Presentation for the lesson "intersection and union of sets." Presentation for the lesson "intersection and union of sets" Notation of some numerical sets

Senina G.N., Senin V.G., MBOU "Secondary School No. 4", Korsakov

MANY. COMBINATORICS.

INTERSECTION AND UNION OF SEVERALITY.

Meta-item – Knowledge

The purpose of our lesson

In Conan Doyle's story “The Five Orange Pips,” the famous detective Sherlock Holmes had to establish the name of a sailing ship. All he knew about this ship was that in January 1883 it was in Pondyshire, in January 1885 in Dundee, and now it was in London. Having compared the lists of sailing ships that were at the indicated times in the indicated places, Sherlock Holmes established that only the American ship Lone Star was included in each of them. As a result, the crime was solved. The detective, having three sets, constructed a new one containing their common elements. It turned out that the new set consists of only one element

goal setting

Let's check your homework

TEXTBOOK

№ 747

TEXTBOOK

№ 749

P ⊂ N ⊂ Z; C ⊂ B ⊂ A; K ⊂ P ⊂ R

Entering into the topic of the lesson and creating conditions for conscious perception of new material.

Intersection and union of sets

Organization and self-organization of students. Organization of feedback

Working with text

TRAINING APPARATUS

№ 319

into each of these sets

Workshop

Working with text

TRAINING APPARATUS

№ 320

Workshop

Working with models

TRAINING APPARATUS

№ 323

Workshop

Working with models

TRAINING APPARATUS

№ 324

Workshop

Set Operations

PROBLEM WORKER

№ 638

PROBLEM WORKER

№ 639

Workshop

Set Operations

PROBLEM WORKER

№ 641

{-1,0,1}; {-5,-4,-3,-2,-1,0,1,2}

{-1,0}; {-4,-3,-2,-1,0,1}

{1}; {-2,-1,0,1,2,3,4}

{-1,0,1}; {-2,-1,0,1,2}

Workshop

Set Operations

TEXTBOOK

№ 757

Properties of zero when multiplying and adding numbers: A ⋅ 0 = 0; A + 0 = A.

Workshop

Set Operations

TEXTBOOK

№ 758

Set Operations

№ 760

TEXTBOOK

Checking the results obtained. Correction

Sets and life

Set is a fundamental concept not only of mathematics, but of the entire surrounding world.

Take any object in your hand right now. Here you have a set consisting of one element.

Take a large bag and start randomly putting various items into it.

There is no pattern in this, but, nevertheless, we are talking about a variety of subjects.

Homework U: pp. 228 – 229, fragment 1 – read;

№ 751, 752, 756, 759.

Summing up, reflection, homework.

Intersection and union of sets.

Kundeleva Oksana Evgenievna

Primary school teacher MBOU NOSH No. 279, Gadzhievo, Murmansk region,

Lesson objectives

form an idea of the union and intersection of two sets
learn to find on the “map of sets” the area of a set that is the intersection or union of two sets
teach to determine whether elements belong to a set, which is the intersection and union of two sets
learn to determine the nature of the relationship between two given sets (intersection, do not intersect, union)

What is a set? A bunch of- is a group of objects, objects or creatures. Name the elements of the set:

“Months of the Year”
"Seasons"
“Continents”
“Flying Hippos”
Polygons

Bat crow penguin

Butterfly tit ostrich

Read the names of the birds. Circle this set. Write the inscription below: “Birds.”

Read the names of animals that can fly. Circle this set and write at the top: “They can fly.”

can fly

How many elements were on intersection of two sets, i.e. simultaneously in two sets? Why?

Intersection of many common part of sets

"AND",

then each of its elements must be on INTERSECTION two sets -

live in two countries at the same time.

Union of sets

If the set name contains the word "OR",

then the element can be anywhere in the territory of two countries - ASSOCIATION -

live in at least one of them.

