle, with four - a quadrilateral, with five - a pentagon, etc.

Sections: Primary school

Class: 2

Goals:

1. Introduce students to the concept of a ray as an infinite figure;
2. Learn to show the beam using a pointer;
3. Continue building computing skills;
4. Improve problem solving skills;
5. Develop the ability to analyze and generalize.

Lesson progress

I. Organizational moment.

Guys, are you ready for the lesson? ( Yes. )
I count on you, friends!
You are a good friendly class.
Everything will work out for you!

II. Motivation for learning activities.

I really want the lesson to be interesting, informative, so that together we repeat and consolidate what we already know and try to discover something new.

III.Updating knowledge.

1. Read the numbers and name the “extra” number in each row:
   a) 90, 30, 40, 51.60;
   b) 88, 64,55,11, 77, 33;
   c) 47, 27, 87, 74, 97, 17;
2. List the numbers in order:
   a) from 20 to 30;
   b) from 46 to 57;
   c) from 75 to 84;
3. Do you think these texts will be tasks?

Change the question in the second text so that it becomes a task.

Change the condition so that the text becomes a task.

Solve the given problems.

IV. Primary absorption new knowledge.

Draw a line like this.

What is it called?

Draw a line like this.

What is it called? What is the difference between a segment and a straight line?

Draw a line like this.

Who knows what it's called?

Look at the picture, you see similar lines, what is it?

This line is called a ray. How does it differ from a straight line and a segment?

This is a very interesting figure: it has a beginning and no end.

And this is how they portray her. ( Work on the board and in notebooks.) Mark a point, apply a ruler to it and draw a line along the ruler.

No matter how long the ruler is, we still won’t be able to draw the entire beam. In the figure we have depicted only part of the beam, which shows the direction of the beam.

The beam can be drawn in any direction:

Draw three different rays in your notebook.

To distinguish one ray from another, we agree to denote the ray by two letters Latin alphabet the way we marked the segments with you. The letters must be written in a strictly defined order: the first letter is written that indicates the beginning of the beam, the second is written above or below the beam.

Look at the picture in the textbook. The red beam is indicated by two letters. What letter indicates the beginning of the ray?

Let's read the entry together: “Beam AB”

Now read the following entries: beam BC, beam MK, beam BA, beam OX.

It is important to learn how to show the beam correctly. We will do this with the end of the pointer. ( Demonstration by the teacher.)

Now look at the poster. ( Prepared in advance, it has 3 rays.) It shows 3 rays. Read the title of each one. When naming a beam, show it with a pointer.

Fizminutka

1, 2, 3, 4, 5
We all know how to count.
We also know how to relax:
Let's put our hands behind our backs,
Let's raise our heads higher
And let's breathe easily.
One, two - head up,
Three, four - the legs are wider,
Five, six - quiet network.
Once - get up, stretch.
Two – bend over, straighten up.
Three - three claps of your hands,
Three nods of the head.
By four – your arms are wider.
Five - wave your arms.
Six - sit quietly at your desk.

V.Initial check of understanding.

1) Working with the textbook.

Is it possible to draw the entire beam?

In what direction can the ray be drawn?

Students name each ray by first reading the letter corresponding to the beginning of the ray.

Students draw a ray in their notebooks and label it with letters.

Place point O in your notebook. Draw a straight line through it. How many rays did you get?

Draw another straight line through this point. How many rays are there now?

VI. Organization of mastering methods of activity.

1) Work in a printed notebook.

Differentiated task.

1st group - No. 19

2nd group - No. 20

3rd group - No. 21

2) Fizminutka – ophthalmic simulator.

3) Working from the textbook

Read what addition methods did Znayka come up with?

Find the results of addition using the same methods.

What is known about the problem?

What do you need to know?

In short – is it more or less?

How to find out the length of a pencil?

Write down your answer.

VII. Reflection.

What new did you learn in the lesson?

What is a beam?

How to draw a ray?

How many rays can be drawn through one point?

Today in class they helped me.....

VIII. Homework.

Beam- is a part of a straight line located on one side of any point lying on this straight line. The beam is also called semidirect.

