A person can tell not only about the properties of an object, but also about relationship, in which this object is located with other objects.
For example:
"Ivan is the son of Andrey";
"Everest is higher than Elbrus";
"Winnie the Pooh is friends with Piglet";
"21 is multiple of 3";
“Kostroma is the same old city as Moscow”;
"A word processor is part of the computer software."

In each of the above sentences, the name of the relationship is highlighted, which denotes the nature of the relationship between the two objects.

Relationship can exist not only between two objects, but also between an object and a set of objects, for example:
"A diskette is a carrier of information";
"Kamchatka is a peninsula (is a peninsula)."

Each of these sentences describes attitude "Is an element of the set".

A relationship can link two sets of objects, for example:
"Wheels are part of cars";
"Butterflies are insects (a type of insect)."

Several objects can be pairwise connected by the same relationship. The corresponding verbal description can be very long and difficult to understand.

Let about settlements A, B, C, D, D and E some of them are known to be connected by rail: settlement A connected by railway with settlements C, D and E, locality E- with settlements C, D and D.

For greater clarity, existing connections ("connected by a railroad") can be depicted with lines on the relationship diagram. Objects on the relationship diagram can be depicted as circles, ovals, dots, rectangles, etc. (Figure 1.2).

Some relationship names change when the object names are swapped, for example: "Above" - ​​"below", "is the father" - "is the son." In this case, the direction of the relationship is indicated by an arrow on the relationship diagram.

So, in fig. 1.3 each arrow points from the father to his son and therefore reflects the attitude of “due to the father” rather than “due to the son”. For example: "Andrey is Ivan's father."

Arrows can be omitted if it is possible to formulate and comply with the rule mutual disposition objects on the diagram. For example if in Fig. 1.3 children's names should always be placed below their father's name, then arrows can be dispensed with.

Such relationship, how “He has a son,” “is connected by a railroad,” “buys,” “heals,” etc. , can only link certain types of objects... And in relationship"Is a part" and "is a variety" any objects can be.

Briefly about the main

The message about an object can contain not only the properties of this object, but also the relationships that connect it with other objects. The name of the relationship indicates the nature of that relationship. Relationships can connect not only two objects, but also an object with a set of objects or two sets.

Any relationship between objects can be clearly described using a relationship diagram ... Objects on the relationship diagram can be depicted as circles, ovals, points, rectangles, etc. Relations between objects can be depicted by lines or arrows.

Questions and tasks

1. State the name of the relationship in each sentence provided. What name can be given to the relation if the names of the objects in the clause are reversed? In which pairs does the name of the relationship not change?
a) Gingerbread man sings a song to Fox.
b) The Little Humpbacked Horse helps Ivan.
c) There is Manezhnaya Square in Moscow.
d) Pilyulkin treats Syrup.
e) The Scarecrow travels with Ell and.

2. For each pair of objects, specify the appropriate relationship.

3. What connection is reflected in each diagram of relations in fig. 1.4-1.8? Choose the correct answer from the following options:
"Is a variety";
"Is a part of";
"Is a condition (reason)";
"preceded".

Varieties of objects and their classification

Of two sets, related by the relationship "is a variety" , one is a subset of the other. For example, the set of parrots is a subset of the set of birds, the set of natural numbers is a subset of the set of integers.

The scheme of the relation "is a variety" we will call the scheme of varieties(fig. 1.9). Such schemes are used in textbooks, catalogs and encyclopedias to describe a wide variety of objects, such as plants, animals, complex sentences, vehicles, etc.

In a species diagram, the name of a subset is always below the name of its enclosing set.

Objects of a subset necessarily have all the features of objects of the set(inherit the attributes of a set) and besides them have their own additional attribute (or several attributes). This additional feature can be a property or an action. For example, any pet needs to be fed, dogs bark and bite, and sled dogs also run in a team.

It is important to understand, what objects themselves are not divided into any sets or subsets. For example, the watermelon is completely "indifferent", it belongs to the family of pumpkin plants, to a subset of striped or spherical objects. Subsets of objects are distinguished and designated by a person, because it is more convenient for him to assimilate and transmit information. The fact is that a person can simultaneously concentrate his attention only on 5-9 objects. To simplify the work with many objects, it is divided into several parts; each of these parts is again divided into parts; those, in turn, again, and so on. The division of a large set into subsets does not occur spontaneously, but according to some characteristics of its objects.

A subset of objects having common features, called a class. Division of a setobjects into classes is called classification. The signs by which one class differs from another are called the basis of the classification.

