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  • Математика

Презентация по математике на тему :" Множества и подмножества"

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Hairutdinova Elvira 587ma KAZAN FEDERAL UNIVERSITY
Content: Objectives in content and language integrated learning (CLIL). Intr...
Objectives in content and language integrated learning (CLIL) In language: to...
Introduction to Sets. Example: Kyesha was in math class with her friend Angie...
. 	A set is a collection of objects that have something in common or follow a...
Every object in a set is unique: The same object cannot be included in the s...
Let's look at some more examples of sets. Example 2: What is the set of all f...
Example 3: What is the set of all even whole numbers between 0 and 10? Solut...
Example 4: Eduardo was in art class when the teacher wrote this on the chalk...
In examples 1 through 4, each set had a different number of elements, and eac...
So for examples 1 through 4, we listed the sets as follows: A = {coat, hat,...
These sets have been listed with roster notation. Roster notation is a list...
. Example 5: Let R be the set of all vowels in the English alphabet. Solution...
There are times when it is not practical to list all the elements of a set....
A = {types of triangles} G = {letters in the English alphabet} J = {prime nu...
When describing a set, It is not necessary to list every element in that se...
We will distinguish between these two methods in examples 10 and 11 below. Ex...
In example 10, set D has 26 elements, so it is easier to describe its eleme...
Glossary. A set is a collection of objects that have something in common or f...
Dictionary.
Exercises. 1.Which of the following is the set of all suits in a standard dec...
2.Which of the following is the set of odd whole numbers less than 10?  a) C...
. 3.Which of the following is the set of all oceans on earth? a)  G = {Atlant...
. 4.Which of the following is the set of all types of matter? a)  X = {iron,...
5. Jennifer listed the set of all letters in the word ‘library’ as shown bel...
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Описание презентации по отдельным слайдам:

№ слайда 1 Hairutdinova Elvira 587ma KAZAN FEDERAL UNIVERSITY
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Hairutdinova Elvira 587ma KAZAN FEDERAL UNIVERSITY

№ слайда 2 Content: Objectives in content and language integrated learning (CLIL). Intr
Описание слайда:

Content: Objectives in content and language integrated learning (CLIL). Introduction to Sets. Glossary. Dictionary. Exercises.

№ слайда 3 Objectives in content and language integrated learning (CLIL) In language: to
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Objectives in content and language integrated learning (CLIL) In language: to learn mathematic’s terms and their translations. In mathematics: The student will be able to: - Define set, inclusive, element, object, and roster notation. - Identify the elements of a given set. - Describe conventions used to list sets. - List the elements of a set using roster notation. - List the elements of a set by describing the set and the rules that its elements follows. - Recognize when to describe a set and its elements instead of listing it in roster notation. - Apply basic set concepts to complete five exercises.

№ слайда 4 Introduction to Sets. Example: Kyesha was in math class with her friend Angie
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Introduction to Sets. Example: Kyesha was in math class with her friend Angie. She whispered to Angie that she had just bought a set of winter clothes. The outerwear collection includes a coat, a hat, a scarf, gloves, and boots. Their teacher, Mrs. Glosser, overheard the conversation and asked them: What is a set? Solution: Luckily for Kyesha and Angie, their classmate Eduardo had a math dictionary with him! He quickly looked up the word "set" and defined it for the class as shown below.

№ слайда 5 . 	A set is a collection of objects that have something in common or follow a
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. A set is a collection of objects that have something in common or follow a rule. The objects in the set are called its elements. Set notation uses curly braces,with elements separated by commas. So the set of outwear for Kyesha would be listed as follows: A = {coat, hat, scarf, gloves, boot} , where A is the name of the set, and the braces indicate that the objects written between them belong to the set.

№ слайда 6 Every object in a set is unique: The same object cannot be included in the s
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Every object in a set is unique: The same object cannot be included in the set more than once.

№ слайда 7 Let's look at some more examples of sets. Example 2: What is the set of all f
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Let's look at some more examples of sets. Example 2: What is the set of all fingers? Solution: P = {thumb, index, middle, ring, little} Note that there are others names for these fingers: The index finger is commonly referred to as the pointer finger; the ring finger is also known as the fourth finger, and the little finger is often referred to as the pinky. Thus, we could have listed the set of fingers as: P = {thumb, pointer, middle, fourth, pinky}

№ слайда 8 Example 3: What is the set of all even whole numbers between 0 and 10? Solut
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Example 3: What is the set of all even whole numbers between 0 and 10? Solution: Q = {2, 4, 6, 8} Note that the use of the word between means that the range of numbers given is not inclusive. As a result, the numbers 0 and 10 are not listed as elements in this set.

№ слайда 9 Example 4: Eduardo was in art class when the teacher wrote this on the chalk
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Example 4: Eduardo was in art class when the teacher wrote this on the chalkboard: In fine arts, primary colors are sets of colors that can be combined to make a useful range of colors. Then she asked the class: What is the set of primary colors? Solution: Eduardo answered: red, blue and yellow. Angie answered: We can use set notation to list the set of all primary colors. Kyesha went to the chalkboard and wrote: X = {red, blue, yellow} The teacher said: Good work everyone. This is a nice combination of art and math!

№ слайда 10 In examples 1 through 4, each set had a different number of elements, and eac
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In examples 1 through 4, each set had a different number of elements, and each element within a set was unique. In these examples, certain conventions were used. The following conventions are used with sets: Capital letters are used to denote sets. Lowercase letters are used to denote elements of sets. Curly braces { } denote a list of elements in a set.