Any ray has a beginning and a direction. Beam start, starting point or beam apex is the point from which the ray emanates. Thus, the ray has a beginning, but no end.

Let's consider three rays with a common origin:

All 3 rays have a common starting point O, But different directions. About each of them we can say: the ray comes from a point O or a ray emanating from a point O .

Additional rays

Any point lying on a straight line divides this straight line into two half-lines, that is, into two parts. Each of these parts will be called an additional ray relative to the second ray:

Additional rays- these are rays that have a common origin, opposite directions and lie on the same straight line. We can also say that rays that complement each other to a straight line are called complementary.

Ray designation

The beam is denoted by one lowercase Latin letter:

beam h.

The ray can also be designated by two points lying on it:

When designating a ray with two points, the first place is marked with a letter indicating the beginning of the ray, and the second place with a letter indicating some other point: ray B.C..

Let's look at the following example:

Beam with origin at point A can be denoted as AB or A.C..

On this page you will find examples and problems with detailed solutions from workbook in mathematics for grade 2 according to the Perspective program authors: Dorofeev G.V., Mirakova T.N. Buka T.B. for the 2018 - 2019 academic year.

Select the desired problem from the list and read its solution or go to the page with the solution.

Topic: Addition and subtraction (repetition)

Page 4 (No. 1)

Fill in the blanks with numbers as shown in the example.

Page 4 (No. 2)

Draw a path from the duck to the lake so that to the left of it there are houses whose number on the roof is less than the number in the window by 9, and to the right - by 8.

Page 4 (No. 3)

Do the calculations. Unscramble the word for the highest mountains on Earth by writing the answers to the examples in ascending order.

Page 4 (#4)

Place a + or - sign in the circle to make the correct entry.

Page 5 (#5)

Compose and solve circular examples.

Page 5 (No. 6)

There is a blue teapot, a green vase and a red cup on the table. Color them so that in the left picture the cup stands in front of the teapot and the vase behind it, and in the right picture there is a teapot in front and a cup behind the vase.

Solution

Page 5 (No. 7) (problem about two snails)

To view the solution, follow the link: No. 7 (problem about two snails)

Page 6 (No. 1)

Three boys - Vitya, Gleb and Misha - are photographing the playground from different sides. Which boy took this photo?

Answer: Gleb took the photo.

Page 6 (No. 2)

Compare.

Solution:

Page 6 (No. 3)

Do the calculations. Decipher the name geometric figure, writing down the answers of the examples in decreasing order.


Solution:
Let's do the calculations first:

Let us arrange the answers received in descending order. We get the following sequence of numbers: 17, 16, 14, 13, 12, 11, 10, 9, 8, 7, 5, 4, 3, 2, 1
Let's substitute the corresponding letters and get the word: QUADAGON.

Page 6 (No. 4)

Fill in the blanks with numbers to make the correct entries.

Solution:

Page 7 (No. 5)

Complete the diagrams and solve the problems.
1. To repair the bench, 8 large nails were used, and 3 more small nails than large ones. How many big and small nails did it take to repair the bench?

Solution:
First, let's fill out the diagram:

1) 8+3=11(g.)
2) 8+11=19 (year)
Answer: 10 nails.

2. One car had 7 seats, and the other had 2 fewer seats. How many seats were there in total in these two cars?

1) 7-2=5 (m.)
2) 7+5=12(m.)
Answer: 12 places.

Page 7 (No. 6)

Measure the length of each segment in centimeters and write down the results.

Solution:
AB = 7 cm, SD = 4 cm, ME = 3 cm.

Page 7 (No. 7)

SO and NOT SO made up words from the bank of letters. SO he composed four words correctly, but NO SO he rearranged the letters in them. Try to read these words. Find and cross out the missing word:

1. POINT
2. RAMYAPYA
3. ZETROCO

First, let's decipher the words:

1. OCTA - POINT
2. RAMYAPYA - STRAIGHT
3. THIRL - LITER
4. ZETROKO - CUT

Superfluous in this list there will be a word - liter, since this is a unit of measurement, and the rest of the words are the simplest geometric figures.