A classification is called natural if the essential features of objects are taken as its basis. An example of natural classification is the classification of living things proposed by Carl Linnaeus (1735). Currently, scientists divide the multitude of all living things into five main kingdoms: plants, fungi, animals, protozoa and prokaryotes. Each kingdom is divided into levels - systematic units. The highest level is called a type. Each type is divided into classes, classes - into detachments, detachments - into families, families - into genera, and genera - into species.

The classification is called artificial if insignificant attributes of objects are taken as its basis. TO artificial classifications include auxiliary classifications (alphabetic subject indexes, nominal catalogs in libraries). An example of an artificial classification is the division of many stars in the sky into constellations, carried out according to signs that had nothing to do with the stars themselves.

We can propose the following classification of objects with which the user interacts in operating system Windows (fig. 1.10).

Briefly about the main

Variation scheme is a schema of "is a kind" relationship between sets and subsets of objects.

Objects of a subset have additional characteristics, in addition to those of objects of the set that includes this subset.

A subset of objects that have common characteristics is called a class. Dividing a set of objects into classes is called classification. The signs by which one class differs from another are called the basis of the classification.

Questions and tasks

1. For each of the specified subsets, name the set with which it is associated with the relationship "is a variety" (what is the common name that answers the question "What is this?"):
a) pronoun;
b) comma;
c) joystick;
d) parallelogram;
e) town hall;
f) a fable;
g) capillary.

2. Find in the list six pairs of sets between which there is a "is a variety" relationship. Define a subset name in each such pair. Name at least one additional property for it:
book;
petrol;
doctor;
milk;
builder;
textbook;
liquid;
directory;
human.

3. Select from the list the names of nine sets that have a "is a variety" relationship. Make a diagram of the varieties:
Apple tree;
conifer tree;
Pine;
fir;
wood;
deciduous tree;
Apple;
trunk;
fruit tree;
Birch;
oak;
larch;
root;
acorn.

4. Using the proposed classification of parallelograms, describe the properties of a square that inherits them from two ancestors at once - a rectangle and a rhombus. What additional properties does a square have:
a) in relation to the rectangle;
b) in relation to the rhombus?

5. Each item lists the objects, grouped by class. For example: table, computer, bow / cow, pen, pot / village, banner, feather - these are nouns classified by gender. Determine the basis of the classifications:
a) spruce, pine, cedar, fir / birch, aspen, linden, poplar;
b) potatoes, onions, cucumbers, tomatoes / apples, oranges, pears, tangerines;
c) rye, silence, lies, lynx / wheat, silence, truth, cat;
d) shirt, jacket, dress, sundress / coat, fur coat, raincoat, wind jacket;
e) wolf, bear, fox, elk / cow, dog, cat, horse.

6. Suggest your classification of computer objects "file" and "document".

Practical work No. 2
"Working with objects in the file system"

1. Open the window My computer... Browse files and folders located on disk WITH:.

2. Use the buttons Forward and Backward on the toolbar Regular buttons to move between previously viewed objects.

3. Select from the menu Command Kind: Page Thumbnails, Tiles, Icons, Table. Watch for changes in the display of folders and files. Find the button on the Common Buttons toolbar that allows you to quickly change the view of folder contents.

4. Using the button Folders display the panel on the left side of the window Folder Browser... Use it to view the files and folders located on the disk again. WITH:... Watch for the changes taking place on the right side of the window.

5. Using the button Search find your own folder - the folder where your work is stored. For this in the window Assistant click on the link to search Files and folders... Enter the folder name and search scope in the appropriate fields.

6. Open your own folder. It should contain subfolders Documents, Blanks_6, Blanks_7, Presentations and Pictures. Review the contents of these folders.

7. The folder Stock_6 contains the files that you used during the work of the computer workshop in the last year. Since you no longer need this folder, delete it (for example, using the context menu command).

8. The Documents, Presentations and Pictures folders contain your last year's work. I would like to keep them.

Create an Archive folder in your own folder. To do this, move the mouse pointer to a blank area of ​​your own folder window and right-click (open the context menu). Execute the command [Create a folder].

Move the Documents, Presentations and Pictures folders one by one to the Archive folder. For this:
1) select the Documents folder and, while holding down the left mouse button, drag the Documents folder to the Nanku Archive;
2) open the context menu of the Punks Presentation, execute the Cut command. Open the Archive folder and use the context menu to paste the Presentations folder into it;
3) cut the Pictures folder and paste it into the Archive folder using the menu bar commands.