What is a subset? Subset- This part of a set included in a given set. Physical education minute One - bend over, straighten up, Two - bend over, stretch, Three - three claps of the hands, three nods of the head. Four arms wider, Five, six - sit down quietly, Seven, eight - let's throw away laziness. Draw the sets:

Many sea inhabitants

Many mammals

Draw the sets:

Many birds

Lots of fish

Even numbers live in a square. Two-digit numbers live in a triangle. Write each number correctly. Color in the area in the picture where even two-digit numbers live.

2, 47, 16, 8, 17, 32, 6, 53

Find the designation of each set in the table and fill in the circles in the picture.

How many sets are indicated by circles? Which set is the largest? What color should you paint the largest circle with? What is the largest one left?

Sets:

animals

Plants

Find and arrange the elements of sets in the figures in the picture: write the first letter of each word from the list

Remember!

The sets do not intersect

The sets do not intersect:

One set is a subset of another

One set is a subset of another:

The sets intersect:

The sets are combined:

See you at

next lesson!!!

A.V. Goryachev, K.I. Gorina et al. Computer science in games and tasks, grade 3, Methodological recommendations for teachers, M., “Ballas”, 2004

A.V. Goryachev, K.I. Gorina et al. Computer science in games and tasks, grade 3, Methodological recommendations for teachers, M., “Ballas”, 2004
A.V. Goryachev, K.I. Gorina and others. Textbook “Informatics in games and tasks”, 3rd grade, part 2, M., “Ballas”, 2004
http://festival.1september.ru/articles/505635/ Computer science lesson on the topic "Set. Subset. Intersection of sets" Shchepina Zinaida Nikolaevna, primary school teacher

Used Books

Multitudes. Set Operations

A BUNCH OF

FIND THE UNION OF SETS

ELEMENT OF THE SET

TYPES OF SETS

FIND THE INTERSECTION OF SETS

RELATIONS BETWEEN

MANY

REPRESENTATION USING EULER CIRCLES

“Multiple is many things that we think of as one”

founder of set theory

Georg Cantor

Set theory concepts

The concept of set is one of the most general and most important mathematical concepts. It was introduced into mathematics by the German scientist Georg Cantor (1845-1918). Following Cantor, the concept of “set” can be defined as follows:

A set is a collection of objects that have a certain property, combined into a single whole.

SET OF PENCILS

THE COLLECTION OF POSTMARKS

FLOCK OF BIRDS

HERD OF COWS

TEA-SET

BOUQUET OF FLOWERS

A set is a collection of objects united according to some characteristic.

Sets are denoted by capital letters of the Latin alphabet: A, B, C, D, etc.

The objects that make up a set are called set elements.

a bunch of

element

Trapezoid, parallelogram, rhombus, square, rectangle

Sphere, cuboid, prism, pyramid, octahedron

Integers

1, 4, 9, 16, 25, 36, 49, 64, 81, 100 ..

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Two-digit even numbers

Set of quadrilaterals

Spatial bodies

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11…

Number squares

Numbers of the decimal number system

10, 12, 14, 16 … 96, 98

many people in the sun

set of right angles of an equilateral triangle

set of intersection points of two parallel lines

An empty set is a set that does not contain any elements.

Notations for some numerical sets:

N – set of natural numbers;

Z – set of integers;

Q – set of rational numbers;

I - set of irrational numbers;

R is the set of real numbers.

TYPES OF SETS

Write down many letters of words

HORSES AND MOVIE

{ K, O, N, I }

{ MOVIE }

Equal sets

TYPES OF SETS

A = (2; 3; 5; 7; 11; 13);

Finite sets

TYPES OF SETS

{1; 4; 9; 16; 25; …};

{10; 20; 30; 40; 50; …};

Infinite sets

Among the sets listed below, indicate finite and infinite sets:

a) a set of numbers that are multiples of 13;

b) the set of divisors of the number 15;

c) many trees in the forest;

d) the set of natural numbers;

e) many rivers of the Rostov region;

f) the set of roots of the equation x + 3 = 11;

g) set of solutions to the inequality x + 1

Specify a set of digits that can be used to write a number:

a) 3254; b) 8797; c) 11000; d) 555555.