Directions and rays

Page 8 - 9

1. Show with an arrow, as in the example, in which direction the white ball needs to be sent so that it, without hitting the edge of the billiard table, knocks into the pocket: a) blue ball, b) red ball, c) yellow ball, d) brown ball .

Let's draw arrows indicating the direction of the white ball in order to knock out each of the balls with the corresponding colors.

2. Draw an arrow in the direction of the wind in each picture.

3. Fill in the blanks with numbers as shown in the example.

4. Draw in the drawing, where possible, with a red pencil a ray with its beginning at point A so that it intersects all rays coming out from point B.

In the figure on the left, you can draw a ray starting at point A so that it intersects all the rays that leave point B.

5. Complete the diagrams and solve the problems.

1) There were 6 gingerbread cookies on one plate, and 5 on the other. Sasha took 8 gingerbread cookies. How many gingerbread cookies are left on the plates?

6. Place a + or - sign in the circle to make the correct entry.

Solution: 15 - 5 = 10 8 + 6 - 3 = 11 14 - 6< 10 15 + 5 = 20 8 + 6 + 3 = 17 14 + 6 > 10

Page 10 - 11

1. Do the calculations. Decipher the mathematical term by writing the answers to the examples in ascending order.

Let's do the calculations and write down the answers in ascending order.

Let's get a mathematical term - direction.

Answer: The encrypted mathematical term is direction.

2. Mark points A, B and C in your notebook as shown in the drawing. Draw a ray with a red pencil with its beginning at point A, and with a green pencil, draw a ray with its beginning at point B so that point C turns out: a) on the red ray, but outside the green ray; b) on red and green rays.

3. Recover your records.

Solution: 11 - 1 - 5 = 5 12 - 2 - 2 = 8 13 - 3 + 1 = 11 14 - 4 - 4 = 6 15 - 5 - 1 = 9 16 - 6 + 2 = 12 17 - 7 - 3 = 7 18 - 8 - 0 = 10 19 - 15 + 9 = 13

4. The cow is 7 years old, the sheep is 4 years old, and the ram is 9 years younger than the cow and sheep together. How old is the ram?

Solution: 1) 7 + 4 = 11 (l.) 2) 11 - 9 = 2 (g.) Answer: the ram is 2 years old.

5. Take measurements. Fill in the blanks with the results obtained. Find and draw with a red pencil the shortest path leading from point A to point B.

Solution:
2 + 3 + 1 + 5 = 11 (cm) Answer: The length of the shortest path from A to B is 11 cm.

6. Determine by what rule the pattern is made. Continue it.

Solution: Let's continue the pattern and get

Number beam

Page 12 - 13

1. The numbers are marked on the beam in the order they appear when counting. Fill in the blanks.

2. The grasshopper in the blue jacket jumped along the number line 3 spaces to the left, and the grasshopper in the red jacket jumped 9 spaces to the right. Mark the points on the number line where the grasshoppers will be in red and blue, respectively. Has the distance between the grasshoppers changed and by how many divisions?

Between the grasshoppers there was 5 divisions. Between the grasshoppers it became 7 divisions. The distance changed to 2 division.

3. Find a sail for each boat so that the answer to the example on the boat is equal to the number on a sail. For the remaining sail, draw a boat and write an example on it.

4. The mass of a box with apples is 12 kg, and with plums it is 5 kg less. Find the mass of the box with plums.

Solution: 12 - 5 = 7 (kg) Answer: the mass of the box with plums is 7 kg.

5. Fill in the gaps in the tables by performing calculations.

6. on each drawing?

7. Three brothers - Vanya, Sasha and Kolya - study at different classes one school. Vanya is younger than Kolya and older than Sasha. Write the name of the oldest brother, middle and youngest.

Solution: Mark the ages of the brothers on the number line. Since Vanya is younger than Kolya, he will be marked to the left on the number line. The problem statement also says that Vanya is older than Sasha, that is, on the number line he will be marked to the right of Sasha. As a result, we get the following straight line.
The older brother's name is Kolya, the middle one is Vanya, the younger one is Sasha.