9. Use the context menu to rename the Blanks_7 folder to Blanks.

10. Make sure your folder has a structure similar to the one below:

Math lesson

Theme: Solving problems to increase and decrease the number several times(lesson in generalization and systematization of knowledge)

Goals: creating conditions for the development of the ability to solve problems of finding a number several times greater or less than a given

UUD:

Cognitive:

general educational -

rightchoose arithmetic operation (multiplication or division) for solving problems of finding a number several times greater or less than a given number;

call the results of all tabular cases of multiplication and division, as well as the addition of single-digit numbers and the corresponding cases of subtraction;

fulfill orally and in writing, addition and subtraction of numbers in the range of 100;

define arithmetic operations for solving a variety of word problems;

realize self-control of the correctness of calculations

brain teaser -

the construction of reasoning in the form of a connection of simple judgments;

find different ways of solving problems;

evaluate the proposed solution to the problem andjustify your assessment.

Regulatory:

take into account the rule in planning and controlling the solution.

Communicative:

take into account different opinions and strive to coordinate different positions in cooperation.

Personal:

expand cognitive interests, educational motives;

are able to work in pairs;

understand the meaning of the boundaries of their own knowledge and "ignorance".

Equipment:

disk "EOR to the textbook of M.I. Moreau. Grade 2 Mathematics ";

reflection cards;

cards for individual work, for work in pairs and groups.

During the classes

I ... Motivation to learning activities

Target: inclusion of students in activities at a personally significant level:"I want it because I can."

Reception of reflection "In one word": students need to choose 3 words out of 12 that most accurately convey their state at the beginning of the lesson, and then at the end:

II ... Actualization and fixation of an individual difficulty in a trial educational action

Target: repetition of the material studied and identification of difficulties in the individual activities of each student.

Individually:

Draw relationships with arrowsmore between the given numbers. Make statements about each pair of numbers.

12 . . 23

One student on the card, the other at the blackboard (on the back side) with mutual checking:

Correct mistakes:

63: 9 = 8 (7) 3 ∙ 6 = 18 (5 + 4) ∙ 2 = 16 (18)

8 ∙ 6 = 54 (48) 45: 5 = 8 (9) 4 ∙ (8 ∙ 0) = 4 (0)

7 ∙ 4 = 28 27: 3 = 7 (9) 56: (7 ∙ 1) = 8

Verbal counting

1. How much 15> 5(on 10)

How many times 15> 5(3 times)

- How to find out how many units one number is greater or less than another? (How many times?)

Form the questions using the numbers 7 and 28 and the word "less".

2. Insert missing numbers and action signs:

5 * □ = 15 (+ 10; ∙ 3) 40 * □ = 5 (: 8; - 35)

9 * □ = 9 (+ 0; - 0; : 1; ∙ 1) 28 * □ = 0 (- 28; ∙ 0)

3. What is the seventh part of the number 63; fifth of 35?(9; 7)

The eighth part of the number is 8. Find this number.(64)

The ninth part of the number is 2. Find this number.(18)

4. A pie costs 6 rubles, and a bun costs 3 rubles more. How much money should I pay for a bun?(9 rubles) * Mom bought 2 rolls with poppy seeds and cottage cheese and one pie. How much money did mom pay? (42 rubles) * Mom paid with a 50-ruble note. How much change did mom get? (8 rubles) What if mom pays with a 100-ruble bill? (58 rubles)

5*. They say that point B lies on the line between points A and C, if moving along this line from A to C (or from C to A) we will definitely pass through point B. This situation is shown in Figure 1.

Draw a line through points M, K, P shown in Figure 2 so that point P lies on it between points M and K.

What is a utterance? What statements have you made about pairs of numbers?

III ... Knowledge inclusion and repetition

The 1st verse of the song "Will there be more ..."

How can our lesson and this song be related?(Perhaps we will solve very difficult problems. The topic of our lesson is "Problem solving" ...)

Why do you need to be able to solve problems? How can this be useful to you in life?

Today we have a generalizing lesson. What knowledge do we need?(We must know what it means to increase and decrease a number several times. How to compare numbers. The multiplication and division table ...)

At computer:

Numbers from 1 to 100. Multiplication and division

Finding the work

Exercise 1; task 2

Perimeter of a rectangle

Assignment 2

1. Frontal work: solving a problem with unnecessary data; changing the question - notebook p. 36 No. 7.

2. Work in pairs (on cards)

Write down the expressions and find their meaning:

Reduce the sum of the numbers 20 and 12 by 4 times( 20 + 12) : 4 = 8

Increase the difference of numbers 11 and 9 by 8 times(11 – 9) ∙ 8 = 16

Reduce the product of 5 and 8 by 45 ∙ 8 – 4 = 36

How much is the sum of the numbers 6 and 3 more than the quotient of the same numbers?

(6 + 3) – (6: 3) = 9 – 2 = 7

Checking visual-signal plots by pictures: students compose expressions, find the answer in pictures and lay out the desired figure in front of them.

