Sets and operations on them outline of a lesson in algebra (Grade 9) on the topic. “Many. Subsets. Operations on sets Summary of sets and operations on them

Municipal educational institution -

Open lesson on the topic: "Sets. Subsets. Operations on sets»

5th grade

math teachers

Sychuk V.D.

MOU - Lyceum №2

G. Saratov - 2008

Lesson: Many. Subsets. Operations on sets.

The purpose of the lesson: 1) repeat the basic concepts of a set, subset,

operations on sets;

2) development of logical thinking through decision

non-standard tasks, systematization and generalization,

development of mathematical speech

3) education of attentiveness, interest in the subject,

Expanding horizons.

Lesson type: iterative-generalizing.

Teaching method: didactic game - competition.

Method of organizing activities: partially searchable.

Equipment: 1) interactive whiteboard;

2) cards with tasks for independent work

And tasks;

3) cards with individual tasks;

Class layout:

1st slide: Number, subject, epigraph.

“Many is many thought as a whole”

Georg Kantor.

During the classes.

I. Organization.

Inform the topic of the lesson, epigraph, lesson plan.

Warm up.
Competition of theorists (independently 3 people on cards on the board).
Independent work with peer review.
Problem solving (collectively).
Homework.
Summary of the lesson.

The class is divided into two groups (by options)

Game conditions: 1) Clear and precise answers;

2) Speed;

3) Discipline.

Teacher's remark: "And may the smartest win in this fight!"

II. Warm up.

1. What does the word "multiple" mean?

A set is a set or collection of objects of the same nature.

2. What names are used to designate sets?

Herd, herd, team, family, orchestra, library.

3. How do sets differ in the number of elements?

Sets are finite, infinite, and the empty set.

4. In what ways can a set be specified?

A set can be specified by enumeration or by using a characteristic property.

5. What property is called a characteristic property?

A characteristic property is a property that all elements of a given set have and no other objects have.

6.2slide:

In this set, all elements, except for one, have some properties.

Describe it and find the extra element.

A = x I x - desert

Extra element - water lily.

7. 3rd slide :

What is a subset of set A?

A set B is called a subset of set A if every element of set B is an element of set A.

8. 4th slide:

9. What is called the intersection of sets A and B?

The intersection of sets A and B is the set that includes those and only those elements that are contained in A and B at the same time.

10. What is called the union of sets A and B?

The union of sets A and B is a set consisting of those elements that are included in at least one of the sets A or B.

11. 5th slide: Find the intersection of geometric shapes

1 2. 6th slide:

III. Competition of theorists

3 people are called and work on cards.

Card#1

Winnie the Pooh and Piglet came to visit the Rabbit. The rabbit treated them to jam. Winnie the Pooh and Piglet ate 32 spoons of jam together, and Winnie the Pooh and Rabbit – 23 spoons of jam.

How many spoons of jam did all three heroes eat?

K card number 2

A = x│хє N; 2≤х≤7

B = x│хє N; 4≤х≤9

Define sets by enumeration. Find AU B; A B; A B; VA. Draw the solution on a number line.

Card #3

Write down all subsets of the set a ;b ;c;d .

There were 5 light bulbs on the stage. How many ways are there to light the stage?

IV. Competition "Who is faster." Independent work

Independent work on cards.

Files with tasks in two versions are on each desk.

After 7 minutes, the guys exchange notebooks and check the answers with the solutions on the interactive whiteboard.

7 slide:

Rating "5" - no errors

"4" - one mistake

"3" - not set

8th slide:

Solution:

Let's denote the cost of a cow -n (A), a sheep - n (B), a goat - n (C) a pig -n (D)

n (A U B U C U D) = 1325 rubles

n (B U C U D) = 425 rubles

n(A U D U B)= 1225 rubles

n (C U D) \u003d 275 rubles

1.n (A) \u003d n (A U B U C U D) - n (B U C U D) \u003d 1325-425 \u003d 900 rubles - the cost of a cow

2.n (C) \u003d n (А U В U С U D) - n (A U D U B) \u003d 1325-1225 \u003d 100 rubles - the cost of a goat

3.n (B) \u003d n (В U C U D) - n (С U D) \u003d 425- 275 \u003d 150 rubles - the cost of a sheep

4.n (D) \u003d n (С U D) -n (C) \u003d 275-100 \u003d 175 rubles - the cost of a pig

Answer: a cow costs 900 rubles, a goat - 100 rubles, a sheep - 150 rubles, a pig - 17

Additional task:

9th slide:

VII. Results of the game

In conclusion, the results are summarized.