8. Numbers from 4 to 9 are written in a row. Try putting a + sign between them
or - so that the result is 7.

Solution: 4 + 5 + 6 - 7 + 8 - 9 = 7

Page 14 - 15

1. A squirrel and a hare are jumping on a number line. First the squirrel jumps, and then the hare. Each jump of a squirrel is equal to 3 divisions, and each jump of a hare is equal to 6 divisions. At what point will each of them be after 3 jumps? Mark these points on the finishing beam with the letters B and Z, respectively.

Solution: Mark the steps of the squirrel and the hare on the number line.
From the figure we see that after 3 steps the Squirrel will be at point 9, and the hare at point 18. Answer: the squirrel will be at point 9, and the hare at point 18.

2. For each picture, make two examples of addition. identical numbers. Solve these examples.

3. Fill in the blanks with numbers such that you get the correct entries.

1) Pasha had 18 rubles. He bought the album for 9 rubles. and a pen for 5 rubles. How much money does Pasha have left?

2) There were 16 liters of milk in the can. First, 7 liters of milk were taken from it, and then another 4 liters. How many liters of milk are left in the can?

3) From a block of butter 14 cm long, cut a piece 5 cm long from one end and 2 cm from the other. Determine the length of the remaining piece of butter.

5. Three classmates - Sonya, Tanya and Vera - are involved in various sports sections: one is in the gymnastics section, the other is in the skiing section, the third is in the swimming section. What kind of sport does each of them do, if it is known that Sonya is not interested in swimming, and Vera is a winner in skiing competitions?

Solution: The problem statement states that Faith- winner in skiing competitions, which means she is engaged in the ski section. It is also said in the problem statement that Sonya is not interested in swimming, and she also does not participate in the ski section, which means she goes in the gymnastics section. And by method of elimination we find that Tanya visits swimming section. Answer: Vera is in the ski section, Sonya is in the gymnastics, and Tanya is in swimming.

Page 16 - 17 - Beam designation

1. Write down the designations of all the rays in the drawing.

Answer: the rays are indicated in the drawing: AB, VU, BE, VD, IR, OG.

2. Do the calculations. Decipher the name fairy tale hero, writing down the answers of the examples in decreasing order.

Answer: the name of the fairy-tale hero Prospero from the work “Three Fat Men” by Yuri Olesh.

3. Complete the short notes and solve the problems.

1) During the summer holidays, Vitya painted 4 portraits, 6 still lifes and 8 landscapes. How many paintings did Vitya paint during the summer holidays?

4. Fill in the blanks on the bows as shown in the example.

5. How many triangles and how many quadrilaterals are there in the star shown in the picture?

	Triangles - 8 Quadrangles - 5

6. Which figure from those numbered on the right is missing in the table? Circle her number. Draw this figure in an empty cell of the table.

Page 18 - 19 - Angle

1. Mark with an arc on the drawing all the corners of the quadrilateral and triangle, as shown in the sample. Fill in the gaps in the sentences.

Solution:
There are only 4 corners in a quadrilateral. There are only 3 angles in a triangle.

2. Nadya is 12 years old, and her sister is 6 years younger. How old is your sister?

Solution: 12 - 6 = 6 (l.) Answer: my sister is 6 years old.

3. Complete the diagram and solve the problem. Try to find two solutions.
The boy had 15 rubles. He bought a bun for 9 rubles and tea for 3 rubles. How much money does the boy have left?

4. Fill in the gaps in the tables by performing calculations.

5. Fill in the blanks as shown in the example.

6. Decipher the words. Cross out the extra word.

RGUC	UCHL	GUOL	ISLOCH
CIRCLE	BEAM	CORNER	NUMBER

Page 20 - 21 - Angle designation

1. On each dial, mark with an arc the angle between the clock hands, as shown in the example.

2. Under each angle, write its designation.

The figures indicate the angles EGM, DAB and KVU.

3. Using these points, draw angles ABC and DEK.

4. Fill in the blanks with numbers such that you get the correct entries.

Solution: 1 dm 2 cm = 12 cm 14 cm = 1 dm 4 cm 1 dm 5 cm = 15 cm 17 cm = 1 dm 7 cm 2 dm 1 cm = 21 cm 11 cm = 1 dm 1 cm

5. Solve the examples and find out the score of the water polo match between the Seals and Walruses teams. It is known that goals were scored against the “Seals”, the answers to which are less than 15, and all the remaining goals were scored against the “Walruses”. Write down the score of the match.