What unites these figures?(These are polygons; flat shapes)

In the group (Polina, Kolya, Lera, Sasha M.) they work according to the card:

1) 60: 30 = 2 (times)

2) 6: 2 = 3

Answer: 3 kg.

2. Independent solution tasks of different difficulty levels(tasks are written in different colors on one card)

Option 1:

There are 45 cars in the parking lot, and there are 9 times less trucks. How many trucks are there?

There are 45 cars in the parking lot, and there are 9 times less trucks. How many trucks and cars are there?

64 kg of cabbage was brought to the dining room, and beets are much less. How many kilograms of beets were brought to the dining room?

How many vegetables were brought to the dining room?

Write expressions to solve this problem.

Option 2:

One box contained 5 kg of pears, and the other 8 times more. How many kilograms of pears are in the second box?

One box contained 5 kg of pears, and the other 8 times more. How many kilograms of pears are in two boxes?

In one box there were 5 kg of pears, and in the other it was several times more. One fourth of all pears were given to children. How many pears were given to children?

Write an expression to solve this problem.

Testing only high-level problems: Students write expressions on the board.

Do you want to help a PhD candidate? Help to compose the problem, which is solved by the expression: 4 ∙ a - 4

(Mom bought 4 pies with cottage cheese, and many times more with jam. How many more pies did mom buy with jam than with cottage cheese?

Mom bought 4 pies with cottage cheese, and with jam a times more. We ate 4 pies with jam. How many jam pies are left?)

IV . Homework students' choice

(54 - 46) 5 (8 3 + 4 4): 4

(15 + 6): 3 (6 4 - 9): 5 8: 4

(25 + 7): 4 (28: 7 + 52): 8 7

71 – 15: 3 28: (7 – 3) + 81: 9

High level challenge:

There is a rectangle with a length of 8 cm and a width of 2 cm. It is necessary to decrease the length and increase the width of this rectangle to get a square, the perimeter of which is equal to the perimeter of this rectangle. Which of these shapes will fit more squares with a side of 1 cm?

When the father was 30 years old, the son was 5. Now the father is twice as older than the son. How old are father and son now?

V ... Reflection of educational activities in the lesson (result)

Filling the table with "One word"

Target: students' awareness of their UD (educational activity), self-assessment of the results of their own and the whole class.

Continue sentences:

I realized that ...

It was interesting…

It was difficult…

I wanted…

I managed…

Correct mistakes:

63: 9 = 8 3 ∙ 6 = 18 (5 + 4) ∙ 2 = 16

8 ∙ 6 = 54 45: 5 = 8 4 ∙ (8 ∙ 0) = 4

7 ∙ 4 = 28 27: 3 = 7 56: (7 ∙ 1) = 8

12 . . 23

They paid 60 rubles for 6 kg of potatoes. How many kilograms of potatoes can you buy for 30 rubles?

____________________________________________________________________________________________________________________________________________________________________________________________________

Consider and evaluate (true or false) this way of solving the problem:

1) 60: 30 = 2 (times)

2) 6: 2 = 3

Answer: 3 kg.

1736, Königsberg. The Pregel River flows through the city. There are seven bridges in the city, located as shown in the picture above. Since ancient times, the inhabitants of Königsberg have fought over the riddle: is it possible to cross all the bridges, passing on each only once? This problem was solved both theoretically, on paper, and in practice, on walks - passing along these very bridges. No one was able to prove that it was unfeasible, but no one could make such a "mysterious" walk across the bridges.

The famous mathematician Leonard Euler succeeded in solving the problem. Moreover, he solved not only this specific problem, but came up with a general method for solving such problems. When solving the problem of the Konigsberg bridges, Euler did the following: he "squeezed" the land into points, and the bridges "stretched" in a line. Such a figure, consisting of points and lines connecting these points, is called GRAPH.

A graph is a collection of a non-empty set of vertices and connections between vertices. The circles are called the vertices of the graph, the lines with the arrows are the arcs, the lines without the arrows are the edges.

Graph types:

1. Directed graph(briefly digraph) - whose edges are assigned a direction.

2. Undirected graph is a graph in which there is no direction of lines.

3. Weighted graph- arcs or edges are weighted (additional information).

Problem solving using graphs:

Objective 1.

Solution: Let us designate the scientists as the vertices of the graph and draw from each vertex of the line to four other vertices. We get 10 lines, which will be considered handshakes.

Objective 2.

8 trees grow on the school plot: apple, poplar, birch, mountain ash, oak, maple, larch and pine. Rowan is higher than larch, apple is higher than maple, oak is lower than birch, but higher than pine, pine is higher than rowan, birch is lower than poplar, and larch is higher than apple. Arrange the trees from lowest to highest.