Characterize set A:

a) A = (1, 3, 5, 7, 9);

b) A = (- 2, - 1, 0, 1, 2);

c) A = (11, 22, 33, 44, 55, 66, 77, 88, 99);

Given sets:

M = (5, 4, 6),

P = (4, 5, 6),

T = (5, 6, 7),

S = {4, 6}.

Which statement is false?

a) M = P b) P ≠ S c) M ≠ T d) P = T

Let A- a set of prime numbers of the form

7n + 2, where n ∈ N.

Is the entry -5 ∈ A correct?

1. In multitude (lion; fox; hyena; elephant; lynx) all elements, except one, have some property. a) describe this property; b) find an element that does not have this property; c) name two more elements that have this property. 2. Name 5 subsets in a set of all colors of the rainbow. 3. What property in In the set of rhombuses, is there a subset of squares?

Example: 8 and 32

BLITZ SURVEY

amphibians, mammals, cold-blooded animals, etc.

What names are used to refer to sets of animals?

BLITZ SURVEY

company, platoon, regiment, division, etc.

What names are used to refer to sets of military personnel?

BLITZ SURVEY

bouquet

What is the name of the many flowers in a vase?

BLITZ SURVEY

equator

What is the name of the set of points on the earth's surface that are equidistant from both poles?

BLITZ SURVEY

village, village, town, town

What are the names of many places inhabited by people?

BLITZ SURVEY

exhibition, gallery

What are the names of the set of paintings?

BLITZ SURVEY

archive

What is the name of a set of documents?

BLITZ SURVEY

flotilla, squadron

What names are used to designate sets of ships?

A – even natural numbers B – two-digit numbers

Find the union of these sets.

A B – be an even natural or two-digit number

Example: 8 and 32

A – even natural numbers B – two-digit numbers

Find the intersection of these sets.

A B – to be an even natural and two-digit number

Example: 32

Given sets:

A = (2; 3; 8),

B = (2; 3; 8; 11),

C = (5; 11).

Find: 1) АУВ; 2) AUC; 3) СУВ.

Given sets:

A = ( a , b , c , d },

B = { c , d , e , f },

C = { c , e , g , k }.

Find: (AUB)UC.

Given sets:

A is the set of all natural numbers that are multiples of 10,

B = (1; 2; 3;…, 41).

Find A∩B.

The solution of the problem

using Euler circles

Leonard Euler- Swiss, German and Russian mathematician who made a significant contribution to the development of mathematics, as well as mechanics, physics, astronomy and a number of applied sciences.

There are 30 people in the class, each of whom sings or dances. It is known that 17 people sing, and 19 people can dance. How many people sing and dance at the same time?

dancing 19

17+19=36, total 30

Solution

Let A be the set of students who can sing. According to the condition, the number of elements in it is equal to n = 17. Let B be the set of students who can dance. The number of elements in it is m = 18. The set coincides with the entire class, because Every student in the class sings or dances. - this is a lot of those students in the class who sing and dance at the same time. Let their number be equal to k.

According to the formula proven above

n + m- k = 17+ 19- k = 30 k = 6.

Answer: 6 students in a class sing and dance at the same time.

The company employs 67 people. Of these, 47 speak English, 35 speak German, and 23 speak both languages. How many people in the company speak neither English nor German?

German 35

English 47

Every student in the class learns English or French. There are 25 students studying English, 27 students studying French and 18 students studying two languages. How many students are there in the class?

German 27

English 25

German only

English only

Answer: there are 34 students in the class

The sets A and B contain 5 and 6 elements, respectively, and the set A ∩ B contains 2 elements. How many elements are in set A U IN?

The union contains 9 elements

Each family living in our house writes out or

newspaper, or magazine, or both. 75 families

subscribe to a newspaper, and 27 families subscribe to a magazine, and only 13 families subscribe to both a magazine and a newspaper. How many families live in our house?

Total: 14 + 13 + 62 =89

At the school sports day, each of the 25 students of the 9th

class fulfilled the standard for either running or high jumping. 7 people fulfilled both standards, and 11 students fulfilled the running standard, but did not fulfill the high jump standard. How many students met the standard: a) running; b) high jump; c) for jumping, provided that the standard for running has not been met?