6. On the table are a blue square, a red triangle and a yellow circle cut out of colored paper. Color the figures so that: a) the triangle is on top, there is a square below it, and a circle is at the very bottom; b) the pieces were in reverse order.

Page 22 - 23 - Sum of identical terms

1. Tick the box, as shown in the example, only for the sums of identical terms. Solve these examples.

2. Write down on the right, as shown in the example, an example of adding identical terms, in which you need to:

1) take 2 each 3 times: 2 + 2 + 2 = 6 2) take 3 each 4 times: 3 + 3 + 3 + 3 = 12 3) take 1 each 8 times: 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 8

Solve these examples.

3. Counting from 1 to 20, mark every third number and color the ball with this number in the picture.

4. Find out the mass of each bag of flour from the picture.

Solution: 1) 10 + 3 = 13 (kg) 2) 13 - 5 = 8 (kg) Answer: the weight of the bag is 8 kg.	Solution: 1) 15 - 3 = 12 (kg) 2) 12 - 3 = 9 (kg) Answer: the weight of the bag is 9 kg.

5. Compare.

Solution: 2 cm + 9 cm< 12 см 14 см - 1 дм = 4 см 6 см + 7 см >11 cm 18 dm - 8 dm = 10 cm 8 cm + 8 cm< 2 дм 15 см - 4 см >1 dm

6. The little bear is hurrying home. Help him find the shortest road - the answer of the example on it will be less than on the other two roads. This will be the bear's house number.

Write the resulting number in the empty box. Color the shapes on the found road with one color.

Page 24 - 25 - Multiplication

1. Match the example with his answer. Tick ​​the sums of identical terms as shown in the example.

2. Write examples using the multiplication sign. Solve them.

3 + 3 + 3 + 3 + 3 + 3 = 3 * 6 = 18 2 + 2 + 2 + 2 + 2 + 2 + 2 = 2 * 7 = 14 4 + 4 + 4 = 4 * 3 = 12 5 + 5 + 5 = 5 * 3 = 15 7 + 7 = 7 * 2 = 14

3. There were 3 squirrels. Each squirrel was given 2 nuts. How many nuts were given to all the squirrels? Draw nuts for each squirrel. Fill in the blanks in the sentence.

Solution:
Take 2 3 times, you get 6.

4. Guess how the numbers in squares and circles are related to each other. Fill in the blanks.

5. There were 12 crows sitting on one tree, and 7 fewer crows on the other. How many crows were there in total on the two trees?

6	Solution: 1) 12 - 7 = 5 (c.) 2) 5 + 12 = 17 (c.) Answer: on two trees 17 crows were sitting.

6. On the dotted line, draw a segment OK, which is 2 cm longer than this segment AB.

7. Draw with a green pencil a path along which the puppy needs to run in order to overcome obstacles and get to the bone.

Page 26 - 27

1. Draw 3 pies on each plate. How many pies did you make? Fill in the blanks in the example and in the sentence.

Solution: 3 * 5 = 15 Take 3 5 times, you get 15.

2. For each boat, find its anchor.

3. Fill in the gaps in the tables by performing calculations.

4. One jar contains 3 liters of honey. How many liters of honey are in 4 of these jars?

5. Fill in the blanks with numbers such that you get the correct entries.

1 dm 3 cm = 13 cm 15 cm = 1 dm 5 cm 1 dm 6 cm = 16 cm 18 cm = 1 dm 8 cm 2 dm 7 cm = 17 cm 10 cm = 1 dm

6. Compose and solve circular examples.

7. How many triangles and how many quadrilaterals do you see in the drawing?

Answer: there are 4 triangles and 6 quadrangles in the drawing.

8. Foma and Erema divided 7 rubles between themselves, and Foma received 3 rubles more than Erema. How much money did each person get: Write your answer.

Solution: 1) 7 - 3 = 4 (r.) 2) 4: 2 = 2 (r.) 3) 2 + 3 = 5 (r.) Answer: Foma got 5 rubles, and Eryomy got 2 rubles.