Solution:

The vertices of the graph are trees, denoted by the first letter of the tree's name. There are two relationships in this task: “to be lower” and “to be higher”. Consider the relationship “to be below” and draw arrows from a lower tree to a higher one. If the problem says that the mountain ash is higher than the larch, then we put the arrow from larch to mountain ash, etc. We get a graph showing that the lowest tree is maple, then apple, larch, rowan, pine, oak, birch and poplar.

Objective 3.

Natasha has 2 envelopes: regular and air, and 3 stamps: rectangular, square and triangular. In how many ways can Natasha choose an envelope and a stamp to send a letter?

Solution:

Below is a breakdown of the tasks.

The position of one unit to the left and right of the given number. After that, the children can easily name the numbers they are looking for: for 7, these will be numbers 6 and 8, for 11, these will be 10 and 12, etc. Exercise 24. Problem with missing data: it is not known how many stamps were pasted on each envelope. For definiteness, we will assume that one stamp was stuck on each envelope. Solution: 12 - 6 = 6. Exercise 27. We remind you that while the problem is being solved without using subtraction. We argue like this: "The figure contains pairs" carrot - radish ". 7 radishes without pairs remained. This means that there are 7 more radishes than carrots, and 7 fewer carrots than radishes. " You can also reason like this: “7 carrots were not enough to make all the pairs. This means that there are 7 fewer carrots than radishes. " It is helpful for the students to provide such explanations themselves. Workbook№ 1 Exercise 3. Based on this figure, it is easy to compose the following problem: “On top shelf 5 cups, on the middle one - 6, and on the bottom there are as many cups as there are on the top and middle shelves together. How many cups are on the bottom shelf? " The solution is obvious. Exercise 6. In each case, you need to draw the reverse machine with an arrow, and then perform the necessary calculations. Exercise 7. Use this exercise to develop children's speech. Let them tell you what actions and in what sequence they will perform: “Take a ruler, put a zero stroke (a stroke with the number 0) to the left end of the segment (the point shown on the left) and turn the ruler so that it is under the right end of the segment ... Now draw a line with a pencil and find out its length. The second end of the segment is located near the line with the number 6. Therefore, the length of the segment is 6 cm. We write the number 6 in the frame. " You can argue differently: “Let us apply a ruler to the points so that the left end of the segment is at the zero line of the ruler. Let's draw a segment and read the number written at its right end. The length of the segment is 6 cm. " Exercise 8. An assignment of an entertaining nature. Invite the children to guess for themselves and tell how to do it. Answer: sine. Exercise 11. The text of the problem is given with a substantive clarity, which will greatly facilitate the choice of action. In this case, to answer the question, you just need to count all the nuts shown in the figure. There are 4 and 8: (4 + 8), 12 in total. Exercise 12. This task is more difficult than the previous one. It can be easily solved by placing the chips. So, we lay out 12 chips (each chip means a postcard that Yura had). Yura has 5 postcards left (let's count 5 chips to the left or right and move them aside). He gave Yulia 7 postcards (12 without 5). Solution: 12 - 5 = 7. Answer: 7. Exercise 14 serves to develop graphic skills. This task is performed by students independently. Exercise 17 The task can be difficult for many children. Therefore, work on it can be done like this. After reading the entire text, pay attention to the question. “The question contains the words“ How much less ... ”. We found the answer to this question by depicting chips in two lines, making pairs. Let's read again the question: "How much less candy is there in the vase?" What do you need to know for this? How many sweets were in the vase and how many they took. How many sweets they took is easy to find: 4 and 6. But how many there were is unknown. Let's think about it: do we need to know how many candies were in the vase? There is no need. After all, the vase contained fewer candies by as much as they were taken. How much did they take, how to find out what action? (Addition.) What numbers do you add? (4 and 6). Let's write down the solution: 4 + 6 = 10. Answer: by 10 ". Exercise 18. The task is similar to the previous one. The difference is that in this case the amount of water in the barrel increased by as many buckets as they were poured into the barrel, that is, by 11 (6 + 5 = 11). Exercise 21. Points can be marked at the ends of the sides, that is, at the vertices of the triangle. For example: a) b) c) Exercise 22. The figure already shows 4 vertices of the quadrangle. Invite students to tell how to draw it correctly. They must say that you need to take a ruler and use it to connect the points in order from the cuts. Then color in the quadrilateral. Topic 4. Comparison of numbers The concepts of “greater than” and “less” related to numbers were encountered in the course before. However, now the most close attention is paid to the theoretical training of children. In lessons 32–34, students will learn how to compare numbers in two ways. The first is connected with the place of a number in the natural row: the earlier the number is called when counting, the smaller it is, and the later, the larger it is. The second way is related to the position of numbers on the ruler scale: the more to the left the number on the scale, the smaller it is; the more to the right, the more. Notes for the teacher Signs< » и « >»To record the results of comparing numbers are not entered in the first class. Instead, colored arrows are used: red stands for "more" and blue for "less." You can compare not only two, but more numbers. As a result, drawings are obtained, which are called graphs in mathematics. Statements about numbers connected by the relationship "less" and "more" are depicted with the help of colored arrows as follows: p. cr. 9 12 10 6 9 less than 12 10 more than 6 Using the columns with colored arrows, you can also depict other relationships, for example, the following: “A dress is more