PPT Sets and Set Operations

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Mathematics 7 Number Sense: Sets and Set Operations:

Mathematics 7 Number Sense: Sets and Set Operations Mr. Gerald DG Banaag Elizabeth Seton School

Essential Questions:

Essential Questions How do we know when an object is intrinsically part of a set or not? Why do we have to consider objects as such? Why do you think the study of the concept of sets important? How is the concept of sets being used in other fields of study? Which is more essential: the learning of the concept of sets or the acquisition of knowledge of the set of real numbers?

What You’ll learn? :

What You’ll learn? KWLH Chart Describe and illustrate well-defined sets, subsets, universal set, and null set. Define and describe the union and intersection of sets and the complement of a set. Use Venn diagram to represent sets, subsets, and set operations. Explain the concept of Venn diagram. Create a Venn diagram of elements classified in different sets. Solve problems involving sets.

Self-assessment questions:

Self-assessment questions Personality Development Why do we have to consider ourselves as part of a group?  Is it possible for someone to be part of more than one group? Is it beneficial to be part of any group? How did you relate the lessons with your personal experiences as a teenager? How do you think these lessons will affect your personality and outlook in life? Learning Process How did you learn the lesson on sets? Which part of the lesson struck you the most? Why?

Exploration:

Exploration Identify the object that does not belong to the group. boat, kalesa , car, bus, airplane carabao , chicken, cow, pig, goat Camiguin , Bukidnon , Basilan, Cebu, Davao del Sur hexagon, quadrilateral, rectangle, rhombus, square 2, 12, 24, 11, 30

Guide Questions:

Guide Questions How do you know when an object does not belong to a group? How do we know if a group is considered a set? How do you identify objects that belong to a particular group? What is your intuitive concept of a set? What do you call objects that belong to a given set? Can you give everyday experiences that use the concept of sets? What is the main characteristic of a set in Mathematics?

definition:

definition ¤ A group or collection of well-defined distinct objects is called a __________. When do we say that a collection is “ well-defined ”? set When do we say that an object belongs to a group? ¤ Each object in a set is called a __________ or an __________ of a set. member element

Dyad activity no.1:

Dyad activity no.1 Determine whether the following is a set or not: The collection of all ESS teachers. Tall students in Grade 7. Rich people in the Philippines. Planets in the Solar System. Beautiful girls in the class. People living on the moon. The collection of all large numbers. The set of all multiples of 5. A group of good writers. Nice people in your class.

Global Issue:

Global Issue “Racism is man’s gravest threat to man - the maximum of hatred for a minimum reason” Abraham J. Heschel (Jewish theologian and philosopher) “At the heart of racism is the religious assertion that God made a creative mistake when He brought some people into being” Friedrich Otto Hertz

Exploration:

Exploration Can you provide possible members of the following groups, if possible? Students over 12 years old in the class. Counting numbers less than 5. Set of letters in the word Philippines. Prime numbers which are even. Handsome boys in the class.

Guide questions:

Guide questions How do you define the terms contained in a set? When do we know if a set if null or empty? Why do we have to identify whether a set is finite or infinite? How do you think these terms can be presented?

Here are ways of describing a set.:

Here are ways of describing a set. The Roster Notation or Listing Method This is a method of describing a set by listing each element of the set inside the symbol { }. In listing the elements of the set, each distinct elements is listed once and the order of the elements does not matter. ex. Colors of the rainbow R = { red, orange, yellow, green, blue, indigo, violet } [List the elements in Exploration # 2]

Here are ways of describing a set.:

Here are ways of describing a set. The Set Builder Notation It is a method that lists the rules that determine whether an object is an element of the set rather than the actual elements. ex. All cities in the Philippines A = {x| x is a city in the Philippines} read as: “A is the set of all x such that x is a city in the Philippines.”

Formative assessment:

Formative assessment Describe the following sets using the specified methods. A. Write a verbal description for each of the following sets: 1. D = {1, 3, 5, 7, . . . } 2. E = {a, b, c, . . . , z} 3. F = {4, 8, 12, 16, . . . , 96} Answer: The set of odd numbers. The set of small letters in the English alphabet. The set of multiples of 4 between 0 and 100.

Formative Assessment:

Formative Assessment Describe the following sets using the specified methods. B. List the elements of the following sets: 1. M = {x |x > 7, x is an odd integer} 2. A = {x |7 < x < 8, x is a counting number} 3. T = {x |x is a city in Metro Manila} 4. H = { x |x is a counting number between 7 and 10 } Answers: M = {9, 11, 13, 15, 17, . . . } A = { } or  T = {Manila, Caloocan, Las Piñas , . . . Pasig} H = {8, 9}

Formative assessment:

Formative assessment Describe the following sets using the specified methods. C. Write a rule for the following: 1. S = {a, e, i , o, u} 2. E = {3, 6, 9, . . . , 30} 3. T = { Monday, Tuesday, Wednesday, . . . , Sunday } Answers: S = {x  x is a vowel in the English alphabet } E = {x  3  x  30, x is a multiple of 3} T = {x  x is a day in week}

Summing up:

Summing up Can you share to the class some new terms you learned today? Which definition struck you the most? If you can share a topic that you learned today to a friend, what would it be? Why?

Homework:

Homework Bring a photo of your favorite actors Define the following: 1. Equal 2. Equivalent 3. cardinality of a set 4. Universal Sets 5. Subsets

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