Page 28 - 29 - Multiplying the number 2

1. Draw 2 carrots for each bunny. How many carrots are there in total? Fill in the blanks in the entry.

Solution:
2 + 2 + 2 = 2 * 3 = 6 (m.)

2. Draw 2 circles on each wing of the butterflies. How many circles did you get?

Solution:
2 + 2 + 2 + 2 + 2 + 2 = 2 * 6 = 12 (k.)

3. Connect each body with a cabin so that the sentence and example mean the same thing.

4. Complete the diagrams and solve the problems.

1) 7 people were dining at one table, and 3 fewer people at the other. How many people were dining at the two tables?

Solution: 1) 7 - 3 = 4 (h.) 2) 7 + 4 = 11 (h.) Answer: 11 people were dining at two tables.

2) 11 people were having lunch in the dining room. Then 6 more people came, and 2 people left. How many people are left in the dining room?

5. From the figures numbered on the right, assemble a “cat” that is missing in the table. Circle the numbers of the required figures. Draw a “cat” in an empty cell of the table.

Page 30 - 31

1. Draw and color 2 circles in each rectangle. How many circles are drawn?

Solution: 2 + 2 + 2 + 2 + 2 = 2 * 5 = 10 (k.)

2. One package contains 2 kg of noodles. How many kilograms of noodles are in 7 such packets?

Solution: 2 + 2 + 2 + 2 + 2 + 2 + 2 = 2 * 7 = 14 (kg) Answer: There are 14 kg of noodles in 7 bags.

3. In the number centipede, each pair of boots is numbered so that if you multiply these numbers, you get the number on the corresponding jersey. Write down the missing numbers.

4. For each example, find the answer and connect the strips, taking into account the break line.

5. Compare.

3 l< 13 л 2 см = 20 дм 20 см = 2 дм 16 кг >10 kg 1 dm = 10 cm 2 dm > 16 cm

6. The ball costs 12 rubles, the doll is 5 rubles more expensive than the ball, and the notebook is 9 rubles cheaper than the ball. How much does the doll cost and how much does the notebook cost? Write down your answers.

Solution: 12 + 5 = 17 (r.) 12 - 9 = 3 (r.) Answer: the doll costs 17 rubles, the notebook costs 3 rubles.

7. Measure the lengths of the segments and write down the results.

MB = 5 cm BC = 2 cm TA = 7 cm EI = 4 cm

8. How many numbers in total will it take to number 14 drawings in the album, starting with number 1?

Solution: Let's write down the numbers of the pictures in order: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 There are 9 single-digit and 5 double-digit numbers in the written sequence. Let's count the number of numbers used: 5 * 2 = 10 (ts.) 10 + 9 = 19 (ts.) Answer: to number 14 drawings in an album you need 19 numbers.

Broken line. Polyline symbol.

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1. Find the broken lines in the picture and circle the closed broken lines in blue, and the open ones in red.

2. In each frame, draw a broken line ABOKM with a green pencil so that in the frame on the left you get a closed broken line, and in the right - an open one.

Closed (left) and open (right) broken lines

3. Do the calculations. Decipher the name of the mathematical science by writing down the answers to the examples in increasing order.

Answer: the name of mathematical science is logic.

4. Draw 3 paths along which Fedya can get to school: a) by bus; b) on a bicycle; c) on foot.

5. Masha has 6 coins, 2 rubles each. each, and another 5 rubles. How many rubles does Masha have in total? Fill in the blanks.

1) 2 * 6 = 12 (r.) 2) 12 + 5 = 17 (r.)

Can Masha buy ice cream for 9 rubles with this money? and lollipops for 6 rubles.

1) 9 + 6 = 15 (r.) 2) 17 > 15

Please tick the correct answer.

Answer: Yes, with her own money Masha can buy herself ice cream for 9 rubles and lollipops for 6 rubles.

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1. In this drawing, circle all the polygons in red pencil.

2. Using these points, construct a polygon ABSDE. Mark its angles SDE and AED with arcs.

3. Solve the examples using the number line as shown in the sample.

Solution:

4. Complete the diagrams and solve the problems.
1) Grandma in the village has 7 geese and 15 chickens. How many fewer geese are there than chickens?