expensive than a blouse”, “Misha is younger than Kolya”, “A pencil is longer than a pen”. At the same time, it is advisable to agree that the blue arrows replace the meaning of similar words with the word less: younger, shorter, cheaper, lower, closer, etc., and the red arrows - words that are similar in meaning to the word more: older, longer, more expensive, higher, farther, etc. 83 For example: K to. s. with. P B M S s. The dress is more expensive than the blouse. Misha is younger than Kolya, Kolya is younger than Seryozha, Misha is younger than Seryozha. Remember the mathematics Each arrow connecting two points of a graph is called an edge, and each point is called a vertex. The figure shows a graph with 4 vertices and 6 edges (blue arrows mean "less"): 3 s. with. with. 1 sec. 5 sec. with. 8 An edge can be in the form of a loop if the relation “equals” or a relation similar to it in terms of meaning: “the same length (width, height, price)”, etc. is depicted. The graph shows the relation “less than or equal” between the numbers 10 , 15, 20 and the graph “equals” between the numbers 1, 3, 8, 5. The graph “equals” consists of some loops. with. 10 15 3 s. with. 20 1 8 5 Using the concept of a graph, you can solve interesting and meaningful problems. For example: “Not all edges are shown on the graph of this relation (you need to depict the missing ones)”, “Determine by this graph which relation is depicted (determine the color of the arrows)”, etc. You can find examples of such tasks in workbook No. 2. 84 Lessons 32–34 compare numbers and images of relationships using graphs; in lessons 35, 36, students get acquainted with the difference comparison rule and learn to apply it to solve problems containing the question: "How much more (less)? .."; in lessons 37–39, problems are solved to find a number that is greater or less than a given number by several units. Rules for comparing numbers (lessons 32, 33) How to enter new material The material of the textbook is divided into two lessons: in the first exercises 1–7 are performed, and in the second, exercises 8–14. First, look at the drawing in the tutorial on p. 62 (exercise 1). It depicts the following situation: a worker walks along a railroad bed and writes on poles in numerical order (read them out loud with the students). Next, ask the questions formulated in the text; after the children have answered them, read the rule. They do not need to memorize this rule word for word. Similar work run with exercise 8 on p. 63 textbooks. How to work with the exercises Tutorial Exercises 2, 3. Recommended form of answer: "Nineteen is more than thirteen, because when counting nineteen they call it later than thirteen", "Eleven is less than fourteen, because when counting eleven they call it before fourteen." Pay attention to the students' correct declension of numbers. Exercise 5. Often explaining why some objects are more numerous than others (in this case there are more blue balls than red ones), the child says: “There are more blue balls than red ones, because when counting the number 4 is called later than the number 3 ". This rationale relates to a completely different question: "Why is 4 greater than 3?" Therefore, the exact answer should be considered as follows: "There are more blue balls than red ones, since 4 is more than 3". If you later want to ask the students, why 85 mu is 4 more than 3, then the answer that we gave above is appropriate: “4 is more than 3, since when counting 4 it is called later than 3”. Exercise 8 In this exercise, you will find a second way to compare numbers using a ruler. Here, children are first introduced to the fact that zero is less than any other number and any other number is greater than zero. Exercise 12. When answering the questions, the students count letters and compare numbers. Exercise 13. Often, as the largest number, students call the one they know: ten, one hundred, one thousand, a million, or some other number, and they consider the smallest number to be 1. Both are wrong. First, listen to the answers and correct them if necessary. Explain that there is no largest number: no matter how large they name, you can add 1 to that number to get a larger number. The smallest number for first graders so far is 0 (zero). Workbook # 2 Exercise 2. Warn the students that in completing the task: "Write down the numbers that are greater than 10 (less than 20)", at your discretion, you need to select only three numbers and write them in the boxes. Exercise 3. Professions of people: agronomist, doctor, teacher, builder, painter. Exercise 5. Answer: 0, 1, 2, 3, 4, 5. There are 6 numbers in total. Depicting Relationships Using Graphs (Lesson 34) How to Introduce New Material Start with short story ... “By comparing two objects in size, we can determine which one is bigger, smaller, higher, lower, longer, shorter. Objects can be compared according to their price, that is, it is possible to find out which one is more expensive or cheaper than another. We compared numbers, found out which of them is greater or less than the other, and expressed the results of comparison in words. Proposals were obtained (in mathematics they are called statements). For example: “Yura is taller than Kolya in height”, 86 “An umbrella is cheaper than a raincoat”, “Three less than six”, “Eight is more than zero”. Today you will learn how to jot down such statements. Let's agree instead of words bigger, higher, older, longer, draw a red arrow, and instead of words smaller, lower, younger, shorter - blue. Look at the chalkboard. It contains a short summary of several true statements about numbers. The blue arrow replaces the word less, and the red arrow replaces more: c. with. K. K. 5 7 9 6 10 5 2 8 Let's read each of these statements. At the same time, we will remember that, when reading a statement, we first name the number from which the arrow goes, then, moving along the arrow, we say the word (“more” or “less”), and then we name the number to which the arrow goes. Let's try to read the first sentence: what number we call first (five), what word we say ("less"), what number we call second (seven). What happens? (Five less than seven.) Now read the rest of the statements yourself. ” How to work with the exercises Textbook Exercise 1. Question to students: "What word replaces the red arrow, the blue arrow?" Read the words above the arrows. Let's