Homework is written on the board in advance:

Make up tasks for 1) intersection and union of geometric shapes, 2) sawing; 3) the assignment of sets and subsets with the help of a characteristic property.

Still, friendship prevailed.

Thanks for the lesson kids!

The process of teaching mathematics should consist of the following steps:

Activating (creating a motivational situation, setting activity goals, drawing up and concretizing an activity plan),

Operational-cognitive (learning new material, primary consolidation and correction)

Reflective-diagnostic (establishing the degree of correspondence between the result and the goal, establishing the nature and causes of difficulties).

Lesson topic: “Subset. Operations on sets»

Lesson type : lesson learning new material.

Logistics: computer, projector, handout, multimedia presentation (own development); textbook "Algebra: Grade 8" author Merzlyak A.G.

Formed results:

Subject: to form the ability to find subsets of a given

sets, intersection and union of sets, illustrate the result

operations on sets using Euler diagrams.

Personal: to form interest in the study of the topic and the desire to apply

acquired knowledge and skills.

Meta-subject: to form the ability to see a mathematical problem in

context of a problem situation in other disciplines, in the environment

life.

Planned results : the student will learn to find subsets

given set, intersection and union of sets, illustrate

the result of operations on a set using Euler diagrams.

During the classes

I. Organizational stage (1 min)

II. Actualization of knowledge (5 min), motivation for learning activities

One day Socrates, surrounded by his disciples, went up to the temple. Towards

the famous Athenian hetaera descended to them. “Here you are proud of your

students, Socrates, - she smiled at him, - but I only need to lightly

beckon them as they leave you and follow me.” the sage

answered like this: “Yes, but you call them down to the warm cheerful valley, and I lead

them upwards, to impregnable, pure peaks.

So today we must climb one step up,

“overcoming” tasks that will be discussed in today's lesson.

Teacher: Let's remember what concept we talked about in the last lesson? (set) What does it consist of? (of elements) What ways of specifying a set do you know? (enumeration of elements, using a characteristic property).

Please complete the tasks on the slide (each in their own notebooks) (5 minutes + self test)(slide 2 )

1. It is known that the set A is the set of single-valued primes. Replace

asterisks signs Є and Є so that the correct statement is obtained:

1) 5*A; 2) 2*A; 3) 8*A.

2. Specify a set by enumeration of elements:

1) proper fractions with denominator 5;

2) digits of the number 1230321.

ΔStudent response

1. 1) 5ЄА; 2) 2ЄА; 3) 8ЄА. 2.1); 2)

III. Learning new material + primary consolidation

A: The concept of subset (13 min)

Teacher: (slide 3) Answer the questions on the slide :

ΔStudent response

Every cow is an artiodactyl, but not every artiodactyl is

cow.

Teacher: A set of cows is part of a set of artiodactyl animals, that is, a set of cows is subset many artiodactyl animals .

The topic of our today's lesson:

Subsets and operations on them (slide 1).

Joint goal setting of the lesson: learn to find subsets of a given set; find out what operations can be performed on sets and learn how to illustrate them.

(Slide 4) - definition of a subset, designation, examples (+ students give their examples), No. 440 (even) - orally.

Definition : set B is called a subset of set A if every element of set B is an element of set A.

IN⊂ A (“set B is a subset of set A”)

A⊃ B ("set A contains set B")

examples:

1. the set of edible mushrooms is a subset of the set of mushrooms;

2. the set of even digits B = is a subset of the set

digits of the decimal number system A = .

№ 440 (even) orally (front work)

Teacher : Complete the written task from the slide (slide 5) (Check at the board).

Task: write down all subsets of the set A =

ΔStudent response

(emphasis on the fact that a set is also a subset of itself).

In: Euler Diagrams (3 min)

Teacher: To illustrate the relationships between sets, schemes are used that are called Euler diagrams. (slide 6).

The slide shows the relationship between a variety of mushrooms and a variety of edible mushrooms; between the set of even numbers and the set of decimal digits. IN -subset A.The diagram allows us to conclude that 1) for some element x to belong to set A, it is sufficient that it belongs to set B; 2) in order for some element x to belong

set B, it is necessary that it belongs to set A (slide 7).

C: Intersection and Union of Sets (21 min)

Teacher: Now, work with a roommate. You have been given a task (slide 8) . Think about how the set C is formed in each case. (2 minutes, work in pairs).