On Sunday, 19 students from our class visited

planetarium, 10 - in the circus and 6 - at the stadium. The planetarium and circus were visited by 5 students; planetarium and stadium - 3; circus and stadium - 1. How many students are in our class if no one managed to visit all three places, and three students did not visit any place?

A BUNCH OF

FIND THE UNION OF SETS

ELEMENT OF THE SET

TYPES OF SETS

FIND THE INTERSECTION OF SETS

RELATIONS BETWEEN

MANY

REPRESENTATION USING EULER-VENN CIRCLES

SOLVING PROBLEMS USING EXISTING KNOWLEDGE

Presentation on the topic “Intersection and union of sets” (elective “Visual Geometry” (3rd grade).

The use of information technology not only revived the educational process (which is especially important if we take into account the psychological characteristics of primary school age, in particular the long-term predominance of visual-figurative thinking over abstract-logical thinking), but also increased the motivation of learning in the classroom.

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Slide captions:

Intersection and union of sets. Kundeleva Oksana Evgenievna Primary school teacher MBOU NOSH No. 279, Gadzhievo, Murmansk region, 2012

The objectives of the lesson are to form an idea of the union and intersection of two sets, to learn to find on the “map of sets” the area of a set that is the intersection or union of two sets, to learn to determine whether elements belong to a set that is the intersection and union of two sets, to learn to determine the nature of the relationship between two given sets (intersection , do not intersect, union)

What is a set? A set is a group of objects, objects or beings.

Name the elements of the set: “Months of the year” “Seasons” “Continents” “Flying hippopotamuses” Polygons

Wasp Bat crow penguin Butterfly tit ostrich sparrow Read the names of the birds. Circle this set. Write the inscription below: “Birds.” BIRDS Read the names of animals that can fly. Circle this set and write at the top: “They can fly.” can fly How many elements were at the intersection of two sets, i.e. simultaneously in two sets? Why?

The intersection of sets is the common part of sets. If the name of a set contains the word “AND”, then each of its elements must be at the INTERCESS of two sets - live in two countries at the same time. !

Union of sets If the name of a set contains the word “OR”, then the element can be anywhere on the territory of two countries - UNION - live in at least one of them. ! ! ! !

What is a subset? A subset is a part of a set that is included in a given set.

Physical education minute One - bend over, straighten up, Two - bend over, stretch, Three - three claps of the hands, three nods of the head. Four arms wider, Five, six - sit down quietly, Seven, eight - let's throw away laziness.

Many sea inhabitants Many mammals Draw the sets:

Draw sets: Many birds Many fish

Even numbers live in a square. Two-digit numbers live in a triangle. Write each number correctly. Color in the area in the picture where even two-digit numbers live. 2, 47, 16, 8, 17, 32, 6, 53 2 47 16 8 17 32 53 6

Find the designation of each set in the table and fill in the circles in the picture. Sets: rectangles quadrilaterals polygons squares How many sets are indicated by circles? Which set is the largest? What color should you paint the largest circle with? What is the largest one left?

Sets: animals Animals Fish Birds Plants Seagull Fox Iceberg Giraffe Pine River Tulip Ant Flounder Find and arrange the elements of the sets in the shapes in the picture: write the first letter of each word from the list

CH K M T R S J A L

Remember! Sets do not intersect Sets do not intersect: One set is a subset of another One set is a subset of another: Sets intersect: Sets combine:

See you in the next lesson!!!

A.V. Goryachev, K.I. Gorina et al. Computer science in games and tasks, grade 3, Methodological recommendations for teachers, M., “Ballas”, 2004 A.V. Goryachev, K.I. Gorina and others. Textbook “Informatics in games and tasks”, 3rd grade, part 2, M., “Ballas”, 2004 http://festival.1september.ru/articles/505635/ Informatics lesson on the topic “Set. Subset. Intersection of sets" Shchepina Zinaida Nikolaevna, primary school teacher Literature used