read a sentence (statement) about pairs of objects. First, about the watermelon and the apple. Remember, first we name the object from which the arrow goes, then we say the word more, finally we name the object to which the arrow comes. Who can read the statement? (A watermelon is bigger than an apple.) Now the second statement is about the chicken and the bear. (A chicken is smaller than a bear.) "Exercise 2. The figures show the statements:" A glass is higher than a cup "," A birch is below a spruce. " Exercise 3 (training). Students are asked to read each statement, keeping in mind that the blue arrow means less and the red arrow means more. Draw their attention to the last figure, which shows two arrows. We read the statements: "Eight is more than six", "Ten is more than four." Note to the teacher Often, when reading a statement like "8 less than 10", it is depicted p. With the help of column 8 10, children also read the “inverse” relation: “10 is more than 8”. But it is not shown in this graph, so you do not need to read it. Exercise 4 Explain to students that each of the Read Sayings activity compares three numbers in pairs: 1 and 3, 3 and 8, 1 and 8, first for less, then more. Note that the pictures differ in color and direction of the arrows. We read the statements: "One is less than three", "Three is less than eight", "One is less than eight"; "Three is more than one", "Eight is more than three", "Eight is more than one." Exercises 5, 8 and 9 are solved using chips that are laid out in two rows (rows) one below the other. These exercises are included in this lesson as preparatory exercises for the next two lessons. Exercise 7. Each figure shows two relationships — greater and less. In the first picture: "12 is less than 18", "18 is more than 12". In the second figure, the statements can be read in different ways, but it is useful to choose some kind of order. For example, first read all the statements depicted with the blue arrows, then all the statements depicted with the red arrows, or you can read the statements in pairs (0 is less than 1, 1 is more than 0, etc.). Workbook No. 2 Exercises 1, 2. In the figures, objects are presented in pairs. To ensure that all children get the same drawings, before talking to them, compare the objects drawn on the left with the objects drawn on the right, using the arrows of the corresponding color. Thus, the arrows will go from left to right (point to point). So, students should draw a red arrow from the oil can to porcini mushroom , a blue arrow from a small fish to a large, 88 red arrow from a circle of cheese to a small piece of cheese. You do not need to read the statements. In exercise 2, after drawing all the arrows, ask the children to read the statements about the objects that they got. For example: "A vase is higher than a candle", "A chicken is lower than an ostrich." Exercise 3. Before completing the drawings, ask the students to explain from which number to which the arrow will go and what color it will be. For example, we read the saying "6 is more than 3". Draw a red arrow from 6 to 3. In the latter case, you should also write numbers near the dots: on the left - 11, on the right - 6. Exercises 4–6. Children need to be told that the pictures depict correct statements about numbers. It is necessary to determine the color of the arrows and draw them along the dashed lines with colored pencils. Let us show the reasoning using one example. In the figure, the arrow goes from 18 to 9, 18 is greater than 9, therefore, the arrow should be red. We draw it. Exercise 9. In this case, numbers are compared in pairs, and everywhere the arrows go from lower numbers to higher numbers. This means that all arrows are blue. An arrow is missing from 0 to 2 (0 is less than 2). Exercise 10. These numbers can be compared both in terms of “more” and in terms of “less”. To be specific, choose one of these relationships and have students draw all arrows. There are three of them. Alternative work can be done: some students draw all blue arrows comparing numbers for "less" and others draw all red arrows comparing numbers for "greater". Exercise 11. The arrows in the picture should indicate the word "more". Missing arrows to draw: from 4 to 3, from 4 to 1, from 3 to 2, from 3 to 1. There should be 6 arrows in total in the figure. Using subtraction to compare two numbers (lessons 35, 36) How to introduce new material Children are almost ready to introduce the rule for comparing two numbers using subtraction, since they used to perform a sufficient number of exercises, finding out how many 89 objects are more or less than others. In this case, chips were used. Students will now learn this by using the action of subtracting from a larger number, a smaller one. Consider the drawing in the textbook on p. 67 (exercise 1). We pose the question: "How many boxes are there more than balls?" The figure contains pairs: box - ball. Three balls were not enough to make all the pairs, three boxes were extra. This means that there are 3 more boxes than balls, and there are 3 fewer balls than boxes. You can say this: "There are as many balls as there are boxes, without three." The number 3 can be determined without a picture. To do this, subtract the number of balls from the number of boxes. After completing several training exercises, introduce in the next lesson the rule that is formulated in the textbook on p. 68. How to work with exercises Tutorial Exercises 2, 3. First solve both problems with the help of chips, laying them in pairs, then use the subtraction action. Records: 10 - 6 = 4 and 12 - 5 = 7 - complete on the board and in notebooks. Exercise 5. The teacher draws the drawing on the blackboard, and the children in their notebooks. 16 17 18 In the course of this work, introduce the concepts of "graph", "vertex of the graph", "edge of the graph". Exercise 8 is intended to train your students to use the number comparison rule. RECOMMENDEDUESMETODIKA. We ask questions: “How do you know how much 3 is less than 5? (To find out how much one number is less than another, subtract the smaller from the larger number.) Name the larger number (5), the smaller number (3). What action are we performing? (Subtraction.) From which number shall we subtract which number? (Subtract 3 from 5.) How much is it? (2.) "Solve the first few examples with detailed analysis. In distant 90