ΔStudent response:

1. Set C contains only elements (letters) that are contained in both set A and set B at the same time.

Teacher: The set consisting of all elements belonging to both set A and set B is called the intersection of sets A and B and is denoted A⋂B(slide 9) . It's easy to represent the intersection of sets using Euler diagrams (slide 10) . What do you think the intersection of two equal sets will be? (slide 11)

Run № 441 (find the intersection of sets and illustrate with Euler diagrams) (2 people at the blackboard).

ΔStudent response:

2. The set C contains elements (letters) that are contained in both sets together.

Teacher: A set consisting of all elements belonging to at least one of the sets: either set A or set B is called the union of sets A and B and is denoted A⋃B(slide 12). It's easy to represent a union of sets using Euler diagrams (slide 13) .

Run № 446 (find union of sets and illustrate with Euler diagrams) (2 people at the blackboard).

(If there is time: assignments on slide 14)

IV. Lesson summary (2 min)

Continue the sentence:

1. Today at the lesson I learned ...

2. It was difficult for me at the lesson ...

3. Homework for me will be…

V. Information about homework (1 min)

§14, no. 441, 444, 447

Start:

Look at the pictures, describe them. And what will happen if we swap the first and second words in these pairs (phrases). Get funny. And in mathematics there is a universal word, all-encompassing, which can replace any first word in these pairs. That word is "many".

Here are more examples of sets: a set of students in our class, a set of planets in the solar system, a set of two-digit numbers, a set of pairs (x; y).

The objects of this set are the elements of this set. Typically, elements are denoted by lowercase (small) Latin letters.

If element a belongs to set A, then write a to A. If element a does not belong to set A, then write to A.

If the set consists of several elements, then curly brackets are used, for example, for 3 elements a, b, c, write A \u003d. This is convenient if the set consists of a small number of elements.

Most often, a set is specified in one of two ways:

The first way is that the set is specified by specifying (by listing all its elements). Using curly braces, which indicate all its elements. But not everything can be set that way.

The second way is to indicatecharacteristic property (characterizes all its elements) of the elements of a set, that is, a property that all elements of a given set and only they have. For example, a set of even numbers.

There is one more special property - the empty set and denoted by a symbol that does not contain a single element. Note that this set is not empty. It contains one element, the empty set. For example, p. 107. (work with the textbook).

Consider a set of numbersA = . Let us single out from this set the elements that are even digits. We get the set B = .

All its elements are elements of the set A.

B is a subset of set A, after seeing the picture they can answer themselves.

It is written like this:

BA or A B read "set B is a subset of set A or set A contains set B" (see examples on page 109).

To illustrate the relationships between sets, diagrams are used that are called Euler diagrams (or Euler circles).

The best way to learn something is to discover it yourself.

D.Poya

Date of: 29.11.17

OPEN LESSON IN 6 "G" class MBOU Mechetinskaya secondary school

Teacher: Bankina Svetlana Nikolaevna

Subject: Sets. The concept of a set, an element of a set, a finite, infinite and empty set.

Type: discovery of new knowledge

Goals:

introduce the concept of "numerical set", "element of the set", "finite set", "infinite set", "empty set";

to form the ability to set the characteristic properties of the set, to name the elements of the set according to the characteristic properties, to give examples of sets;

educate the culture of mathematical speech.

Lesson outline:

organizational stage. Motivation of educational activity of students

Setting the goal and objectives of the lesson .. Introduction to the topic of the lesson

Updating of basic knowledge. Mathematical dictation. Problem

Primary assimilation of new knowledge. Working with new concepts

Primary consolidation of the studied. Working with new concepts

Primary check of understanding of new material on the topic “Sets. The concept of a set, an element of a set, a finite, infinite and empty set"

Primary fastening.

Information about homework, instructions for its implementation. Fizkultminutka.

Development of the ability to apply new knowledge, the formation of UUD. Monitoring

Reflection (summing up)

During the classes:

1. Organizational moment.

My friends! I'm very happy
Enter your friendly class.
And for me already a reward
Attention of your smart eyes.

The director of our school Nedovedeeva Lidia Vasilievna and Avramenko Inna Mikhailovna, deputy director for water resources management of the MBOU secondary school in the city of Zernograd, came to our lesson. Hello.