№ слайда 11 So for examples 1 through 4, we listed the sets as follows: A = {coat, hat,
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So for examples 1 through 4, we listed the sets as follows: A = {coat, hat, scarf, gloves, boots} P = {thumb, index, middle, ring, little} Q = {2, 4, 6, 8} X = {red, blue, yellow}

№ слайда 12 These sets have been listed with roster notation. Roster notation is a list
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These sets have been listed with roster notation. Roster notation is a list of elements, separated by commas, enclosed in curly braces. The curly braces are used to indicate that the elements written between them belong to that set. Let's look at some more examples of sets listed with roster notation.

№ слайда 13 . Example 5: Let R be the set of all vowels in the English alphabet. Solution
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. Example 5: Let R be the set of all vowels in the English alphabet. Solution: R = {a, e, i, o, u} Example 6:Let G be the set of all whole numbers less than ten. Solution: G = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} Example 7:Let T be the set of all days in a week. Solution: T = {Monday, Tuesday, Wednesday, Thursday, Friday} Example 8:Let X be the set of odd numbers less than 12. Solution: X = {1, 3, 5, 7, 9, 11} Example 9: Let Y be the set of all continents of the world. Solution: Y = {Asia, Africa, North America, South America, Antarctica, Europe, Australia}

№ слайда 14 There are times when it is not practical to list all the elements of a set.
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There are times when it is not practical to list all the elements of a set. In this case, it is better to describe the set. The rule that the elements follow can be given in the braces. For example: R = {vowels} means Let R be the set of all vowels in the English alphabet. This is especially useful when working with large sets, as shown below.

№ слайда 15 A = {types of triangles} G = {letters in the English alphabet} J = {prime nu
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A = {types of triangles} G = {letters in the English alphabet} J = {prime numbers less than 100} M = {state capitals in the US}

№ слайда 16 When describing a set, It is not necessary to list every element in that se
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When describing a set, It is not necessary to list every element in that set. Thus, there are two methods for indicating a set of objects: listing the elements; 2) describing the elements.

№ слайда 17 We will distinguish between these two methods in examples 10 and 11 below. Ex
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We will distinguish between these two methods in examples 10 and 11 below. Example 10: What is the set of all letters in the English alphabet? Listing elements: D = {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z} Describing elements: D = {letters in the English alphabet} Example 11: What is the set of all states in the Unites States? Solution: R = {all states in the US}

№ слайда 18 In example 10, set D has 26 elements, so it is easier to describe its eleme
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In example 10, set D has 26 elements, so it is easier to describe its elements than to list them. Similarly, in example 11, set R has 50 elements, so it is easier to describe its elements.

№ слайда 19 Glossary. A set is a collection of objects that have something in common or f
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Glossary. A set is a collection of objects that have something in common or follow a rule. The objects in the set are called its elements.  Set theory is the branch of mathematics that studies sets, which are collections. Set notation is a precise way of describing which items belong in a set and which do not. Specific symbols are used in set notation. of objects. An inclusive range of numbers includes the first and last number and all numbers in between. Roster notation is a list of elements, separated by commas, enclosed in curly braces.

№ слайда 20 Dictionary.
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Dictionary.

№ слайда 21 Exercises. 1.Which of the following is the set of all suits in a standard dec
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Exercises. 1.Which of the following is the set of all suits in a standard deck of playing cards?  a) R = [ace, two, three, four, five, six, seven, eight, nine, ten, jack, queen, king].  b) S = {hearts, diamonds, clubs, spades}.  c)T = {jokers}.  d)None of the above. ANSWER: b)

№ слайда 22 2.Which of the following is the set of odd whole numbers less than 10?  a) C
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2.Which of the following is the set of odd whole numbers less than 10?  a) C = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.  b) D = {0, 2, 4, 6, 8}.  c) E = {1, 3, 5, 7, 9}.  d) None of the above. ANSWER: c)

№ слайда 23 . 3.Which of the following is the set of all oceans on earth? a)  G = {Atlant
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. 3.Which of the following is the set of all oceans on earth? a)  G = {Atlantic, Pacific, Arctic, Indian, Antarctic}.  b) E = {Amazon, Nile, Mississippi, Rio Grande, Niagara}.  c) F = {Asia, Africa, North America, South America, Antarctica, Europe, Australia}.  d) All of the above. ANSWER: a)

№ слайда 24 . 4.Which of the following is the set of all types of matter? a)  X = {iron,
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. 4.Which of the following is the set of all types of matter? a)  X = {iron, aluminum, nickel, copper, gold, silver}.  b) Y = {hydrogen, oxygen, nitrogen, carbon dioxide}.  c) Z = {liquids, solids, gases, plasmas}.  d) None of the above. ANSWER: c)

№ слайда 25 5. Jennifer listed the set of all letters in the word ‘library’ as shown bel
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5. Jennifer listed the set of all letters in the word ‘library’ as shown below. What is wrong with this set? A = {l, i, b, r, a, r, y} a) A capital letter is used to represent this set. b)  It uses curly braces. c) It uses commas. d)The objects in this set are not unique. ANSWER: d)

№ слайда 26
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Презентация разработана на английском  языке!!!Презентация оформлена очень красочно и к каждому примеру соответствуют различные рисунки, что очень помогает для объяснения темы. 

Здесь представлю дополнительные задачи для укрепления темы.

Задача 

Задай свойством множества А и В:

 

 

Каждый ли заяц является животным? Всякое ли животное является зайцем? Какое из этих множеств является частью другого?

 

Решение:

  • B - животные
  • A - зайцы
  • Каждый заяц является животным
  • Не каждое животное является зайцем
  • Зайцы являются частью множества животные

 

 

Задача 

Задай свойством множества, изображённые на рисунке. Какое из них является подмножеством другого? Сделай записи.

 

Автор
Дата добавления 10.12.2014
Раздел Математика
Подраздел Презентации
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Номер материала 183372
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