I Organizing time

II Knowledge update. Verbal counting.

· Count to 20 and back.

Count from 11 to 19.

Count from 16 to 7.

· What number is 2 units to the left of 15?

· What are the 2 numbers that follow the number 18?

· "Lost" numbers. Find these numbers and restore order.

· Name the numbers of this series a) greater than 17; b) smaller 7.

· How to determine on a scale a number greater or less than a given one?

· Which number when counting is called before: more or less?

· Which number is greater: 5 or 6? Why?

· Which number is less than 32 or 23? Why?

Bottom line: - I see that you memorized how to compare numbers.

III Leading dialogue.

Do you know how to compare objects by size? What words do you use for this?

What words do you use when comparing objects in height?

And if you are comparing items in length?

When we compare something, we say sentences or statements. Eg: "Seryozha is taller than Kolya", "A textbook is more expensive than a notebook."

Try to make a statement with the given word “cheaper”.

And with the word "younger"?

What have you made up now?

And what are these sentences called in the language of mathematics?

IV Lesson topic message.

Today you will learn how to represent statements graphically.

V Problematic question.

What do you think can be used to replace the words "less" and "more"?

VI Discovery of new knowledge

Let's check your assumptions. (To remove and turn over notices: more, higher, longer, heavier - the graph is red on the back. Similarly, with notices, less, lower, shorter, lighter - the graph is blue).

Conclusion: - So, to designate words larger, higher, longer, heavier, we use a red graph, and to designate words smaller, lower, shorter, lighter - graph in blue.

Textbook work pp. 90-91 # 1. Let's make the first sentence.

Remember: first, we name the object from which the arrow comes, then we pronounce the word that is written above the arrow, and we name the object to which the arrow comes.

Who will read the first statement

Reading the output

Vii Work according to the textbook. Training exercises.

P.91, No. 2 - 3.

IX Work in a notebook. Exercises in graphing relationships.

Pp. 60-61, no. 1 - 3

Outcome: - How to represent the word "more" graphically? And the word "less"?

X Repetition and consolidation of what has been learned.

Work in notebook No. 3 No. 6.

What is the most convenient way to add the numbers 3 and 9?

What rule do you know?

Check the boxes for the examples to be solved based on this rule.

Work according to the textbook.

P. 93 # 9 (work with geometric material).

How do we measure line segments? What is the longest segment? What's the shortest?

Compare the lengths of the green and blue segments. What arrow do we designate this relationship?

P. 93 No. 10 (work with the table)

Find answers to questions using the data in the table.

P. 94 No. 18

How are we going to reason while solving this problem?

The ratio of 11 is greater than 10 graphically.

XI Lesson summary.

What new did you learn in the lesson?

What tasks did you like?