Lesson motto: The best way to learn something is to discover it yourself. D. Poya (slide number 1)

2. Guys, did each of you think about the purpose for which he came to the lesson today?

I will try to help you find your purpose. On the screen you see a list of personal goals (slide 2) one of the students reads all the goals. Choose a goal for yourself from this list, write down its number in your notebook and try to achieve it during the lesson. At the end of the lesson, we will analyze whether you have achieved it or not, and why.

3. All students in your class are divided into how many groups? ... By what property? .. for a labor lesson .. (a group of boys and a group of girls); for an English lesson ... (2 groups on the list) in other words, there is a set of students in these groups and each set has its own property.

Sets of any items or objects united by a common property are called SET.

The concept of a set is the simplest mathematical concept, it is not defined, but only explained with the help of examples, a lot of books on a shelf, a lot of points on a line, a lot of class students, etc.

The word SET replaces the word "many" mathematicians use regardless of how many objects it contains.

The topic of today's lesson will be ... .. "Many"... (slide 3)

4. Since we have a math lesson, let's turn to numbers and think about whether there is any connection between numbers and sets. To start, let's write mathematical dictation:(slide 4)

D. Write down the divisors of the number 5

They exchanged cards. Verification is carried out through the presentation. (slide 5)

Those who are satisfied with their work raised their hands. Well done!

5. And now let's discuss what the resulting groups of numbers are. … That's right, these are also sets, only numeric ones. Let us denote the number obtained in the first question as set A, in the second - B .... (slide5) What do our sets consist of? ... That's right, from numbers that are commonly called elements of numerical sets. What element of the set is the number 7?

In this case, a record is made: we say the number 7 is an element of the set A, A =. Students make appropriate entries in notebooks (one student or the teacher himself on the board). Does set A have only element 7?

So what do we call a number set? The response is recorded.

6. What do you think, what sets are there? A, B, C, D - a finite set.

And the set D... that's right, infinite. A set that does not have any elements is called an empty set and you see that this is set C, the empty set is denoted by .

7. To practice the skills of operating with the terms "numerical set", "finite set", "infinite set", "element of the set", "belong to the set", etc. students, under the guidance of a teacher, proceed to work with a textbook (slide 6) Work continues with assignments p. 91 No. 322 - orally.

p.91 No. 323 (a, c, e)

8. After discussing the solutions, the students write down their homework. (slide 7)

P. 11 No. 324; 325

Physical education (slide 8)

Together with you, we counted and talked about numbers,

And now we stood up together, stretched our bones.

On the count of times we will squeeze the fist, on the count of two in the elbows we will squeeze.

On the count of three - press to the shoulders, on 4 - to heaven

Well caved in, and smiled at each other

Let's not forget about the five - we will always be kind.

On the count of six, I ask everyone to sit down.

Numbers, I, and you, friends, are together friendly 7th.

9. In the final part of the lesson, the acquired knowledge is monitored. What are the sets?

Independent work:(slide 9)

For the assessment of "3" -Card to the topic "Sets" 1 lesson.

For a rating of "4" card + No. 322 (2)

For a rating of "5" card + No. 323 (g)

10. Achieving personal results (slide 10)

Guys, today is the first lesson of learning a new topic, so I will put only excellent and good marks in the journal. We will continue in the next lesson.

FI _______________

Mathematical dictation:


	Write single digit natural numbers that are multiples of 7
	Write Single Digit Prime Numbers
	Write down numbers greater than 20 and less than 30 that are multiples of 2
	Write down the divisors of 5
	Write down numbers that are multiples of 100
	How many horses live on the moon?

FI _______________

Mathematical dictation:


	Write single digit natural numbers that are multiples of 7
	Write Single Digit Prime Numbers
	Write down numbers greater than 20 and less than 30 that are multiples of 2
	Write down the divisors of 5
	Write down numbers that are multiples of 100
	How many horses live on the moon?

FI _______________

Mathematical dictation:


	Write single digit natural numbers that are multiples of 7
	Write Single Digit Prime Numbers
	Write down numbers greater than 20 and less than 30 that are multiples of 2
	Write down the divisors of 5
	Write down numbers that are multiples of 100
	How many horses live on the moon?

FI _______________

Mathematical dictation:


	Write single digit natural numbers that are multiples of 7
	Write Single Digit Prime Numbers
	Write down numbers greater than 20 and less than 30 that are multiples of 2
	Write down the divisors of 5
	Write down numbers that are multiples of 100
	How many horses live on the moon?

6th grade. Card for the topic " Sets» 1 lesson.