5. Put + or - signs in the circles so that you get the correct entries.

Solution: 13 + 2 - 8 = 7 7 + 5 + 4 = 16 6 + 10 - 3 = 13 9 - 8 + 11 = 12

6. Compare.

Solution: 1 dm 2 cm - 7 cm< 6 см 15 см - 1 дм >4 cm 1 dm 4 cm + 5 cm< 2 дм 11 см + 3 см < 1 дм

7. Fill in the blanks by completing the calculations.

Multiplying the number 3

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1. For each chicken, draw 3 grains. How many grains did you get? Fill in the blanks.

Solution: 3 + 3 + 3 + 3 + 3 = 3 * 5 = 15 (z.)

2. Label the vertices of each polygon with letters on the drawing.
How many letters did you need? Write it down.

Solution:
To designate polygons, 9 letters were needed: A, B, C, O, M, P, T, E, X.

3. Using these points, draw an open broken line ABSDE.

Measure the length of each link and calculate the total.

Solution:
AB + BS + SD + DE =

4. Check if the given examples are circular. If yes, then connect them with a line so that the answer of the previous example is the first number in the next example.

5) Complete the diagram and solve the problem. One set has 12 cups, and the other has 6 cups less. How many cups are there in two sets?

Solution: 1) 12 - 6 = 6 (hours) 2) 12 + 6 = 18 (hours) Answer: There are 18 cups in two sets.

6. The family has three children: two boys and a girl. Their names begin with the letters A, B, G. Among the letters A and B there is the initial letter of the name of only one boy. Among V and G there is the initial letter of the name of only another boy. What letter does the girl's name start with?

Solution: The problem statement says that among the letters A and B there is the initial letter of the name only one boyToA , which means the second letter from A and B is the initial letter of the girl’s name. By the method of elimination we find that second brother's name - starts with the letter G . Also in the problem statement it is said that among V and G there is the initial letter of the name just another boy .Since we found out that the second boy’s name begins with the letter G, then A girl's name starts with the letter B . Respectively with a letter And the name of the first brother begins . Answer: The first brother's name begins with the letter "A", the second brother's name begins with the letter "G", the girl's name begins with the letter "B".

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1. Draw and color 3 cucumbers on each plate. How many cucumbers are there in total?

3 + 3 + 3 + 3 = 12 cucumbers.

2. One can contains 3 kg of paint. How many kilograms of paint are in 6 of these cans?

3 + 3 + 3 + 3 + 3 + 3 = 3 * 6 = 18 kg.

3. Connect each suitcase with its handle so that the sentence and example mean the same thing.

4. Compare.

2 * 2 = 2 + 2 3 * 3 > 3 + 3 2 * 5 > 2 + 5 2 * 3 > 2 + 3 3 * 4 > 3 + 4 3 * 6 > 3 + 6 2 * 4 > 2 + 4 3 * 5 > 3 + 5 2 * 8 > 2 + 8

5. Who will score a goal first in the match between the “Squares” and “Triangles” teams? The rules are as follows: a football player can only pass the ball to the player whose jersey number is equal to the answer of the example written under this football player. For example, player number 7 will pass the ball to football player number 6, since 2 * 3 = 6. Draw a smooth line diagram of the ball passing from player to player. Kick the ball into the goal.

The goal was scored by a player from the Triangles team! at number 3.

6. Compare.

14 kg > 4 kg 12 cm > 1 dm 1 dm 3 cm< 2 дм 18 л >10 l 2 dm > 10 cm 1 dm 7 cm = 17 cm

7. Lyuba is 11 years old, Nadya is 4 years younger than Lyuba, and Vera is 7 years older than Nadya. How old is Nadya and how old is Vera? Write down your answers.

Nadya is 11 - 4 = 7 years old. Vera is 7 + 7 = 14 years old.

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1. Fill in the blanks in the tables.

2. Solve the examples using the number line.

3. Do the calculations. Decipher the name of the heroine of the fairy tale, arranging the answers of the examples in ascending order.